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2013-10-20
Nonequilibrium stationary state for a damped rotator
Perturbative construction of the nonequilibrium steady state of a rotator under a stochastic forcing while subject to torque and friction
1310.5379v1
2013-11-07
Spin-Orbit Torques and Anisotropic Magnetization Damping in Skyrmion Crystals
The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics in cubic chiral magnets. Our results demonstrate that spin-orbit torques play a significant role in the current-induced skyrmion velocity. The dissipative spin-orbit torque generates a relativistic Magnus force on the skyrmions, whereas the reactive spin-orbit torque yields a correction to both the drift velocity along the current direction and the transverse velocity associated with the Magnus force. The spin-orbit torque corrections to the velocity scale linearly with the skyrmion size, which is inversely proportional to the spin-orbit coupling. Consequently, the reactive spin-orbit torque correction can be the same order of magnitude as the non-relativistic contribution. More importantly, the dissipative spin-orbit torque can be the dominant force that causes a deflected motion of the skyrmions if the torque exhibits a linear or quadratic relationship with the spin-orbit coupling. In addition, we demonstrate that the skyrmion velocity is determined by anisotropic magnetization damping parameters governed by the skyrmion size.
1311.1778v1
2013-11-13
Recent progress in attractors for quintic wave equations
We report on new results concerning the global well-posedness, dissipativity and attractors of the damped quintic wave equations in bounded domains of R^3.
1311.3290v1
2014-01-19
Analytical Solution of Mathieu Equation
The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.
1401.5348v1
2014-06-10
Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the essential features of Wigner's little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the $Sp(2)$ symmetry to that of $SL(2,c)$ corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincar\'e sphere contains the $SL(2,c)$ symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.
1406.2403v1
2014-06-11
Quantum critical metals in $4-ε$ dimensions
We study the quantum theory of a Fermi surface coupled to a gapless boson scalar in $D=4-\epsilon$ spacetime dimensions as a simple model for non-Fermi liquids (NFL) near a quantum phase transition. Our analysis takes into account the full backreaction from Landau damping of the boson, and obtains an RG flow that proceeds through three distinct stages. Above the scale of Landau damping the Fermi velocity flows to zero, while the coupling evolves according to its classical dimension. Once damping becomes important, its backreaction leads to a crossover regime where dynamic and static damping effects compete and the fermion self-energy does not respect scaling. Below this crossover and having tuned the boson to criticality, the theory flows to a $z=3$ scalar interacting with a NFL. By increasing the number of bosonic flavors, the phase diagram near the quantum critical point interpolates between a superconducting dome fully covering the NFL behavior, and a phase where NFL effects become important first, before the onset of superconductivity. A generic prediction of the theory is that the Fermi velocity and quasiparticle residue vanish with a power-law $\omega^\epsilon$ as the fixed point is approached. These features may be useful for understanding some of the phenomenology of high $T_c$ materials in a systematic $\epsilon$--expansion.
1406.3029v2
2014-10-15
A comparison of weak-turbulence and PIC simulations of weak electron-beam plasma interaction
Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit the results agree well, but increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. This may be important in, for example, the theory of solar radio bursts, where the spectrum of Langmuir waves is critical. Additionally we establish lower limits on the number of simulation particles needed to accurately reproduce the electron and wave distributions in their saturated states, and to reproduce their intermediate states and time evolution.
1410.4046v2
2015-03-31
Existence of the global attractor for the plate equation with nonlocal nonlinearity in R^{n}
We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.
1503.09123v1
2015-05-07
Theory for Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities
We construct a theory for Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We model the semiconductor by one conduction and one valence band which consist of electrons and holes that interact via a Coulomb interaction. Moreover, we incorporate screening effects by using a contact interaction with the scattering length for a Yukawa potential and describe in this manner the crossover from exciton gas to electron-hole plasma as we increase the excitation level of the semiconductor. We then show that the dynamics of the light in the microcavities is damped due to the coupling to the semiconductor. Furthermore, we demonstrate that on the electron-hole plasma side of the crossover, which is relevant for the Bose-Einstein condensation of light, this damping can be described by a single dimensionless damping parameter that depends on the external pumping. Hereafter, we propose to probe the superfluidity of light in these nano-fabricated semiconductor microcavities by making use of the differences in the response in the normal or superfluid phase to a sudden rotation of the trap. In particular, we determine frequencies and damping of the scissors modes that are excited in this manner. Moreover, we show that a distinct signature of the dynamical Casimir effect can be observed in the density-density correlations of the excited light fluid.
1505.01732v2
2015-08-21
Which verification qubits perform best for secure communication in noisy channel?
In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy environment (e.g., in amplitude damping, phase damping, collective dephasing and collective rotation noise channels) by comparing the decoy-qubit assisted schemes of secure quantum communication that use single qubit states as decoy qubits with the schemes that use entangled states as decoy qubits. Our study reveals that the single qubit assisted scheme perform better in some noisy environments, while some entangled qubits assisted schemes perform better in other noisy environments. Specifically, single qubits assisted schemes perform better in amplitude damping and phase damping noisy channels, whereas a few Bell-state-based decoy schemes are found to perform better in the presence of the collective noise. Thus, if the kind of noise present in a communication channel (i.e., the characteristics of the channel) is known or measured, then the present study can provide the best choice of decoy qubits required for implementation of schemes of secure quantum communication through that channel.
1508.05237v1
2015-08-30
Spin-transfer torque based damping control of parametrically excited spin waves in a magnetic insulator
The damping of spin waves parametrically excited in the magnetic insulator Yttrium Iron Garnet (YIG) is controlled by a dc current passed through an adjacent normal-metal film. The experiment is performed on a macroscopically sized YIG(100nm)/Pt(10nm) bilayer of 4x2 mm^2 lateral dimensions. The spin-wave relaxation frequency is determined via the threshold of the parametric instability measured by Brillouin light scattering (BLS) spectroscopy. The application of a dc current to the Pt film leads to the formation of a spin-polarized electron current normal to the film plane due to the spin Hall effect (SHE). This spin current exerts a spin transfer torque (STT) in the YIG film and, thus, changes the spin-wave damping. Depending on the polarity of the applied dc current with respect to the magnetization direction, the damping can be increased or decreased. The magnitude of its variation is proportional to the applied current. A variation in the relaxation frequency of +/-7.5% is achieved for an applied dc current density of 5*10^10 A/m^2.
1508.07517v1
2015-09-08
Model comparison for the density structure across solar coronal waveguides
The spatial variation of physical quantities, such as the mass density, across solar atmospheric waveguides governs the timescales and spatial scales for wave damping and energy dissipation. The direct measurement of the spatial distribution of density, however, is difficult and indirect seismology inversion methods have been suggested as an alternative. We applied Bayesian inference, model comparison, and model-averaging techniques to the inference of the cross-field density structuring in solar magnetic waveguides using information on periods and damping times for resonantly damped magnetohydrodynamic (MHD) transverse kink oscillations. Three commonly employed alternative profiles were used to model the variation of the mass density across the waveguide boundary. Parameter inference enabled us to obtain information on physical quantities such as the Alfv\'en travel time, the density contrast, and the transverse inhomogeneity length scale. The inference results from alternative density models were compared and their differences quantified. Then, the relative plausibility of the considered models was assessed by performing model comparison. Our results indicate that the evidence in favor of any of the three models is minimal, unless the oscillations are strongly damped. In such a circumstance, the application of model-averaging techniques enables the computation of an evidence-weighted inference that takes into account the plausibility of each model in the calculation of a combined inversion for the unknown physical parameters.
1509.02340v1
2015-09-15
Resonance vibration of impact oscillator with biharmonic excitation
We consider a damped impact oscillator subject to the action of a biharmonic force. The conditions for the existence and stability of almost periodic resonance solutions are investigated.
1509.05381v1
2015-11-08
On 2d incompressible Euler equations with partial damping
We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.
1511.02530v1
2015-12-11
The Ping Pong Pendulum
Many damped mechanical systems oscillate with increasing frequency as the amplitude decreases. One popular example is Euler's Disk, where the point of contact rotates with increasing rapidity as the energy is dissipated. We study a simple mechanical pendulum that exhibits this behaviour.
1512.03700v1
2016-01-26
Fast convex optimization via inertial dynamics with Hessian driven damping
We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where $\Phi:\mathcal H\to\mathbb R$ is a smooth convex function acting on a real Hilbert space $\mathcal H$, and $\alpha$, $\beta$ are positive parameters. This inertial system combines an isotropic viscous damping which vanishes asymptotically, and a geometrical Hessian driven damping, which makes it naturally related to Newton's and Levenberg-Marquardt methods. For $\alpha\geq 3$, $\beta >0$, along any trajectory, fast convergence of the values $$\Phi(x(t))- \min_{\mathcal H}\Phi =\mathcal O\left(t^{-2}\right)$$ is obtained, together with rapid convergence of the gradients $\nabla\Phi(x(t))$ to zero. For $\alpha>3$, just assuming that $\Phi$ has minimizers, we show that any trajectory converges weakly to a minimizer of $\Phi$, and $ \Phi(x(t))-\min_{\mathcal H}\Phi = o(t^{-2})$. Strong convergence is established in various practical situations. For the strongly convex case, convergence can be arbitrarily fast depending on the choice of $\alpha$. More precisely, we have $\Phi(x(t))- \min_{\mathcal H}\Phi = \mathcal O(t^{-\frac{2}{3}\alpha})$. We extend the results to the case of a general proper lower-semicontinuous convex function $\Phi : \mathcal H \rightarrow \mathbb R \cup \{+\infty \}$. This is based on the fact that the inertial dynamic with Hessian driven damping can be written as a first-order system in time and space. By explicit-implicit time discretization, this opens a gate to new $-$ possibly more rapid $-$ inertial algorithms, expanding the field of FISTA methods for convex structured optimization problems.
1601.07113v1
2016-03-28
Stabilization of gravity water waves
This paper is devoted to the stabilization of the incompressible Euler equation with free surface. We study the damping of two-dimensional gravity waves by an absorbing beach where the water-wave energy is dissipated by using the variations of the external pressure.
1603.08541v1
2016-06-14
Precession Relaxation of Viscoelastic Oblate Rotators
Perturbations of all sorts destabilise the rotation of a small body and leave it in a non-principal spin state. In such a state, the body experiences alternating stresses generated by the inertial forces. This yields nutation relaxation, i.e., evolution of the spin towards the principal rotation about the maximal-inertia axis. Knowledge of the timescales needed to damp the nutation is crucial in studies of small bodies' dynamics. In the literature hitherto, nutation relaxation has always been described with aid of an empirical quality factor $\,Q\,$ introduced to parameterise the energy dissipation rate. Among the drawbacks of this approach was its inability to describe the dependence of the relaxation rate upon the current nutation angle. This inability stemmed from our lack of knowledge of the quality factor's dependence on the forcing frequency. In this article, we derive our description of nutation damping directly from the rheological law obeyed by the material. This renders us the nutation damping rate as a function of the current nutation angle, as well as of the shape and the rheological parameters of the body. In contradistinction from the approach based on an empirical $\,Q\,$-factor, our development gives a zero damping rate in the spherical-shape limit. Our method is generic and applicable to any shape and to any linear rheological law. However, to simplify the developments, here we consider a dynamically oblate rotator with a Maxwell rheology.
1606.04559v3
2016-09-07
Quasi-stability and Exponential Attractors for A Non-Gradient System---Applications to Piston-Theoretic Plates with Internal Damping
We consider a nonlinear (Berger or Von Karman) clamped plate model with a {\em piston-theoretic} right hand side---which include non-dissipative, non-conservative lower order terms. The model arises in aeroelasticity when a panel is immersed in a high velocity linear potential flow; in this case the effect of the flow can be captured by a dynamic pressure term written in terms of the material derivative of the plate's displacement. The effect of fully-supported internal damping is studied for both Berger and von Karman dynamics. The non-dissipative nature of the dynamics preclude the use of strong tools such as backward-in-time smallness of velocities and finiteness of the dissipation integral. Modern quasi-stability techniques are utilized to show the existence of compact global attractors and generalized fractal exponential attractors. Specific results depending on the size of the damping parameter and the nonlinearity in force. For the Berger plate, in the presence of large damping, the existence of a proper global attractor (whose fractal dimension is finite in the state space) is shown via a decomposition of the nonlinear dynamics. This leads to the construction of a compact set upon which quasi-stability theory can be implemented. Numerical investigations for appropriate 1-D models are presented which explore and support the abstract results presented herein.
1609.02211v1
2016-10-26
On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings
We consider the synchronization problem of swing equations, a second-order Kuramoto-type model, on connected networks with inhomogeneous dampings. This was largely motivated by its relevance to the dynamics of power grids. We focus on the estimate of the region of attraction of synchronous states which is a central problem in the transient stability of power grids. In the recent literature, D\"{o}rfler, Chertkov, and Bullo [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 2005-2010] found a condition for the synchronization in smart grids. They pointed out that the region of attraction is an important unsolved problem. In [SIAM J. Control Optim., 52 (2014), pp. 2482-2511], only a special case was considered where the oscillators have homogeneous dampings and the underlying graph has a diameter less than or equal to 2. There the analysis heavily relies on these assumptions; however, they are too strict compared to the real power networks. In this paper, we continue the study and derive an estimate on the region of attraction of phase-locked states for lossless power grids on connected graphs with inhomogeneous dampings. Our main strategy is based on the gradient-like formulation and energy estimate. We refine the assumptions by constructing a new energy functional which enables us to consider such general settings.
1610.08437v1
2016-10-31
A quest for new physics inside the neutron
The lecture presents an overview of the quest for the new physics in low energy neutron phenomena. In addition to the traditional topics the quantum damping of $n$ $\bar{n}$ oscillations is discussed.
1610.10046v1
2016-11-28
First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO
Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15,538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electro-static actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nNrms was required to maintain the acoustic mode at its minimum amplitude.
1611.08997v1
2016-12-19
Improving the efficiency of joint remote state preparation in noisy environment with weak measurement
Quantum secure communication provides a new way for protecting the security of information. As an important component of quantum secure communication, remote state preparation (RSP) can securely transmit a quantum state from a sender to a remote receiver. The existence of quantum noise severely affects the security and reliability of quantum communication system. In this paper, we study the method for improving the efficiency of joint RSP (JRSP) subjected to noise with the help of weak measurement and its reversal measurement. Taking a GHZ based deterministic JRSP as an example, we utilize the technique of weak measurement and its reversal to suppress the effect of the amplitude-damping noise firstly. Our study shows that the fidelity of the output state can be improved in the amplitude-damping noise. We also study the effect of weak measurement and its reversal in other three types of noise usually encountered in real-world, namely, the bit-flip, phase-flip (phase-damping) and depolarizing noise. Our results show that the weak measurement has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise, while has slight effect for suppressing the depolarizing noise. Our study is suitable for JRSP and RSP, and will be helpful for improving the efficiency of multiparticle entanglement based quantum secure communication in real implementation.
1612.06020v1
2017-03-21
Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics
We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a $1/f$ thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, $\phi = 4.5\cdot 10^{-6}$, agrees well with the quality factor ($Q$) of the fundamental beam mode ($\phi = Q^{-1}$). In conjunction with $Q$ measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such "structural damping" on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.
1703.07134v2
2017-03-29
Comment on "Spreading widths of giant resonances in spherical nuclei: damped transient response" by Severyukhin et al. [arXiv:1703.05710]
We argue whether physics of universal approach of Severyukhin et al. [arXiv:1703.05710] is approved.
1703.10003v1
2017-05-16
Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of propagation and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its shape and frequency and amplitude of the oscillatory tail. The numerical results are in a good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load and on-site damping. When the damping is moderate, the analysis remains in the frame of the reduced-order model. It is possible to consider the solution for the front propagating in the damped chain as a perturbation of the undamped dynamics. This approach yield reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime. The gradient nonlinearity generically turns negligible, and the propagating front converges to the exact solution obtained from a simple linear continuous model.
1705.05555v1
2017-08-16
The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere
High spatial and temporal resolution images of a sunspot, obtained simultaneously in multiple optical and UV wavelengths, are employed to study the propagation and damping characteristics of slow magnetoacoustic waves up to transition region heights. Power spectra are generated from intensity oscillations in sunspot umbra, across multiple atmospheric heights, for frequencies up to a few hundred mHz. It is observed that the power spectra display a power-law dependence over the entire frequency range, with a significant enhancement around 5.5 mHz found for the chromospheric channels. The phase-difference spectra reveal a cutoff frequency near 3 mHz, up to which the oscillations are evanescent, while those with higher frequencies propagate upwards. The power-law index appears to increase with atmospheric height. Also, shorter damping lengths are observed for oscillations with higher frequencies suggesting frequency-dependent damping. Using the relative amplitudes of the 5.5 mHz (3 minute) oscillations, we estimate the energy flux at different heights, which seems to decay gradually from the photosphere, in agreement with recent numerical simulations. Furthermore, a comparison of power spectra across the umbral radius highlights an enhancement of high-frequency waves near the umbral center, which does not seem to be related to magnetic field inclination angle effects.
1708.04835v1
2017-08-29
Spin wave damping arising from phase coexistence below $T_c$ in colossal magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_3$
While the spin dynamics of La$_{0.7}$Ca$_{0.3}$MnO$_3$ in the ferromagnetic phase are known to be unconventional, previous measurements have yielded contradictory results regarding the damping of spin wave excitations. Neutron spectroscopy measurements on a sample with a transition temperature of $T_c$=257 K, higher than most single crystals, unambiguously reveal an anomalous increase in spin wave damping for excitations approaching the Brillouin zone boundary along the [$100$] direction that cannot be explained as an artifact due to a noninteracting phonon branch. Spin waves throughout the ($HK0$) plane display a common trend where the spin wave damping is dependent upon the excitation energy, increasing for energies above roughly 15 meV and reaching a full width at half maximum of at least 20 meV. The results are consistent with a model of intrinsic spatial inhomogeneity with phase separated regions approximately 18 {\AA} in size persisting over a large range of temperatures below $T_c$.
1708.08960v2
2017-09-08
Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems
In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter values, an eigenspace analysis is used to determine output consensus. The extension to parameter-independent stability is characterized by a coloring problem, named the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes of the graph can be colored red, blue and black in such a way that (i) every damped node is black, (ii) every black node has blue neighbors if and only if it has red neighbors, and (iii) not all nodes in the graph are black. Such a colored graph is referred to as a richly balanced colored graph. Parameter-independent stability is guaranteed if there does not exist a richly balanced coloring. The RBC problem is shown to cover another well-known graph coloring scheme known as zero forcing sets. That is, if the damped nodes form a zero forcing set in the graph, then a richly balanced coloring does not exist and thus, parameter-independent stability is guaranteed. However, the full equivalence of zero forcing sets and parameter-independent stability holds only true for tree graphs. For more general graphs with few fundamental cycles an algorithm, named chord node coloring, is proposed that significantly outperforms a brute-force search for solving the NP-complete RBC problem.
1709.02629v1
2017-10-11
Collisional damping rates for plasma waves
The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the first time, a unified kinetic theory in which collective processes and collisional dynamics are systematically incorporated from first principles. One of the outcomes of such a formalism is the rigorous derivation of collisional damping rates for Langmuir and ion-acoustic waves, which can be contrasted to the heuristic customary approach. However, the results are given only in formal mathematical expressions. The present Brief Communication numerically evaluates the rigorous collisional damping rates by considering the case of plasma particles with Maxwellian velocity distribution function so as to assess the consequence of the rigorous formalism in a quantitative manner. Comparison with the heuristic ("Spitzer") formula shows that the accurate damping rates are much lower in magnitude than the conventional expression, which implies that the traditional approach over-estimates the importance of attenuation of plasma waves by collisional relaxation process. Such a finding may have a wide applicability ranging from laboratory to space and astrophysical plasmas.
1710.03874v1
2017-10-20
Tidal dissipation in rotating fluid bodies: the presence of a magnetic field
We investigate effects of the presence of a magnetic field on tidal dissipation in rotating fluid bodies. We consider a simplified model consisting of a rigid core and a fluid envelope, permeated by a background magnetic field (either a dipolar field or a uniform axial field). The wavelike tidal responses in the fluid layer are in the form of magnetic-Coriolis waves, which are restored by both the Coriolis force and the Lorentz force. Energy dissipation occurs through viscous damping and Ohmic damping of these waves. Our numerical results show that the tidal dissipation can be dominated by Ohmic damping even with a weak magnetic field. The presence of a magnetic field smooths out the complicated frequency-dependence of the dissipation rate, and broadens the frequency spectrum of the dissipation rate, depending on the strength of the background magnetic field. However, the frequency-averaged dissipation is independent of the strength and structure of the magnetic field, and of the dissipative parameters, in the approximation that the wave-like response is driven only by the Coriolis force acting on the non-wavelike tidal flow. Indeed, the frequency-averaged dissipation quantity is in good agreement with previous analytical results in the absence of magnetic fields. Our results suggest that the frequency-averaged tidal dissipation of the wavelike perturbations is insensitive to detailed damping mechanisms and dissipative properties.
1710.07690v2
2017-11-30
Implications of dark matter cascade decay from DAMPE, HESS, Fermi-LAT and AMS02 data
Recent high-energy cosmic $e^\pm$ measurement from the DArk Matter Particle Explorer (DAMPE) satellite confirms the deviation of total cosmic ray electron spectrum above 700-900 GeV from a simple power law. In this paper we demonstrate that the cascade decay of dark matter (DM) can account for DAMPE's TeV $e^+e^-$ spectrum. We select the least constraint DM decay channel into four muons as the benchmark scenario, and perform an analysis with propagation variance in both DM signal and the Milky Way's electron background. The best-fit of the model is obtained for joint DAMPE, Fermi-Large Area Telescope (Fermi-LAT), High Energy Stereoscopic System (HESS), high energy electron data sets, and with an $\mathcal{O}(10^{26})$ second decay lifetime, which is consistent with existing gamma ray and cosmic microwave background limits. We compare the spectral difference between the cascade decay of typical final-state channels. The least constrained $4\mu$ channels give good fits to the electron spectrum's TeV scale down-turn, yet their low energy spectrum has tension with sub-TeV positron data from AMS02. We also consider a three-step cascade decay into eight muons, and also a gamma-ray constrained $4\mu,4b$ mixed channel, to demonstrate that a further softened cascade decay signal would be required for the agreement with all the data sets.
1712.00370v3
2017-12-04
Scalar dark matter, Type II Seesaw and the DAMPE cosmic ray $e^+ + e^-$ excess
The DArk Matter Particle Explorer (DAMPE) has reported a measurement of the flux of high energy cosmic ray electrons plus positrons (CREs) in the energy range between $25$ GeV and $4.6$ TeV. With unprecedented high energy resolution, the DAMPE data exhibit an excess of the CREs flux at an energy of around $1.4$ TeV. In this letter, we discuss how the observed excess can be understood in a minimal framework where the Standard Model (SM) is supplemented by a stable SM singlet scalar as dark matter (DM) and type II seesaw for generating the neutrino mass matrix. In our framework, a pair of DM particles annihilates into a pair of the SM SU(2) triplet scalars ($\Delta$s) in type II seesaw, and the subsequent $\Delta$ decays create the primary source of the excessive CREs around $1.4$ TeV. The lepton flavor structure of the primary source of CREs has a direct relationship with the neutrino oscillation data. We find that the DM interpretation of the DAMPE excess determines the pattern of neutrino mass spectrum to be the inverted hierarchy type, taking into account the constraints from the Fermi-LAT observations of dwarf spheroidal galaxies.
1712.00869v2
2017-12-07
Nonlinear growth of structure in cosmologies with damped matter fluctuations
We investigate the nonlinear evolution of structure in variants of the standard cosmological model which display damped density fluctuations relative to cold dark matter (e.g. in which cold dark matter is replaced by warm or interacting DM). Using N-body simulations, we address the question of how much information is retained from different scales in the initial linear power spectrum following the nonlinear growth of structure. We run a suite of N-body simulations with different initial linear matter power spectra to show that, once the system undergoes nonlinear evolution, the shape of the linear power spectrum at high wavenumbers does not affect the non-linear power spectrum, while it still matters for the halo mass function. Indeed, we find that linear power spectra which differ from one another only at wavenumbers larger than their half-mode wavenumber give rise to (almost) identical nonlinear power spectra at late times, regardless of the fact that they originate from different models with damped fluctuations. On the other hand, the halo mass function is more sensitive to the form of the linear power spectrum. Exploiting this result, we propose a two parameter model of the transfer function in generic damped scenarios, and show that this parametrisation works as well as the standard three parameter models for the scales on which the linear spectrum is relevant.
1712.02742v2
2017-12-11
DAMPE excess from decaying right-handed neutrino dark matter
The flux of high-energy cosmic-ray electrons plus positrons recently measured by the DArk Matter Particle Explorer (DAMPE) exhibits a tentative peak excess at an energy of around $1.4$ TeV. In this paper, we consider the minimal gauged $U(1)_{B-L}$ model with a right-handed neutrino (RHN) dark matter (DM) and interpret the DAMPE peak with a late-time decay of the RHN DM into $e^\pm W^\mp$. We find that a DM lifetime $\tau_{DM} \sim 10^{28}$ s can fit the DAMPE peak with a DM mass $m_{DM}=3$ TeV. This favored lifetime is close to the current bound on it by Fermi-LAT, our decaying RHN DM can be tested once the measurement of cosmic gamma ray flux is improved. The RHN DM communicates with the Standard Model particles through the $U(1)_{B-L}$ gauge boson ($Z^\prime$ boson), and its thermal relic abundance is controlled by only three free parameters: $m_{DM}$, the $U(1)_{B-L}$ gauge coupling ($\alpha_{BL}$), and the $Z^\prime$ boson mass ($m_{Z^\prime}$). For $m_{DM}=3$ TeV, the rest of the parameters are restricted to be $m_{Z^\prime}\simeq 6$ TeV and $0.00807 \leq \alpha_{BL} \leq 0.0149$, in order to reproduce the observed DM relic density and to avoid the Landau pole for the running $\alpha_{BL}$ below the Planck scale. This allowed region will be tested by the search for a $Z^\prime$ boson resonance at the future Large Hadron Collider.
1712.03652v3
2017-12-11
A Statistical Study on The Frequency-Dependent Damping of Slow-mode Waves in Polar Plumes and Interplumes
We perform a statistical study on the frequency-dependent damping of slow waves propagating along polar plumes and interplumes in the solar corona. Analysis of a large sample of extreme ultraviolet (EUV) imaging data with high spatial and temporal resolutions obtained from AIA/SDO suggests an inverse power-law dependence of the damping length on the periodicity of slow waves (i.e., the shorter period oscillations exhibit longer damping lengths), in agreement with the previous case studies. Similar behavior is observed in both plume and interplume regions studied in AIA 171 \AA\ and AIA 193 \AA\ passbands. It is found that the short-period (2--6 min) waves are relatively more abundant than their long period (7--30 min) counterparts in contrast to the general belief that the polar regions are dominated by the longer-period slow waves. We also derived the slope of the power spectra ($\mathrm{\alpha}$, the power-law index) statistically to better understand the characteristics of turbulence present in the region. It is found that the $\mathrm{\alpha}$ values and their distributions are similar in both plume and interplume structures across the two AIA passbands. At the same time, the spread of these distributions also indicates the complexity of the underlying turbulence mechanism.
1712.03673v1
2018-02-18
On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation
We develop a provably energy stable discontinuous Galerkin spectral element method (DGSEM) approximation of the perfectly matched layer (PML) for the three and two space dimensional (3D and 2D) linear acoustic wave equations, in first order form, subject to well-posed linear boundary conditions. First, using the well-known complex coordinate stretching, we derive an efficient un-split modal PML for the 3D acoustic wave equation. Second, we prove asymptotic stability of the continuous PML by deriving energy estimates in the Laplace space, for the 3D PML in a heterogeneous acoustic medium, assuming piece-wise constant PML damping. Third, we develop a DGSEM for the wave equation using physically motivated numerical flux, with penalty weights, which are compatible with all well-posed, internal and external, boundary conditions. When the PML damping vanishes, by construction, our choice of penalty parameters yield an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate. Fourth, to ensure numerical stability when PML damping is present, it is necessary to systematically extend the numerical numerical fluxes, and the inter-element and boundary procedures, to the PML auxiliary differential equations. This is critical for deriving discrete energy estimates analogous to the continuous energy estimates. Finally, we propose a procedure to compute PML damping coefficients such that the PML error converges to zero, at the optimal convergence rate of the underlying numerical method. Numerical experiments are presented in 2D and 3D corroborating the theoretical results.
1802.06388v1
2018-08-05
Dispersion, damping, and intensity of spin excitations in the single-layer (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+δ}$ cuprate superconductor family
Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured the dispersion and damping of spin excitations (magnons and paramagnons) in the high-$T_\mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+\delta}$ (Bi2201), for a large doping range across the phase diagram ($0.03\lesssim p\lesssim0.21$). Selected measurements with full polarization analysis unambiguously demonstrate the spin-flip character of these excitations, even in the overdoped sample. We find that the undamped frequencies increase slightly with doping for all accessible momenta, while the damping grows rapidly, faster in the (0,0)$\rightarrow$(0.5,0.5) nodal direction than in the (0,0)$\rightarrow$(0.5,0) antinodal direction. We compare the experimental results to numerically exact determinant quantum Monte Carlo (DQMC) calculations that provide the spin dynamical structure factor $S(\textbf{Q},\omega)$ of the three-band Hubbard model. The theory reproduces well the momentum and doping dependence of the dispersions and spectral weights of magnetic excitations. These results provide compelling evidence that paramagnons, although increasingly damped, persist across the superconducting dome of the cuprate phase diagram; this implies that long range antiferromagnetic correlations are quickly washed away, while short range magnetic interactions are little affected by doping.
1808.01682v1
2018-09-19
Critical exponent for the semilinear wave equations with a damping increasing in the far field
We consider the Cauchy problem of the semilinear wave equation with a damping term \begin{align*} u_{tt} - \Delta u + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times \mathbb{R}^N,\quad u(0,x) = \varepsilon u_0(x), \ u_t(0,x) = \varepsilon u_1(x), \quad x\in \mathbb{R}^N, \end{align*} where $p>1$ and the coefficient of the damping term has the form \begin{align*} c(t,x) = a_0 (1+|x|^2)^{-\alpha/2} (1+t)^{-\beta} \end{align*} with some $a_0 > 0$, $\alpha < 0$, $\beta \in (-1, 1]$. In particular, we mainly consider the cases $ \alpha < 0, \beta =0$ or $\alpha < 0, \beta = 1$, which imply $\alpha + \beta < 1$, namely, the damping is spatially increasing and effective. Our aim is to prove that the critical exponent is given by $ p = 1+ \frac{2}{N-\alpha}$. This shows that the critical exponent is the same as that of the corresponding parabolic equation $c(t,x) v_t - \Delta v = |v|^p$. The global existence part is proved by a weighted energy estimates with an exponential-type weight function and a special case of the Caffarelli-Kohn-Nirenberg inequality. The blow-up part is proved by a test-function method introduced by Ikeda and Sobajima (arXiv:1710.06780v1). We also give an upper estimate of the lifespan.
1809.06994v1
2018-10-16
Dark matter gets DAMPE
The DArk Matter Particle Explorer (DAMPE) recently reported an excess of electrons/positrons above expected background fluxes even when a double power-law background spectrum is assumed. Several dark matter models that involve TeV-scale leptophilic WIMPs have been suggested in the literature to account for this excess. All of these models are associated with the presence of a nearby dark matter clump/over-density. In this work we set out to explore how current constraints from observational data impact the suggested parameter space for a dark matter explanation of the DAMPE excess, as well as make projections of the capacity of LOFAR and the up-coming SKA to observe indirect radio emissions from the nearby dark matter over-density. We show that LOFAR is incapable of probing the parameter space for DAMPE excess models, unless the dark matter clump is in the form of an ultra-compact mini halo. Fermi-LAT limits on dark matter annihilation are unable to probe these models in all cases. Limits derived from diffuse Coma cluster radio emission can probe a substantial portion of the parameter space and muon neutrino limits inferred from galactic centre gamma-ray fluxes heavily restrict muon coupling for the proposed WIMPs. The SKA is shown to able to fully probe the parameter space of all the studied models using indirect emissions from the local dark matter over-density.
1810.07176v2
2018-11-15
Damping rate of a fermion in ultradegenerate chiral matter
We compute the damping rate of a fermion propagating in a chiral plasma when there is an imbalance between the densities of left- and right-handed fermions, after generalizing the hard thermal loop resummation techniques for these systems. In the ultradegenerate limit, for very high energies the damping rate of this external fermion approaches a constant value. Closer to the two Fermi surfaces, however, we find that the rate depends on both the energy and the chirality of the fermion, being higher for the predominant chirality. This comes out as a result of its scattering with the particles of the plasma, mediated by the exchange of Landau damped photons. In particular, we find that the chiral imbalance is responsible for a different propagation of the left and right circular polarised transverse modes of the photon, and that a chiral fermion interacts differently with these two transverse modes. We argue that spontaneous radiation of energetic fermions is kinematically forbidden, and discuss the time regime where our computation is valid.
1811.06394v3
2018-12-16
Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure
Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric 'breathing' mode and the buckling mode. In this paper we argue that the precise frequency dependence of the damping does not matter as most of the damping happens at a single frequency (the breathing frequency). In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.
1812.06526v2
2019-01-09
Turbulent dynamo in a weakly ionized medium
The small-scale turbulent dynamo is an important process contributing to the cosmic magnetization. In partially ionized astrophysical plasmas, the dynamo growth of magnetic energy strongly depends on the coupling state between ions and neutrals and the ion-neutral collisional damping effect. A new damping stage of turbulent dynamo in a weakly ionized medium was theoretically predicted by Xu \& Lazarian (2016). By carrying out a 3D two-fluid dynamo simulation, here we for the first time numerically confirmed the physical conditions and the linear-in-time growth of magnetic field strength of the damping stage of dynamo. The dynamo-amplified magnetic field has a characteristic length as the damping scale, which increases with time and can reach the injection scale of turbulence after around eight largest eddy-turnover times given sufficiently low ionization fraction and weak initial magnetic field. Due to the weak coupling between ions and neutrals, most turbulent energy carried by neutrals cannot be converted to the magnetic energy, resulting in a relatively weak magnetic field at the end of dynamo. This result has important implications for the growth of magnetic fields in the partially ionized interstellar medium and shock acceleration of Galactic cosmic rays.
1901.02893v1
2019-01-25
Quantum speed limit time for correlated quantum channel
Memory effects play a fundamental role in the dynamics of open quantum systems. There exist two different views on memory for quantum noises. In the first view, the quantum channel has memory when there exist correlations between successive uses of the channels on a sequence of quantum systems. These types of channels are also known as correlated quantum channels. In the second view, memory effects result from correlations which are created during the quantum evolution. In this work we will consider the first view and study the quantum speed limit time for a correlated quantum channel. Quantum speed limit time is the bound on the minimal time which is needed for a quantum system to evolve from an initial state to desired states. The quantum evolution is fast if the quantum speed limit time is short. In this work, we will study the quantum speed limit time for some correlated unital and correlated non-unital channels. As an example for unital channels we choose correlated dephasing colored noise. We also consider the correlated amplitude damping and correlated squeezed generalized amplitude damping channels as the examples for non-unital channels. It will be shown that the quantum speed limit time for correlated pure dephasing colored noise is increased by increasing correlation strength, while for correlated amplitude damping and correlated squeezed generalized amplitude damping channels quantum speed limit time is decreased by increasing correlation strength.
1901.08917v4
2019-02-17
Finite-size effects on sound damping in stable computer glasses
In this brief note we comment on the recent results presented in arXiv:1812.08736v1
1902.06225v1
2019-05-04
A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science
In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows. We concentrate on two equations: one is a damped second-order total variation flow, which is primarily motivated by the application of image denoising; the other is a damped second-order mean curvature flow for level sets of scalar functions, which is related to a non-convex variational model capable of correcting displacement errors in image data (e.g. dejittering). For the former equation, we prove the existence and uniqueness of the solution. For the latter, we draw a connection between the equation and some second-order geometric PDEs evolving the hypersurfaces which are described by level sets of scalar functions, and show the existence and uniqueness of the solution for a regularized version of the equation. The latter is used in our algorithmic development. A general algorithm for numerical discretization of the two nonlinear PDEs is proposed and analyzed. Its efficiency is demonstrated by various numerical examples, where simulations on the behavior of solutions of the new equations and comparisons with first-order flows are also documented.
1905.01457v2
2019-07-08
Single-spectrum prediction of kurtosis of water waves in a non-conservative model
We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher order Nonlinear Schr\"odinger equation (NLS). During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted.
1907.03490v1
2019-08-20
Synthetic Extreme-ultraviolet Emissions Modulated by Leaky Fast Sausage Modes in Solar Active Region Loops
We study the extreme-ultraviolet (EUV) emissions modulated by leaky fast sausage modes (FSMs) in solar active region loops and examine their observational signatures via spectrometers like EIS. After computing fluid variables of leaky FSMs with MHD simulations, we forward-model the intensity and spectral properties of the Fe X 185~\AA~and Fe XII 195~\AA~lines by incorporating non-equilibrium ionization (NEI) in the computations of the relevant ionic fractions. The damping times derived from the intensity variations are then compared with the wave values, namely the damping times directly found from our MHD simulations. Our results show that in the equilibrium ionization cases, the density variations and the intensity variations can be either in phase or in anti-phase, depending on the loop temperature. NEI considerably impacts the intensity variations but has only marginal effects on the derived Doppler velocity or Doppler width. We find that the damping time derived from the intensity can largely reflect the wave damping time if the loop temperature is not drastically different from the nominal formation temperature of the corresponding emission line. These results are helpful for understanding the modulations to the EUV emissions by leaky FSMs and hence helpful for identifying FSMs in solar active region loops.
1908.07131v1
2019-10-24
Frequency criteria for exponential stability
We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on dissipativity theory. Applications are given to convergence rates for certain perturbations of the damped harmonic oscillator.
1910.10855v2
2019-11-05
IW And-Type State in IM Eridani
IW And stars are a recently recognized group of dwarf novae which are characterized by a repeated sequence of brightening from a standstill-like phase with damping oscillations followed by a deep dip. Kimura et al. (2019) recently proposed a model based on thermal-viscous disk instability in a tilted disk to reproduce the IW And-type characteristics. IM Eri experienced the IW And-type phase in 2018 and we recorded three cycles of the (damping) oscillation phase terminated by brightening. We identified two periods during the IW And-type state: 4-5 d small-amplitude (often damping) oscillations and a 34-43 d long cycle. This behavior is typical for an IW And-type star. The object gradually brightened within the long cycle before the next brightening which terminated the (damping) oscillation phase. This observation agrees with the increasing disk mass during the long cycle predicted by a model of thermal-viscous disk instability in a tilted disk (Kimura et al. 2019). We, however, did not succeed in detecting negative superhumps, which are considered to be the signature of a tilted disk.
1911.01587v1
2019-11-28
Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$Γ$ model on a honeycomb lattice
We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $\Gamma$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $\alpha$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $\Gamma = K>0$, where $K$ is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra.
1911.12829v2
2019-12-10
A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization with Applications
This paper proposes a novel stochastic version of damped and regularized BFGS method for addressing the above problems.
1912.04456v1
2019-12-27
Ultralow mechanical damping with Meissner-levitated ferromagnetic microparticles
Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, due to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical modes of a levitated ferromagnetic microsphere, using a dc SQUID (Superconducting Quantum Interference Device) with a single pick-up coil. The measured frequencies are in agreement with a finite element simulation based on ideal Meissner effect. For two specific modes we find further substantial agreement with analytical predictions based on the image method. We measure damping times $\tau$ exceeding $10^4$ s and quality factors $Q$ beyond $10^7$, improving by $2-3$ orders of magnitude over previous experiments based on the same principle. We investigate the possible residual loss mechanisms besides gas collisions, and argue that much longer damping time can be achieved with further effort and optimization. Our results open the way towards the development of ultrasensitive magnetomechanical sensors with potential applications to magnetometry and gravimetry, as well as to fundamental and quantum physics.
1912.12252v3
2020-01-22
Wide Area Measurement System-based Low Frequency Oscillation Damping Control through Reinforcement Learning
Ensuring the stability of power systems is gaining more attraction today than ever before, due to the rapid growth of uncertainties in load and renewable energy penetration. Lately, wide area measurement system-based centralized controlling techniques started providing a more flexible and robust control to keep the system stable. But, such a modernization of control philosophy faces pressing challenges due to the irregularities in delays of long-distance communication channels and response of equipment to control actions. Therefore, we propose an innovative approach that can revolutionize the control strategy for damping down low frequency oscillations in transmission systems. Proposed method is enriched with a potential of overcoming the challenges of communication delays and other non-linearities in wide area damping control by leveraging the capability of the reinforcement learning technique. Such a technique has a unique characteristic to learn on diverse scenarios and operating conditions by exploring the environment and devising an optimal control action policy by implementing policy gradient method. Our detailed analysis and systematically designed numerical validation prove the feasibility, scalability and interpretability of the carefully modelled low-frequency oscillation damping controller so that stability is ensured even with the uncertainties of load and generation are on the rise.
2001.07829v1
2020-02-13
Semi-realistic tight-binding model for spin-orbit torques
We compute the spin-orbit torque in a transition metal heterostructure using Slater-Koster parameterization in the two-center tight-binding approximation and accounting for d-orbitals only. In this method, the spin-orbit coupling is modeled within Russel-Saunders scheme, which enables us to treat interfacial and bulk spin-orbit transport on equal footing. The two components of the spin-orbit torque, dissipative (damping-like) and reactive (field-like), are computed within Kubo linear response theory. By systematically studying their thickness and angular dependence, we were able to accurately characterize these components beyond the traditional "inverse spin galvanic" and "spin Hall" effects. Whereas the conventional field-like torque is purely interfacial, we unambiguously demonstrate that the conventional the damping-like torque possesses both an interfacial and a bulk contribution. In addition, both field-like and damping-like torques display substantial angular dependence with strikingly different thickness behavior. While the planar contribution of the field-like torque decreases smoothly with the nonmagnetic metal thickness, the planar contribution of the damping-like torque increases dramatically with the nonmagnetic metal thickness. Finally, we investigate the self-torque exerted on the ferromagnet when the spin-orbit coupling of the nonmagnetic metal is turned off. Our results suggest that the spin accumulation that builds up inside the ferromagnet can be large enough to induce magnetic excitations.
2002.05533v1
2020-02-14
One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates
This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every $t\geq 0$, where $\Sigma$ is a given subset of $\mathbb R^2$. The study is performed within an $L^p$ functional framework, $p\in [1, +\infty]$. We aim at determining conditions on $\Sigma$ ensuring existence and uniqueness of solutions of that wave equation as well as strong stability and uniform global asymptotic stability of its solutions. In the latter case, we also study the decay rates of the solutions and their optimality. We first establish a one-to-one correspondence between the solutions of that wave equation and the iterated sequences of a discrete-time dynamical system in terms of which we investigate the above mentioned issues. This enables us to provide a simple necessary and sufficient condition on $\Sigma$ ensuring existence and uniqueness of solutions of the wave equation as well as an efficient strategy for determining optimal decay rates when $\Sigma$ verifies a generalized sector condition. As an application, we solve two conjectures stated in the literature, the first one seeking a specific optimal decay rate and the second one associated with a saturation type of damping. In case the boundary damping is subject to perturbations, we derive sharp results regarding asymptotic perturbation rejection and input-to-state issues.
2002.06186v3
2020-03-30
Optimal absorption of acoustical waves by a boundary
In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The well-posedness of the model is shown in a class of domains with d-set boundaries (N -- 1 $\le$ d < N). We introduce a class of admissible Lipschitz boundaries, in which an optimal shape of the wall exists in the following sense: We prove the existence of a Radon measure on this shape, greater than or equal to the usual Lebesgue measure, for which the corresponding solution of the Helmholtz problem realizes the infimum of the acoustic energy defined with the Lebesgue measure on the boundary. If this Radon measure coincides with the Lebesgue measure, the corresponding solution realizes the minimum of the energy. For a fixed porous material, considered as an acoustic absorbent, we derive the damping parameters of its boundary from the corresponding time-dependent problem described by the damped wave equation (damping in volume).
2003.13250v2
2020-04-24
Suppression of the longitudinal coupled bunch instability in DA$Φ$NE in collisions with a crossing angle
In DAFNE, the Frascati $e^+e^-$ collider operating since 1998, an innovative collision scheme, the crab waist, has been successfully implemented during the years 2008-09. During operations for the Siddharta experiment an unusual synchrotron oscillation damping effect induced by beam-beam collisions has been observed. Indeed, when the longitudinal feedback is off, the positron beam becomes unstable with currents above 200-300 mA due to coupled bunch instability. The longitudinal instability is damped by colliding the positron beam with a high current electron beam (of the order of 2 A). A shift of about -600 Hz in the residual synchrotron sidebands is observed. Precise measurements have been performed by using both a commercial spectrum analyzer and the diagnostic capabilities of the longitudinal bunch-by-bunch feedback. The damping effect has been observed in DAFNE for the first time during collisions with the crab waist scheme. Our explanation, based both on theoretical consideration and modeling simulation, is that beam collisions with a large crossing angle produce longitudinal tune shift and spread, providing Landau damping of synchrotron oscillations.
2004.11902v1
2020-05-08
Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping
We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schr\"odinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation of the spectrum. In the latter, only the fundamental frequency and the upper and lower sidebands are retained. Plane wave solutions to the NLSE exhibit modulation instability (MI) within a frequency band determined by a linear stability analysis. For modulation frequencies inside the MI-band, we experimentally demonstrate that forcing and damping cause a separatrix crossing during the evolution. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general. When the system is damped by the viscosity of the water, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside the separatrix. Furthermore, for modulation frequencies outside the conventional MI-band, we experimentally demonstrate that contrary to the linear prediction, we do observe a growth and decay cycle of the plane-wave modulation. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution.
2005.03931v1
2020-05-13
Damping of a micro-electromechanical oscillator in turbulent superfluid $^4$He: A novel probe of quantized vorticity in the ultra-low temperature regime
We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^4$He on the motion of a micro-electromechanical systems (MEMS) resonator. We find that the MEMS is uniquely sensitive to quantum turbulence present in the fluid. To generate turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to the MEMS and driven at large amplitude. We observe that at low velocity, the MEMS is damped by the turbulence, and that above a critical velocity, $v_c \simeq 5\,$mm\,s$^{-1}$, the turbulent damping is greatly reduced. We find that above $v_c$, the damping of the MEMS is reduced further for increasing velocity, indicating a velocity dependent coupling between the surface of the MEMS and the quantized vortices constituting the turbulence. We propose a model of the interaction between vortices in the fluid and the surface of the MEMS. The sensitivity of these devices to a small number of vortices and the almost unlimited customization of MEMS open the door to a more complete understanding of the interaction between quantized vortices and oscillating structures, which in turn provides a new route for the investigation of the dynamics of single vortices.
2005.06570v1
2020-06-10
Online PMU-Based Wide-Area Damping Control for Multiple Inter-Area Modes
This paper presents a new phasor measurement unit (PMU)-based wide-area damping control (WADC) method to suppress the critical inter-area modes of large-scale power systems. Modal participation factors, estimated by a practically model-free system identification approach, are used to select the most suitable synchronous generators for control through the proposed WADC algorithm. It is shown that multiple inter-area modes can be sufficiently damped by the proposed approach without affecting the rest of the modes, while only a few machines are needed to perform the control. The proposed technique is applied to the IEEE 68-bus and the IEEE 145-bus systems, including the test cases with PMU measurement noise and with missing PMUs. The simulation results clearly demonstrate the good adaptivity of the control strategy subjected to network model changes, its effective damping performance comparing to power system stabilizers (PSSs), and its great potential for near real-time implementation.
2006.05651v1
2020-06-14
A general formulation for the magnetic oscillations in two dimensional systems
We develop a general formalism for the magnetic oscillations (MO) in two dimensional (2D) systems. We consider general 2D Landau levels, which may depend on other variable or indices, besides the perpendicular magnetic field. In the ground state, we obtain expressions for the MO phase and amplitude. From this we use a Fourier expansion to write the MO, with the first term being a sawtooth oscillation. We also consider the effects of finite temperature, impurities or lattice imperfections, assuming a general broadening of the Landau levels. We develop two methods for describing these damping effects in the MO. One in terms of the occupancy of the Landau levels, the other in terms of reduction factors, which results in a generalization of the Lifshits-Kosevich (LK) formula. We show that the first approach is particularly useful at very low damping, when only the states close to the Fermi energy are excited. In contrast, the LK formula may be more convenient at higher damping, when only few terms are needed in its harmonic expansion. We compare different damping situations, showing how the MO are broadened in each case. The general formulation presented allows to relate the properties of the MO with those of the 2D systems.
2006.07944v2
2020-07-19
Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping
In this paper, the smooth solution of the physical vacuum problem for the one dimensional compressible Euler equations with time-dependent damping is considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder continuous. The coefficient of the damping depends on time, given by this form $\frac{\mu}{(1+t)^\lambda}$, $\lambda$, $\mu>0$, which decays by order $-\lambda$ in time. Under the assumption that $0<\lambda<1$, $0<\mu$ or $\lambda=1$, $2<\mu$, we will prove the global existence of smooth solutions and convergence to the modified Barenblatt solution of the related porous media equation with time-dependent dissipation and the same total mass when the initial data of the Euler equations is a small perturbation of that of the Barenblatt solution. The pointwise convergence rates of the density, velocity and the expanding rate of the physical vacuum boundary are also given. The proof is based on space-time weighted energy estimates, elliptic estimates and Hardy inequality in the Lagrangian coordinates. Our result is an extension of that in Luo-Zeng [Comm. Pure Appl. Math. 69 (2016), no. 7, 1354-1396], where the authors considered the physical vacuum free boundary problem of the compressible Euler equations with constant-coefficient damping.
2007.14802v2
2020-08-03
Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities
We consider in this article the damped wave equation, in the \textit{scale-invariant case} with combined two nonlinearities, which reads as follows: \begin{displaymath} \d (E) \hspace{1cm} u_{tt}-\Delta u+\frac{\mu}{1+t}u_t=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty), \end{displaymath} with small initial data.\\ Compared to our previous work \cite{Our}, we show in this article that the first hypothesis on the damping coefficient $\mu$, namely $\mu < \frac{N(q-1)}{2}$, can be removed, and the second one can be extended from $(0, \mu_*/2)$ to $(0, \mu_*)$ where $\mu_*>0$ is solution of $(q-1)\left((N+\mu_*-1)p-2\right) = 4$. Indeed, owing to a better understanding of the influence of the damping term in the global dynamics of the solution, we think that this new interval for $\mu$ describe better the threshold between the blow-up and the global existence regions. Moreover, taking advantage of the techniques employed in the problem $(E)$, we also improve the result in \cite{LT2,Palmieri} in relationship with the Glassey conjecture for the solution of $(E)$ but without the nonlinear term $|u|^q$. More precisely, we extend the blow-up region from $p \in (1, p_G(N+\sigma)]$, where $\sigma$ is given by \eqref{sigma} below, to $p \in (1, p_G(N+\mu)]$ giving thus a better estimate of the lifespan in this case.
2008.02109v3
2020-08-26
Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures
We perform a detailed analysis of the phase transition between the uniform superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At mean-field level we demonstrate that at temperature $T\to 0$ the gradient term in the effective action can be tuned to zero for experimentally relevant sets of parameters, thus providing an avenue to realize a quantum Lifshitz point. We subsequently analyze damping processes affecting the order-parameter field across the phase transition. We show that, in the low energy limit, Landau damping occurs only in the symmetry-broken phase and affects exclusively the longitudinal component of the order-parameter field. It is however unavoidably present in the immediate vicinity of the phase transition at temperature $T=0$. We subsequently perform a renormalization-group analysis of the system in a situation, where, at mean-field level, the quantum phase transition is second order (and not multicritical). We find that, at $T$ sufficiently low, including the Landau damping term in a form derived from the microscopic action destabilizes the renormalization group flow towards the Wilson-Fisher fixed point. This signals a possible tendency to drive the transition weakly first-order by the coupling between the order-parameter fluctuations and fermionic excitations effectively captured by the Landau damping contribution to the order-parameter action.
2008.11782v1
2020-09-10
Electron Landau Damping of Kinetic Alfvén Waves in Simulated Magnetosheath Turbulence
Turbulence is thought to play a role in the heating of the solar wind plasma, though many questions remain to be solved regarding the exact nature of the mechanisms driving this process in the heliosphere. In particular, the physics of the collisionless interactions between particles and turbulent electromagnetic fields in the kinetic dissipation range of the turbulent cascade remains incompletely understood. A recent analysis of an interval of Magnetosphere Multiscale (MMS) observations has used the field-particle correlation technique to demonstrate that electron Landau damping is involved in the dissipation of turbulence in the Earth's magnetosheath. Motivated by this discovery, we perform a high-resolution gyrokinetic numerical simulation of the turbulence in the MMS interval to investigate the role of electron Landau damping in the dissipation of turbulent energy. We employ the field-particle correlation technique on our simulation data, compare our results to the known velocity-space signatures of Landau damping outside the dissipation range, and evaluate the net electron energization. We find qualitative agreement between the numerical and observational results for some key aspects of the energization and speculate on the nature of disagreements in light of experimental factors, such as differences in resolution, and of developing insights into the nature of field-particle interactions in the presence of dispersive kinetic Alfv\'en waves.
2009.05010v1
2020-11-09
Plasmon energy losses in shear bands of metallic glass
Shear bands resulting from plastic deformation in cold-rolled Al$_{88}$Y$_{7}$Fe$_{5}$ metallic glass were observed to display alternating density changes along their propagation direction. Electron-energy loss spectroscopy (EELS) was used to investigate the volume plasmon energy losses in and around shear bands. Energy shifts of the peak centre and changes in the peak width (FWHM) reflecting the damping were precisely determined within an accuracy of a few meV using an open source python module (Hyperspy) to fit the shapes of the plasmon and zero-loss peaks with Lorentzian functions. The maximum bulk plasmon energy shifts were calculated for the bright and dark shear band segments relative to the matrix to be about 38 and 14 meV, respectively. The damping was observed to be larger for the denser regions. The analysis presented here suggests that the changes in the plasmons are caused by two contributions: (i) Variable damping in the shear band segments due to changes in the medium-range order (MRO). This affects the static structure factor S(k), which, in turn, leads to either reduced or increased damping according to the Ziman-Baym formula. (ii) The ionic density and the effective electron mass appearing in the zero-momentum plasmon frequency formula $E_p(q=0)$ are coupled and give rise to small variations in the plasmon energy. The model predicts plasmon energy shifts in the order of meV.
2011.04396v3
2020-11-16
Thresholds for loss of Landau damping in longitudinal plane
Landau damping mechanism plays a crucial role in providing single-bunch stability in LHC, High-Luminosity LHC, other existing as well as previous and future (like FCC) circular hadron accelerators. In this paper, the thresholds for the loss of Landau damping (LLD) in the longitudinal plane are derived analytically using the Lebedev matrix equation (1968) and the concept of the emerged van Kampen modes (1983). We have found that for the commonly-used particle distribution functions from a binomial family, the LLD threshold vanishes in the presence of the constant inductive impedance Im$Z/k$ above transition energy. Thus, the effect of the cutoff frequency or the resonant frequency of a broad-band impedance on beam dynamics is studied in detail. The findings are confirmed by direct numerical solutions of the Lebedev equation as well as using the Oide-Yokoya method (1990). Moreover, the characteristics, which are important for beam operation, as the amplitude of residual oscillations and the damping time after a kick (or injection errors) are considered both above and below the threshold. Dependence of the threshold on particle distribution in the longitudinal phase space is also analyzed, including some special cases with a non-zero threshold for Im$Z/k = const$. All main results are confirmed by macro-particle simulations and consistent with available beam measurements in the LHC.
2011.07985v1
2020-12-04
Quantum Circuits for Collective Amplitude Damping in Two-Qubit Systems
Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise effects. Hence, they are called noisy-intermediate scale quantum devices. In order to accomplish efficient quantum computation with using these machines, a key issue is going to be the coherent control of individual and collective quantum noises. In this work, we focus on a latter type and investigate formulations of the collective quantum noises represented as quantum circuits. To simplify our discussions and make them concrete, we analyze collective amplitude damping processes in two-qubit systems. As verifications of our formalisms and the quantum circuits, we demonstrate digital quantum simulations of the collective amplitude damping by examining six different initial conditions with varying the number of execution of an overall operation for our quantum simulations. We observe that our results show good numerical matching with the solution of quantum master equation for the two-qubit systems as we increase such a number. In addition, we explain the essence of the way to extend our formalisms to analyze the collective amplitude damping in larger qubit systems. These results pave the way for establishing systematic approaches to control the quantum noises and designing large-scale quantum computers.
2012.02410v1
2020-12-10
Dimensional analysis of spring-wing systems reveals performance metrics for resonant flapping-wing flight
Flapping-wing insects, birds, and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy that may enable high dynamic efficiency. However, recent experiments highlight losses due to damping in the insect thorax that could reduce the benefit of those elastic elements. We performed experiments on, and simulations of a dynamically-scaled robophysical flapping model with an elastic element and biologically-relevant structural damping to elucidate the roles of body mechanics, aerodynamics, and actuation in spring-wing energetics. We measured oscillatory flapping wing dynamics and energetics subject to a range of actuation parameters, system inertia, and spring elasticity. To generalize these results, we derive the non-dimensional spring-wing equation of motion and present variables that describe the resonance properties of flapping systems: $N$, a measure of the relative influence of inertia and aerodynamics, and $\hat{K}$, the reduced stiffness. We show that internal damping scales with $N$, revealing that dynamic efficiency monotonically decreases with increasing $N$. Based on these results, we introduce a general framework for understanding the roles of internal damping, aerodynamic and inertial forces, and elastic structures within all spring-wing systems.
2012.05428v1
2021-01-22
Measurements and analysis of response function of cold atoms in optical molasses
We report our experimental measurements and theoretical analysis of the position response function of a cloud of cold atoms residing in the viscous medium of an optical molasses and confined by a magneto-optical trap (MOT). We measure the position response function by applying a transient homogeneous magnetic field as a perturbing force. We observe a transition from a damped oscillatory motion to an over-damped relaxation, stemming from a competition between the viscous drag provided by the optical molasses and the restoring force of the MOT. Our observations are in both qualitative and quantitative agreement with the predictions of a theoretical model based on the Langevin equation. As a consistency check, and as a prototype for future experiments, we also study the free diffusive spreading of the atomic cloud in our optical molasses with the confining magnetic field of the MOT turned off. We find that the measured value of the diffusion coefficient agrees with the value predicted by our Langevin model, using the damping coefficient. The damping coefficient was deduced from our measurements of the position response function at the same temperature.
2101.09118v2
2021-03-11
Nontrivial damping of quantum many-body dynamics
Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schr\"odinger picture. We show that a nontrivial damping in the Schr\"odinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.
2103.06646v2
2021-03-24
Multimode piezoelectric shunt damping of thin plates with arrays of separately shunted patches, method, and experimental validation
Two-dimensional thin plates are widely used in many applications. Shunt damping is a promising way for the attenuation of vibration of these electromechanical systems. It enables a compact vibration damping method without adding significant mass and volumetric occupancy. Analyzing the dynamics of such electromechanical systems requires precise modeling tools that properly consider the coupling between the piezoelectric elements and the host structure. Although the concept of shunt damping has been studied extensively in the literature, most of the studies do not provide a formulation for modeling the multiple piezoelectric patches that are scattered on the host structure and shunted separately. This paper presents a methodology and a formulation for separately shunted piezoelectric patches for achieving higher performance on vibration attenuation. The Rayleigh-Ritz method is used for performing modal analysis and obtaining the frequency response functions of the electro-mechanical system. The developed model includes mass and stiffness contribution of the piezoelectric patches as well as the electromechanical coupling effect. In this study, the piezoelectric patches are shunted via separate electrical circuits and compared with the ones those are shunted via interconnected electrical circuits. For verification, system-level finite element simulations are performed in ANSYS software and compared with the analytical model results. An experimental setup is also built to validate the performance of the separately shunted piezoelectric patches. The effectiveness of the method is investigated for a broader range of frequencies and it was shown that separately shunted piezoelectric patches are more effective compared to connected for a wide range of frequencies.
2103.13179v1
2021-03-29
Nonequilibrium Dynamics of the Chiral Quark Condensate under a Strong Magnetic Field
Strong magnetic fields impact quantum-chromodynamics (QCD) properties in several situations; examples include the early universe, magnetars, and heavy-ion collisions. These examples share a common trait: time evolution. A prominent QCD property impacted by a strong magnetic field is the quark condensate, an approximate order parameter of the QCD transition between a high-temperature quark-gluon phase and a low-temperature hadronic phase. We use the linear sigma model with quarks to address the quark condensate time evolution under a strong magnetic field. We use the closed time path formalism of nonequilibrium quantum field theory to integrate out the quarks and obtain a mean-field Langevin equation for the condensate. The Langevin equation features dissipation and noise kernels controlled by a damping coefficient. We compute the damping coefficient for magnetic field and temperature values achieved in peripheral relativistic heavy-ion collisions and solve the Langevin equation for a temperature quench scenario. The magnetic field changes the dissipation and noise pattern by increasing the damping coefficient compared to the zero-field case. An increased damping coefficient increases fluctuations and time scales controlling condensate's short-time evolution, a feature that can impact hadron formation at the QCD transition. The formalism developed here can be extended to include other order parameters, hydrodynamic modes, and system's expansion to address magnetic field effects in complex settings as heavy-ion collisions, the early universe, and magnetars.
2103.15665v1
2021-04-09
Taming the pinch singularities in the two-loop neutrino self-energy in a medium
We consider the calculation of the thermal self-energy of a neutrino that propagates in a medium composed of fermions and scalars interacting via a Yukawa-type coupling, in the case that the neutri no energy is much larger than the fermion and scalar masses, as well as the temperature and chemical potentials of the background. In this kinematic regime the one-loop contribution to the imaginary part of the self-energy is negligible. We consider the two-loop contribution and we encounter the so-called pinch singularities which are known to arise in higher loop self-energy calculations in Thermal Field Theory. With a judicious use of the properties and parametrizations of the thermal propagators the singularities are treated effectively and actually disappear. From the imaginary part of the self-energy, we obtain a precise formula for the damping matrix expressed in terms of integrals over the background particle distributions. The formulas predict a specific dependence of the damping terms on the neutrino energy, depending on the background conditions. For guidance to estimating the effects in specific contexts, we compute the damping terms for several limiting cases of the momentum distribution functions of the background particles. We discuss briefly the connection between the results of our calculations for the damping matrix and the decoherence effects described in terms of the Lindblad equation.
2104.04459v2
2021-06-20
Life-cycle assessment for flutter probability of a long-span suspension bridge based on field monitoring data
Assessment of structural safety status is of paramount importance for existing bridges, where accurate evaluation of flutter probability is essential for long-span bridges. In current engineering practice, at the design stage, flutter critical wind speed is usually estimated by the wind tunnel test, which is sensitive to modal frequencies and damping ratios. After construction, structural properties of existing structures will change with time due to various factors, such as structural deteriorations and periodic environments. The structural dynamic properties, such as modal frequencies and damping ratios, cannot be considered as the same values as the initial ones, and the deteriorations should be included when estimating the life-cycle flutter probability. This paper proposes an evaluation framework to assess the life-cycle flutter probability of long-span bridges considering the deteriorations of structural properties, based on field monitoring data. The Bayesian approach is employed for modal identification of a suspension bridge with the main span of 1650 m, and the field monitoring data during 2010-2015 is analyzed to determine the deterioration functions of modal frequencies and damping ratios, as well as their inter-seasonal fluctuations. According to the historical trend, the long-term structural properties can be predicted, and the probability distributions of flutter critical wind speed for each year in the long term are calculated. Consequently, the life-cycle flutter probability is estimated, based on the predicted modal frequencies and damping ratios.
2106.10694v1
2021-07-17
Theoretical and numerical study of vibrational resonance in a damped softening Duffing oscillator
We study the possibility of occurrence of vibrational resonance in a softening Duffing oscillator in the underdamped and overdamped cases both theoretically as well as numerically. The oscillator is driven by two periodic forces. Numerically we find that in the underdamped case two oscillatory solutions are obtained in a limited range of the parameters considered (damping coefficient and amplitude of the high frequency force) for a fixed frequency and amplitude of the low frequency periodic force depending on the initial conditions. These solutions have distinct response amplitude to the low frequency force. When damping is gradually increased, only one oscillatory solution is observed. Vibrational resonance is observed in both the regions of oscillation. The analytical approximation yields only one oscillatory solution for all damping values. Analytically, the peak in the area bounded by the phase portrait as a function of the amplitude of the high frequency force is connected to vibrational resonance. Also, the values of the frequency of the low frequency forcing and the amplitude of the high frequency forcing at which vibrational resonance is found to occur are obtained. In the overdamped case, vibrational resonance is not observed for the softening Duffing oscillator thus showing a marked contrast to the overdamped bistable oscillator
2107.08302v1
2021-07-28
Optimal gamma-ray selections for monochromatic line searches with DAMPE
The DArk Matter Particle Explorer (DAMPE) is a space high-energy cosmic-ray detector covering a wide energy band with a high energy resolution. One of the key scientific goals of DAMPE is to carry out indirect detection of dark matter by searching for high-energy gamma-ray line structure. To promote the sensitivity of gamma-ray line search with DAMPE, it is crucial to improve the acceptance and energy resolution of gamma-ray photons. In this paper, we quantitatively prove that the photon sample with the largest ratio of acceptance to energy resolution is optimal for line search. We therefore develop a line-search sample specifically optimized for the line search. Meanwhile, in order to increase the statistics, we also selected the so called BGO-only photons that convert into $e^+e^-$ pairs only in the BGO calorimeter. The standard, the line-search, and the BGO-only photon samples are then tested for line search individually and collectively. The results show that a significantly improved limit could be obtained from an appropriate combination of the date sets, and the increase is about 20\% for the highest case compared with using the standard sample only.
2107.13208v2
2021-07-28
Magnetic field induced asymmetric splitting of the output signal
In this paper we have investigated the dynamics of a damped harmonic oscillator in the presence of an electromagnetic field. The transients for the two dimensional harmonic oscillator imply about the modulation of the frequency of the oscillator by the velocity dependent non conservative force from an applied magnetic field. Except a special condition, the motion is in general quasi periodic nature even in the absence of damping. Another interesting finding is that the magnetic field may induce an asymmetric splitting of the spectrum of the output signal with two peaks in the case of a driven damped two dimensional harmonic oscillator. One more additional peak may appear for the three dimensional case. In some cases the spectrum may have similarity with the Normal Zeeman Effect. At the same time one may observe to appear the anti resonance phenomenon even for the driven damped cyclotron motion where the system with the purely non conservative force fields is driven by an electric field. Finally, our calculation exhibits how the magnetic field can modulate the phase difference (between input and output signals) and the efficiency like quantity of the energy storing process. Thus the present study might be applicable in the areas related to the refractive index, the barrier crossing dynamics and autonomous stochastic resonance, respectively.
2107.13305v1
2021-07-28
Evolution of a Mode of Oscillation Within Turbulent Accretion Disks
We investigate the effects of subsonic turbulence on a normal mode of oscillation [a possible origin of the high-frequency quasi-periodic oscillations (HFQPOs) within some black hole accretion disks]. We consider perturbations of a time-dependent background (steady state disk plus turbulence), obtaining an oscillator equation with stochastic damping, (mildly) nonlinear restoring, and stochastic driving forces. The (long-term) mean values of our turbulent functions vanish. In particular, turbulence does not damp the oscillation modes, so `turbulent viscosity' is not operative. However, the frequency components of the turbulent driving force near that of the mode can produce significant changes in the amplitude of the mode. Even with an additional (phenomenological constant) source of damping, this leads to an eventual `blowout' (onset of effects of nonlinearity) if the turbulence is sufficiently strong or the damping constant is sufficiently small. The infrequent large increases in the energy of the mode could be related to the observed low duty cycles of the HFQPOs. The width of the peak in the power spectral density (PSD) is proportional to the amount of nonlinearity. A comparison with observed continuum PSDs indicates the conditions required for visibility of the mode.
2107.13546v1
2021-07-31
Oscillating scalar dissipating in a medium
We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.
2108.00254v1
2021-08-02
Large-amplitude longitudinal oscillations in solar prominences simulated with different resolutions
Large-amplitude longitudinal oscillations (LALOs) in solar prominences have been widely studied in the last decades. However, their damping and amplification mechanisms are not well understood. In this study, we investigate the attenuation and amplification of LALOs using high-resolution numerical simulations with progressively increasing spatial resolutions. We performed time-dependent numerical simulations of LALOs using the 2D magnetic configuration that contains a dipped region. After the prominence mass loading in the magnetic dips, we triggered LALOs by perturbing the prominence mass along the magnetic field. We performed the experiments with four values of spatial resolution. In the simulations with the highest resolution, the period shows a good agreement with the pendulum model. The convergence experiment revealed that the damping time saturates at the bottom prominence region with improving the resolution, indicating the existence of a physical reason for the damping of oscillations. At the prominence top, the oscillations are amplified during the first minutes and then are slowly attenuated. The characteristic time suggests more significant amplification in the experiments with the highest spatial resolution. The analysis revealed that the energy exchange between the bottom and top prominence regions is responsible for the attenuation and amplification of LALOs. The high-resolution experiments are crucial for the study of the periods and the damping mechanism of LALOs. The period agrees with the pendulum model only when using high enough spatial resolution. The results suggest that numerical diffusion in simulations with insufficient spatial resolution can hide important physical mechanisms, such as amplification of oscillations.
2108.01143v1
2021-08-05
Complexity analysis of quantum teleportation via different entangled channels in the presence of noise
Quantum communication is one of the hot topics in quantum computing, where teleportation of a quantum state has a slight edge and gained significant attention from researchers. A large number of teleportation schemes have already been introduced so far. Here, we compare the teleportation of a single qubit message among different entangled channels such as the two-qubit Bell channel, three-qubit GHZ channel, two- and three-qubit cluster states, the highly entangled five-qubit Brown \emph{et al.} state and the six-qubit Borras \emph{et al.} state. We calculate and compare the quantum costs in each of the cases. Furthermore, we study the effects of six noise models, namely bit-flip noise, phase-flip noise, bit-phase flip noise, amplitude damping, phase damping and the depolarizing error that may affect the communication channel used for the teleportation. An investigation on the variation of the initial state's fidelity with respect to the teleported state in the presence of the noise model is performed. A visual representation of the variation of fidelity for various values of the noise parameter $\eta$ is done through a graph plot. It is observed that as the value of noise parameter in the range $\eta \in [0,0.5]$, the fidelity decreases in all the entangled channels under all the noise models. After that, in the Bell channel, GHZ channel and three-qubit cluster state channel, the fidelity shows an upward trend under all the noise models. However, in the other three channels, the fidelity substantially decreases in the case of amplitude damping, phase damping and depolarizing noise, and even it reaches zero for $\eta = 1$ in Brown \emph{et al.} and Borras \emph{et al.} channels.
2108.02641v1
2021-08-06
Noncontact friction: Role of phonon damping and its nonuniversality
While obtaining theoretical predictions for dissipation during sliding motion is a difficult task, one regime that allows for analytical results is the so-called noncontact regime, where a probe is weakly interacting with the surface over which it moves. Studying this regime for a model crystal, we extend previously obtained analytical results and confirm them quantitatively via particle based computer simulations. Accessing the subtle regime of weak coupling in simulations is possible via use of Green-Kubo relations. The analysis allows to extract and compare the two paradigmatic mechanisms that have been found to lead to dissipation: phonon radiation, prevailing even in a purely elastic solid, and phonon damping, e.g., caused by viscous motion of crystal atoms. While phonon radiation is dominant at large probe-surface distances, phonon damping dominates at small distances. Phonon radiation is furthermore a pairwise additive phenomenon so that the dissipation due to interaction with different parts (areas) of the surface adds up. This additive scaling results from a general one-to-one mapping between the mean probe-surface force and the friction due to phonon radiation, irrespective of the nature of the underlying pair interaction. In contrast, phonon damping is strongly nonadditive, and no such general relation exists. We show that for certain cases, the dissipation can even {\it decrease} with increasing surface area the probe interacts with. The above properties, which are rooted in the spatial correlations of surface fluctuations, are expected to have important consequences when interpreting experimental measurements, as well as scaling with system size.
2108.03025v3
2021-09-14
Design of a HOM-Damped 166.6 MHz Compact Quarter-Wave beta=1 Superconducting Cavity for High Energy Photon Source
Superconducting cavities with low RF frequencies and heavy damping of higher order modes (HOM) are desired for the main accelerator of High Energy Photon Source (HEPS), a 6 GeV synchrotron light source promising ultralow emittance currently under construction in Beijing. A compact 166.6 MHz superconducting cavity was proposed adopting a quarter-wave beta=1 geometry. Based on the successful development of a proof-of-principle cavity, a HOM-damped 166.6 MHz compact superconducting cavity was subsequently designed. A ferrite damper was installed on the beam pipe to reduce HOM impedance below the stringent threshold of coupled-bunch instabilities. Being compact, RF field heating on the cavity vacuum seal was carefully examined against quenching the NbTi flange. The cavity was later dressed with a helium vessel and the tuning mechanism was also realized. Excellent RF and mechanical properties were eventually achieved. Finally, the two-cavity string was designed to ensure smooth transitions among components and proper shielding of synchrotron light. This paper presents a complete design of a fully dressed HOM-damped low-frequency beta=1 superconducting cavity for HEPS.
2109.06560v1
2021-11-13
Effects of microplastics and surfactants on surface roughness of water waves
In this paper, we study the flow physics underlying the recently developed remote sensing capability of detecting oceanic microplastics, which is based on the measurable surface roughness reduction induced by the presence of microplastics on the ocean surface. In particular, we are interested in whether this roughness reduction is caused by the microplastics as floating particles, or by the surfactants which follow similar transport paths as microplastics. For this purpose, we experimentally test the effects of floating particles and surfactants on surface roughness, quantified by the mean square slope (MSS), with waves generated by a mechanical wave maker or by wind. For microplastics, we find that their effect on wave energy and MSS critically depends on the surface area fraction of coverage, irrespective of the particle sizes in the test range. The damping by particles is observed only for fractions above $O(5-10\%)$, which is much higher than the realistic ocean condition. For surfactants, their damping effect on mechanically generated irregular waves generally increases with the concentration of surfactants, but no optimal concentration corresponding to maximum damping is observed, in contrast to previous studies based on monochromatic waves. In wind-wave experiments, the presence of surfactants suppresses the wave generation, due to the combined effects of reduced wind shear stress and increased wave damping. For the same wind speed, the wind stress is identified to depend on the concentration of surfactants with a power-law relation. The implications of these findings to remote sensing are discussed.
2111.07021v1
2021-11-15
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the magnetization. The numerical method is based on the second-order backward differentiation formula in time, combined with an implicit treatment of the linear diffusion term and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to normalize the numerical solution at a point-wise level. This numerical scheme has shown extensive advantages in the practical computations for the physical model with large damping parameters, which comes from the fact that only a linear system with constant coefficients (independent of both time and the updated magnetization) needs to be solved at each time step, and has greatly improved the numerical efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme has not been available. In this paper, we provide a rigorous error estimate of the numerical scheme, in the discrete $\ell^{\infty}(0,T; \ell^2) \cap \ell^2(0,T; H_h^1)$ norm, under suitable regularity assumptions and reasonable ratio between the time step-size and the spatial mesh-size. In particular, the projection operation is nonlinear, and a stability estimate for the projection step turns out to be highly challenging. Such a stability estimate is derived in details, which will play an essential role in the convergence analysis for the numerical scheme, if the damping parameter is greater than 3.
2111.07537v1
2021-11-17
United Nation Security Council in Quantum World: Experimental Realization of Quantum Anonymous Veto Protocols using IBM Quantum Computer
United Nation (UN) security council has fifteen members, out of which five permanent members of the council can use their veto power against any unfavorable decision taken by the council. In certain situation, a member using right to veto may prefer to remain anonymous. This need leads to the requirement of the protocols for anonymous veto which can be viewed as a special type of voting. Recently, a few protocols for quantum anonymous veto have been designed which clearly show quantum advantages in ensuring anonymity of the veto. However, none of the efficient protocols for quantum anonymous veto have yet been experimentally realized. Here, we implement 2 of those protocols for quantum anonymous veto using an IBM quantum computer named IBMQ Casablanca and different quantum resources like Bell, GHZ and cluster states. In this set of proof-of-principle experiments, it's observed that using the present technology, a protocol for quantum anonymous veto can be realized experimentally if the number of people who can veto remains small as in the case of UN council. Further, it's observed that Bell state based protocol implemented here performs better than the GHZ/cluster state based implementation of the other protocol in an ideal scenario as well as in presence of different types of noise (amplitude damping, phase damping, depolarizing and bit-flip noise). In addition, it's observed that based on diminishing impact on fidelity, different noise models studied here can be ordered in ascending order as phase damping, amplitude damping, depolarizing, bit-flip.
2111.09028v1
2021-12-03
The Importance of Electron Landau Damping for the Dissipation of Turbulent Energy in Terrestrial Magnetosheath Plasma
Heliospheric plasma turbulence plays a key role in transferring the energy of large-scale magnetic field and plasma flow fluctuations to smaller scales where the energy can be dissipated, ultimately leading to plasma heating. High-quality measurements of electromagnetic fields and electron velocity distributions by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath present a unique opportunity to characterize plasma turbulence and to determine the mechanisms responsible for its dissipation. We apply the field-particle correlation technique to a set of twenty MMS magnetosheath intervals to identify the dissipation mechanism and quantify the dissipation rate. It is found that 95% of the intervals have velocity-space signatures of electron Landau damping that are quantitatively consistent with linear kinetic theory for the collisionless damping of kinetic Alfv\'en waves. About 75% of the intervals contain asymmetric signatures, indicating a local imbalance of kinetic Alfv\'en wave energy flux in one direction along the magnetic field than the other. About one third of the intervals have an electron energization rate with the same order-of-magnitude as the estimated turbulent cascade rate, suggesting that electron Landau damping plays a significant, and sometimes dominant, role in the dissipation of the turbulent energy in these magnetosheath intervals.
2112.02171v1
2022-01-01
Extremely strong DLAs at high redshift: Gas cooling and H$_2$ formation
We present a spectroscopic investigation with VLT/X-shooter of seven candidate extremely strong damped Lyman-$\alpha$ absorption systems (ESDLAs, $N(\text{HI})\ge 5\times 10^{21}$ cm$^{-2}$) observed along quasar sightlines. We confirm the extremely high column densities, albeit slightly (0.1~dex) lower than the original ESDLA definition for four systems. We measured low-ionisation metal abundances and dust extinction for all systems. For two systems we also found strong associated H$_2$ absorption $\log N(\text{H$_2$)[cm$^{-2}$]}=18.16\pm0.03$ and $19.28\pm0.06$ at $z=3.26$ and $2.25$ towards J2205+1021 and J2359+1354, respectively), while for the remaining five we measured conservative upper limits on the H$_2$ column densities of typically $\log N(\text{H$_2$)[cm$^{-2}$]}<17.3$. The increased H$_2$ detection rate ($10-55$% at 68% confidence level) at high HI column density compared to the overall damped Lyman-$\alpha$ population ($\sim 5-10$%) confirms previous works. We find that these seven ESDLAs have similar observed properties as those previously studied towards quasars and gamma-ray burst afterglows, suggesting they probe inner regions of galaxies. We use the abundance of ionised carbon in excited fine-structure level to calculate the cooling rates through the CII $\lambda$158$\mu$m emission, and compare them with the cooling rates from damped Lyman-$\alpha$ systems in the literature. We find that the cooling rates distribution of ESDLAs also presents the same bimodality as previously observed for the general (mostly lower HI column density) damped Lyman-$\alpha$ population.
2201.00245v1
2022-01-05
Stability of the discrete time-crystalline order in spin-optomechanical and open cavity QED systems
Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in which the spins can be all-to-all coupled. In the thermodynamic limit, it is shown that the existence of dephasing can destroy the coherence of the system and finally lead the system to its trivial steady state. Without dephasing, eternal DTC is displayed in the weak damping regime, which may be destroyed by increasing the all-to-all spin coupling or the spin damping. By contrast, the all-to-all coupling is constructive to the DTC in the moderate damping regime. We also focus on a model which can be experimentally realized by a suspended hexagonal boron nitride (hBN) membrane with a few spin color centers under microwave drive and Floquet magnetic field. Signatures of transient DTC behavior are demonstrated in both weak and moderate dissipation regimes without spin dephasing. Relevant experimental parameters are also discussed for realizing transient DTC order in such an hBN optomechanical system.
2201.01568v2
2022-01-20
Sharp resolvent estimate for the Baouendi-Grushin operator and applications
In this article we study the semiclassical resolvent estimate for the non-selfadjoint Baouendi-Grushin operator on the two-dimensional torus $\mathbb{T}^2=\mathbb{R}^2/(2\pi\mathbb{Z})^2$ with H\"older dampings. The operator is subelliptic degenerating along the vertical direction at $x=0$. We exhibit three different situations: (i) the damping region verifies the geometric control condition with respect to both the non-degenerate Hamiltonian flow and the vertical subelliptic flow; (ii) the undamped region contains a horizontal strip; (iii) the undamped part is a line. In all of these situations, we obtain sharp resolvent estimates. Consequently, we prove the optimal energy decay rate for the associated damped waved equations. For (i) and (iii), our results are in sharp contrast to the Laplace resolvent since the optimal bound is governed by the quasimodes in the subelliptic regime. While for (ii), the optimality is governed by the quasimodes in the elliptic regime, and the optimal energy decay rate is the same as for the classical damped wave equation on $\mathbb{T}^2$. Our analysis contains the study of adapted two-microlocal semiclassical measures, construction of quasimodes and refined Birkhoff normal-form reductions in different regions of the phase-space. Of independent interest, we also obtain the propagation theorem for semiclassical measures of quasimodes microlocalized in the subelliptic regime.
2201.08189v2
2022-02-24
Coherence of ion cyclotron resonance for damping ion cyclotron waves in space plasmas
Ion cyclotron resonance is one of the fundamental energy conversion processes through field-particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyro-phase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90) degrees, consistent with the ongoing energy conversion from wave-fields to particles. By invoking plasma kinetic theory, we demonstrate that the field-particle correlation for the damping ion cyclotron waves in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ($\delta \mathbf{E'}_{\mathrm {wave,\perp}}$), the ion current density ($\delta \mathbf{J}_\mathrm {i,\perp}$) and the energy transfer rate ($\delta \mathbf{J}_\mathrm {i,\perp}\cdot \delta \mathbf{E'}_{\mathrm {wave,\perp}}$) exhibit quasi-periodic oscillations, and the integrated work done by the electromagnetic field on the ions are positive, indicates that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.
2202.11967v1
2022-03-15
Search for gamma-ray line signals around the black hole at the galactic center with DAMPE observation
The adiabatic growth of a black hole (BH) may enhance the dark matter (DM) density surrounding it, causing a spike in the DM density profile. The spike around the supermassive BH at the center of the Milky Way may lead to a dramatic enhancement of the gamma-ray flux of DM annihilation from the galactic center (GC). In this work, we analyze the gamma-ray data of the innermost region (i.e., the inner 1$^\circ$) of the GC to search for potential line-like signals from the BH spike. Such line-like signals could be generated in the process of DM particles annihilating into double photons. We adopt the gamma-ray data from the Dark Matter Particle Explorer (DAMPE). Although the DAMPE has a much smaller effective area than the Fermi-LAT, the gamma-ray line search can benefit from its unprecedented high energy resolution. No significant line-like signals are found in our analysis. We derive upper limits on the cross section of the annihilation based on this non-detection. We find that despite the DAMPE's small effective area for photon detection, we can still place strong constraints on the cross section ($\left<\sigma v\right>\lesssim10^{-27}\,{\rm cm^3\,s^{-1}}$) in the spike scenario due to the very bright model-expected flux from the spike. Our results indicate that either DM does not annihilate primarily through the $\gamma\gamma$ channel in the mass range we considered or no sharp density spike is present at the GC.
2203.08078v1
2022-03-15
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compared to alternative techniques because the integrand in the frequency space often has a higher regularity than that in the physical space. However, when designing a numerical quadrature method for most Fourier pricing approaches, two key aspects affecting the numerical complexity should be carefully considered: (i) the choice of damping parameters that ensure integrability and control the regularity class of the integrand and (ii) the effective treatment of high dimensionality. We propose an efficient numerical method for pricing European multi-asset options based on two complementary ideas to address these challenges. First, we smooth the Fourier integrand via an optimized choice of the damping parameters based on a proposed optimization rule. Second, we employ sparsification and dimension-adaptivity techniques to accelerate the convergence of the quadrature in high dimensions. The extensive numerical study on basket and rainbow options under the multivariate geometric Brownian motion and some L\'evy models demonstrates the advantages of adaptivity and the damping rule on the numerical complexity of quadrature methods. Moreover, for the tested two-asset examples, the proposed approach outperforms the COS method in terms of computational time. Finally, we show significant speed-up compared to the Monte Carlo method for up to six dimensions.
2203.08196v4
2022-03-25
Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves
The spatially periodic breather solutions (SPBs) of the nonlinear Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the effects of nonlinear dissipation and higher order nonlinearities on the routes to stability of the SPBs in the framework of the nonlinear damped higher order nonlinear Schr\"odinger (NLD-HONLS) equation. The initial data used in the experiments are generated by evaluating exact SPB solutions at time $T_0$. The number of instabilities of the background Stokes wave and the damping strength are varied. The Floquet spectral theory of the NLS equation is used to interpret and provide a characterization of the perturbed dynamics in terms of nearby solutions of the NLS equation. Significantly, as $T_0$ is varied, tiny bands of complex spectrum are observed to pinch off in the Floquet decomposition of the NLD-HONLS data, reflecting the breakup of the SPB into a waveform that is close to either a one or two "soliton-like" structure. For wide ranges of $T_0$, i.e. for solutions initialized in the early to middle stage of the development of the MI, all rogue waves are observed to occur when the spectrum is close to a one or two soliton-like state. When the solutions are initialized as the MI is saturating, rogue waves also can occur after the spectrum has left a soliton-like state. Other novel features arise due to nonlinear damping: enhanced asymmetry, two timescales in the evolution of the spectrum and a delay in the growth of instabilities due to frequency downshifting.
2203.13488v2
2022-03-25
Investigating the effect of noise channels on the quality of unitary t-designs
Unitary t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomised benchmarking. However, experimental realisations of t-designs are subject to noise. Here we investigate the effect of noise channels on the quality of single-qubit t-designs. The noise channels we study are bit flips, phase flips, bit and phase flips, phase damping, amplitude damping, and depolarising noise. We consider two noise models: the first has noise applied before the t-design unitary operations, while the second has noise applied after the unitary operations. We show that the single-qubit 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and 5-designs suggest that a 2t-design is significantly more sensitive to noise than a (2t-1)-design and that, with the exception of amplitude damping, a (2t+1)-design is as sensitive to noise as a 2t-design. Numeric results also reveal substantial variations in sensitivity to noise throughout the Bloch sphere. In particular, t-designs appear to be most sensitive to noise when acting on pure states and least sensitive to noise for the maximally mixed state. For depolarising noise, we show that our two noise models are equivalent, and for the other noise channels, numeric results obtained for the model where noise is applied after the unitaries reflect the transformation of the noise channel into a depolarising channel, an effect exploited in randomised benchmarking with 2-designs.
2203.13771v2
2022-04-25
Geometrical aspects of contact mechanical systems and field theories
Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems, both regular and singular. Some of these extensions are the subject of this thesis. Recently there has been a growing interest in studying dissipative mechanical systems from a geometric perspective using contact geometry. In this thesis we review what has been done in this topic and go deeper, studying symmetries and dissipated quantities of contact systems, and developing the Skinner-Rusk formalism for these systems. With regard to classical field theory, we introduce the notion of k-precosymplectic manifold and use it to give a geometric description of singular nonautonomous field theories. We also devise a constraint algorithm for these systems. Field theories with damping are described through a modification of the De Donder-Weyl Hamiltonian field theory. This is achieved by combining contact geometry and k-symplectic structures, resulting in the k-contact formalism. We introduce two notions of dissipation laws, generalizing the concept of dissipated quantity. These developments are also applied to Lagrangian field theory. The Skinner-Rusk formulation for k-contact systems is described in detail and we show how to recover the Lagrangian and Hamiltonian formalisms from it. Throughout the thesis we present several examples in mechanics and field theory. The most remarkable mechanical examples are the damped harmonic oscillator, the motion in a gravitational field with friction, the parachute equation and the damped simple pendulum. In field theory, we study the damped vibrating string, the Burgers' equation, the Klein-Gordon equation and its relation with the telegrapher's equation, and the Maxwell's equations with dissipation.
2204.11537v1
2022-06-20
Swinging a playground swing: torque controls for inducing sustained oscillations
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in a regular pattern. This article studies these mechanics. Two models of a swing with torques as controls that we consider are identical to popular models of modern robotics: the Acrobot and reaction wheel pendulum. However, the control task of sustaining the swing's regular oscillations by a static feedback control is new and challenging, especially when damping in the joint connecting the swing to the frame is considered. We develop two types of controls to accomplish this task. One works for small damping and is based on linearizing the undamped system by a suitable preliminary feedback control. The other works for large damping. In the steady state, the resulting closed-loop system describes a harmonically driven damped pendulum (a simple system known for its complex behavior), including chaotic motion for some parameter values. To address such complexities, we build free parameters into the controls, then adjust them based on simulations to avoid chaos and achieve regular oscillations that are seen on playgrounds.
2206.09579v1
2022-07-01
Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate
We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile's rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to $\simeq\!\sqrt{3}\omega$ and the other at $\simeq\!2\omega$, where $\omega$ is the trap frequency. The breathing mode at $\sim\!\sqrt{3}\omega$ dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at $\simeq\!2\omega$, on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.
2207.00209v2