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2022-09-21
Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping
We consider wave equations with a special type of log-fractional damping. We study the Cauchy problem for this model in the whole space, and we obtain an asymptotic profile and optimal estimates of solutions as time goes to infinity in L^2-sense. A maximal discovery of this note is that under the effective damping, in case of n = 1 L^2-norm of the solution blows up in infinite time, and in case of n = 2 L^2-norm of the solution never decays and never blows up in infinite time. The latter phenomenon seems to be a rare case.
2209.10154v2
2022-09-25
Origin of Immediate Damping of Coherent Oscillations in Photoinduced Charge Density Wave Transition
In stark contrast to the conventional charge density wave (CDW) materials, the one-dimensional CDW on the In/Si(111) surface exhibits immediate damping of the CDW oscillation during the photoinduced phase transition. Here, by successfully reproducing the experimentally observed photoinduced CDW transition on the In/Si(111) surface by performing real-time time-dependent density functional theory (rt-TDDFT) simulations, we demonstrate that photoexcitation promotes valence electrons from Si substrate to empty surface bands composed primarily of the covalent p-p bonding states of the long In-In bonds, generating interatomic forces to shorten the long bonds and in turn drives coherently the structural transition. We illustrate that after the structural transition, the component of these surface bands occurs a switch among different covalent In bonds, causing a rotation of the interatomic forces by about {\pi}/6 and thus quickly damping the oscillations in feature CDW modes. These findings provide a deeper understanding of photoinduced phase transitions.
2209.12135v1
2022-10-11
QKD in the NISQ era: enhancing secure key rates via quantum error correction
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on the IBM quantum processors, that B92 is the optimal protocol under amplitude-damping and generalized amplitude-damping noise. We then show that the security of the noisy BBM92 protocol crucially depends on the type and the mode of distribution of an entangled pair. Finally, we implement an error-corrected BB84 protocol using dual-rail encoding on a noisy quantum processor, and show that the dual-rail BB84 implementation outperforms the conventional BB84 in the presence of noise. Our secure key rate calculation also takes into account the effects of CNOT imperfections on the error rates of the protocols.
2210.05297v1
2022-10-17
Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{PT}$ symmetry, K symmetry and localized damping
We study an imaginary stark ladder model and propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of a $K$-symmetry and passive $\mathcal{PT}$ symmetry, the model exhibits quite different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive $\mathcal{PT}$-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a $K$-symmetry restoring transition, characterized by the emergence of pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from $\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-broken states, and finally to stark localized states. In the framework of the quantum open system governed by Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of single particle correlation function is governed by the Hamiltonian of the imaginary stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.
2210.08725v3
2022-10-18
A quasi-local inhomogeneous dielectric tensor for arbitrary distribution functions
Treatments of plasma waves usually assume homogeneity, but the parallel gradients ubiquitous in plasmas can modify wave propagation and absorption. We derive a quasilocal inhomogeneous correction to the plasma dielectric for arbitrary distributions by expanding the phase correlation integral and develop a novel integration technique that allows our correction to be applied in many situations and has greater accuracy than other inhomogeneous dielectric formulas found in the literature. We apply this dielectric tensor to the lower-hybrid current drive problem and demonstrate that inhomogeneous wave damping does not affect the lower-hybrid wave's linear damping condition, and in the non-Maxwellian problem damping and propagation should remain unchanged except in the case of waves with very large phase velocities.
2210.10214v1
2022-11-04
On the collisional damping of plasma velocity space instabilities
For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rate of the ideal instability has a sensitive dependence on the distribution function. The whistler instability driven by electrostatically trapped electrons is used as an example to elucidate such a strong collisional damping effect of plasma velocity space instabilities, which is confirmed by first-principles kinetic simulations.
2211.02723v3
2022-11-12
Exponential Stability and exact controllability of a system of coupled wave equations by second order terms (via Laplacian) with only one non-smooth local damping
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman estimate, we prove that our system is strongly stable without any geometric condition. Secondly, using a combination of the multiplier techniques and the frequency domain approach, we show that our system is exponentially stable under \textbf{(PMGC)} condition on the damping region without any restriction on wave propagation speed (i.e whether the two wave equations propagate at the same speed or not)
2211.06706v2
2022-11-10
Generalized Bagley-Torvik Equation and Fractional Oscillators
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of state: critical point, phase change, and lambda transition.
2211.07575v1
2022-11-21
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study of nonlinear wave equations. The novelty consists in the introduction of tools from the Orlicz spaces theory to handle the nonlinear term emerging from the pressure $p \equiv p(\rho)$, which admits different asymptotic behavior for large and small values of $\rho-1$, being $\rho$ the density. Hence we can establish, in high dimensions $n\in\{2,3\}$, unified upper bounds of the lifespan estimate depending only on the dimension $n$ and on the damping strength, and independent of the adiabatic index $\gamma>1$. We conjecture our results to be optimal. The method employed here not only improves the known upper bounds of the lifespan for $n\in\{2,3\}$, but has potential application in the study of related problems.
2211.11377v1
2022-11-24
A brief introduction to the mathematics of Landau damping
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research School on Kinetic Theory, November 14--18, 2022. These notes are mainly on Vlasov-Poisson in $(x,v) \in \mathbb T^d \times \mathbb R^d$ however a brief discussion of the important case of $(x,v) \in \mathbb R^d \times \mathbb R^d$ is included at the end. The focus will be nonlinear and these notes include a proof of Landau damping on $(x,v) \in \mathbb T^d \times \mathbb R^d$ in the Vlasov--Poisson equations meant for graduate students, post-docs, and others to learn the basic ideas of the methods involved. The focus is also on the mathematical side, and so most references are from the mathematical literature with only a small number of the many important physics references included. A few open problems are included at the end. These notes are not currently meant for publication so they may not be perfectly proof-read and the reference list might not be complete. If there is an error or you have some references which you think should be included, feel free to send me an email and I will correct it when I get a chance.
2211.13707v1
2022-12-04
Vibration suppression of a state-of-the-art wafer gripper
In this paper the implementation of piezoelectrics to a state-of-the-art wafer gripper is investigated. The objective is to propose and validate a solution method, which includes a mechanical design and control system, to achieve at least 5% damping for two eigenmodes of a wafer gripper. This objective serves as a 'proof of concept' to show the possibilities of implementing a state-of-the-art damping method to an industrial application, which in turn can be used to dampen different thin structures. The coupling relation between the piezoelectrics and their host structure were used to design the placement of the piezoelectric patches, together with modal analysis data of the a state-of-the-art wafer gripper. This data had been measured through an experimental setup. Active damping has been succesfully implemented onto the wafer gripper where positive position feedback (PPF) is used as a control algorithm to dampen two eigenmodes.
2212.01854v1
2022-12-20
Algebra of L-banded Matrices
Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an analytically optimized vector damping was proposed for memory message-passing (iterative) algorithms. As a result, it yields a special class of covariance matrices called L-banded matrices. In this paper, we show these matrices have broad algebraic properties arising from their L-banded structure. In particular, compact analytic expressions for the LDL decomposition, the Cholesky decomposition, the determinant after a column substitution, minors, and cofactors are derived. Furthermore, necessary and sufficient conditions for an L-banded matrix to be definite, a recurrence to obtain the characteristic polynomial, and some other properties are given. In addition, we give new derivations of the determinant and the inverse. (It's crucial to emphasize that some works have independently studied matrices with this special structure, named as L-matrices. Specifically, L-banded matrices are regarded as L-matrices with real and finite entries.)
2212.12431v3
2023-01-23
Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance
We provide a quantitative evaluation of non-Markovianity (NM) for an XX chain of interacting qubits with one end coupled to a reservoir. The NM of several non-Markovian spectral densities is assessed in terms of various quantum state distance (QSD) measures. Our approach is based on the construction of the density matrix of the open chain, without the necessity of a master equation. For the quantification of NM we calculate the dynamics of the QSD measures between the Markovian-damped and various types of non-Markovian-damped cases. Since in the literature several QSD measures, appear in forms that imply trace preserving density matrices, we introduced appropriate modifications so as to render them applicable to the case of decaying traces. The results produce remarkable consistency between the various QSD measures. They also reveal a subtle and potentially useful interplay between qubit-qubit interaction and non-Markovian damping. Our calculations have also uncovered a surprisingly dramatic slowing-down of dissipation by the squared Lorentzian reservoir.
2301.09323v2
2023-01-26
Optimisation of Power Grid Stability Under Uncertainty
The increased integration of intermittent and decentralised forms of power production has eroded the stability margins of power grids and made it more challenging to ensure reliable and secure power transmission. Reliable grid operation requires system-scale stability in response to perturbations in supply or load; previous studies have shown that this can be achieved by tuning the effective damping parameters of the generators in the grid. In this paper, we present and analyse the problem of tuning damping parameters when there is some uncertainty in the underlying system. We show that sophisticated methods that assume no uncertainty can yield results that are less robust than those produced by simpler methods. We define a quantile-based metric of stability that ensures that power grids remain stable even as worst-case scenarios are approached, and we develop optimisation methods for tuning damping parameters to achieve this stability. By comparing optimisation methods that rely on different assumptions, we suggest efficient heuristics for finding parameters that achieve highly stable and robust grids.
2301.11215v1
2023-02-11
Uniform stabilization for the semi-linear wave equation with nonlinear Kelvin-Voigt damping
This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood of the boundary according to the Geometric Control Condition. While the second one is a frictional damping and we consider it hurting the geometric condition of control. We show uniform decay rate results of the corresponding energy for all initial data taken in bounded sets of finite energy phase-space. The proof is based on obtaining an observability inequality which combines unique continuation properties and the tools of the Microlocal Analysis Theory.
2302.05667v1
2023-02-20
Exponentially stable breather solutions in nonautonomous dissipative nonlinear Schrödinger lattices
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively. Notably, quasiperiodic breathers cannot exist in the system without damping and driving. Afterwards the existence of a global uniform attractor for the dissipative dynamics of the system is shown. For strong dissipation we prove that the global uniform attractor has finite fractal dimension and consists of a single trajectory that is confined to a finite dimensional subspace of the infinite dimensional phase space, attracting any bounded set in phase space exponentially fast. Conclusively, for strong damping and periodic (quasiperiodic) forcing the single periodic (quasiperiodic) breather solution possesses a finite number of modes and is exponentially stable.
2302.09869v2
2023-02-11
Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Bardeen black hole surrounded by perfect fluid dark matter
Bardeen black hole surrounded by perfect fluid dark matter for a massless scalar field. Our result shows that the oscillation frequency of quasinormal modes is enhanced as magnetic charge $g$ or the dark matter parameter $\alpha$ increases. For damping rate of quasinormal modes, the influence of them is different. Specifically, the increase of dark matter parameter $\alpha$ makes the damping rate increasing at first and then decreasing. While the damping rate is continuously decreasing with the increase of the magnetic charge $g$. Moreover, we find that the increase of the dark matter parameter $\alpha$ enhances the power emission spectrum whereas magnetic charge $g$ suppresses it. This means that the lifespan of black holes increases for smaller value of $\alpha$ and larger value of $g$ when other parameters are fixed. Finally, the absorption cross section of the considered black hole is calculated with the help of the partial wave approach. Our result suggests that the absorption cross section decreases with the dark matter $\alpha$ or the magnetic charge $g$ increasing.
2302.10758v1
2023-02-24
A Numerical Approach for Modeling the Shunt Damping of Thin Panels with Arrays of Separately Piezoelectric Patches
Two-dimensional thin plates are widely used in many aerospace and automotive applications. Among many methods for the attenuation of vibration of these mechanical structures, piezoelectric shunt damping is a promising way. It enables a compact vibration damping method without adding significant mass and volumetric occupancy. Analyzing the dynamics of these electromechanical systems requires precise modeling tools that properly consider the coupling between the piezoelectric elements and the host structure. This paper presents a methodology for separately shunted piezoelectric patches for achieving higher performance on vibration attenuation. The Rayleigh-Ritz method is used for performing the modal analysis and obtaining the frequency response functions of the electro-mechanical system. 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.
2302.12525v1
2023-02-27
Enhancing quantum synchronization through homodyne measurement, noise and squeezing
Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task, but preferably in the semi-classical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator, and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semi-classical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.
2302.13465v2
2023-03-06
Larmor precession in strongly correlated itinerant electron systems
Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.
2303.03468v2
2023-03-19
Asymptotic-preserving finite element analysis of Westervelt-type wave equations
Motivated by numerical modeling of ultrasound waves, we investigate robust conforming finite element discretizations of quasilinear and possibly nonlocal equations of Westervelt type. These wave equations involve either a strong dissipation or damping of fractional-derivative type and we unify them into one class by introducing a memory kernel that satisfies non-restrictive regularity and positivity assumptions. As the involved damping parameter is relatively small and can become negligible in certain (inviscid) media, it is important to develop methods that remain stable as the said parameter vanishes. To this end, the contributions of this work are twofold. First, we determine sufficient conditions under which conforming finite element discretizations of (non)local Westervelt equations can be made robust with respect to the dissipation parameter. Secondly, we establish the rate of convergence of the semi-discrete solutions in the singular vanishing dissipation limit. The analysis hinges upon devising appropriate energy functionals for the semi-discrete solutions that remain uniformly bounded with respect to the damping parameter.
2303.10743v1
2023-03-31
Measurement of the cosmic p+He energy spectrum from 46 GeV to 316 TeV with the DAMPE space mission
Recent observations of the light component of the cosmic-ray spectrum have revealed unexpected features that motivate further and more precise measurements up to the highest energies. The Dark Matter Particle Explorer (DAMPE) is a satellite-based cosmic-ray experiment that is operational since December 2015, continuously collecting data on high-energy cosmic particles with very good statistics, energy resolution, and particle identification capabilities. In this work, the latest measurements of the energy spectrum of proton+helium in the energy range from 46 GeV to 316 TeV are presented. Among the most distinctive features of the spectrum, a spectral hardening at $\sim$600 GeV has been observed, along with a softening at $\sim$29 TeV measured with a 6.6$\sigma$ significance. Moreover, by measuring the energy spectrum up to 316 TeV, a strong link is established between space- and ground-based experiments, also suggesting the presence of a second hardening at $\sim$150 TeV.
2304.00137v4
2023-04-18
Edge-selective extremal damping from topological heritage of dissipative Chern insulators
One of the most important practical hallmarks of topological matter is the presence of topologically protected, exponentially localised edge states at interfaces of regions characterised by unequal topological invariants. Here, we show that even when driven far from their equilibrium ground state, Chern insulators can inherit topological edge features from their parent Hamiltonian. In particular, we show that the asymptotic long-time approach of the non-equilibrium steady state, governed by a Lindblad Master equation, can exhibit edge-selective extremal damping. This phenomenon derives from edge states of non-Hermitian extensions of the parent Chern insulator Hamiltonian. The combination of (non-Hermitian) topology and dissipation hence allows to design topologically robust, spatially localised damping patterns.
2304.09040v3
2023-04-25
Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition
We study the electronic spectral function of a metal in the vicinity of an antiferromagnetic (AFM) quantum critical point, focusing on a situation where the bare bandwidth of the spin fluctuations is significantly smaller than the Fermi energy. In this limit, we identify a range of energies where the fermionic quasiparticles near the "hot spots'' on the Fermi surface are strongly scattered by the quantum critical fluctuations, whereas the damping of the AFM fluctuations by the electrons is negligible. Within a one-loop approximation, there is a parameter range where the $T=0$ spectral function at the hot spots has a "precursor gap'' feature, with a local maximum at a finite frequency. However, the ratio of the bare spin wave velocity to the Fermi velocity required to obtain a precursor gap is probably too small to explain experiments in the electron-doped cuprate superconductors (He et al., Proc. Natl. Acad. Sci 116, 3449 (2019)). At lower frequencies, the Landau damping of the AFM fluctuations becomes important, and the electronic spectral function has the familiar ${\omega}^{-1/2}$ singularity. Our one-loop perturbative results are supported by a numerical Monte Carlo simulation of electrons coupled to an undamped, nearly-critical AFM mode.
2304.12697v1
2023-05-04
Vibrational resonance in a damped and two-frequency driven system of particle on a rotating parabola
In the present work, we examine the role of nonlinearity in vibrational resonance (VR) of a forced and damped form of a velocity-dependent potential system. Many studies have focused on studying the vibrational resonance in different potentials, like bistable potential, asymmetrically deformed potential, and rough potential. In this connection, velocity-dependent potential systems are very important from a physical point of view (Ex: pion-pion interaction, cyclotrons and other electromagnetic devices influenced by the Lorentz force, magnetrons, mass spectrometers). They also appear in several mechanical contexts. In this paper, we consider a nonlinear dynamical system with velocity-dependent potential along with additional damping and driven forces, namely a particle moving on a rotating-parabola system, and study the effect of two-frequency forcing with a wide difference in the frequencies. We report that the system exhibits vibrational resonance in a certain range of nonlinear strength. Using the method of separation of motions (MSM), an analytical equation for the slow oscillations of the system is obtained in terms of the parameters of the fast signal. The analytical computations and the numerical studies concur well.
2305.02674v1
2023-05-06
Stochastic wave equation with Hölder noise coefficient: well-posedness and small mass limit
We construct unique martingale solutions to the damped stochastic wave equation $$ \mu \frac{\partial^2u}{\partial t^2}(t,x)=\Delta u(t,x)-\frac{\partial u}{\partial t}(t,x)+b(t,x,u(t,x))+\sigma(t,x,u(t,x))\frac{dW_t}{dt},$$ where $\Delta$ is the Laplacian on $[0,1]$ with Dirichlet boundary condition, $W$ is space-time white noise, $\sigma$ is $\frac{3}{4}+\epsilon$ -H\"older continuous in $u$ and uniformly non-degenerate, and $b$ has linear growth. The same construction holds for the stochastic wave equation without damping term. More generally, the construction holds for SPDEs defined on separable Hilbert spaces with a densely defined operator $A$, and the assumed H\"older regularity on the noise coefficient depends on the eigenvalues of $A$ in a quantitative way. We further show the validity of the Smoluchowski-Kramers approximation: assume $b$ is H\"older continuous in $u$, then as $\mu$ tends to $0$ the solution to the damped stochastic wave equation converges in distribution, on the space of continuous paths, to the solution of the corresponding stochastic heat equation. The latter result is new even in the case of additive noise.
2305.04068v2
2023-05-08
Information capacity analysis of fully correlated multi-level amplitude damping channels
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multi-level amplitude damping channels. We investigate some of the information capacities of the simplest member of multi-level Amplitude Damping Channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.
2305.04481v2
2023-05-09
Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain
Lifespan estimates for semilinear damped wave equations of the form $\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain endowed with the Dirichlet boundary condition are dealt with. For the critical case of the semilinear heat equation $\partial_tv-\Delta v=v^2$ with the Dirichlet boundary condition and the initial condition $v(0)=\varepsilon f$, the corresponding lifespan can be estimated from below and above by $\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. This paper clarifies that the same estimates hold even for the critical semilinear damped wave equation in the exterior of the unit ball under the restriction of radial symmetry. To achieve this result, a new technique to control $L^1$-type norm and a new Gagliardo--Nirenberg type estimate with logarithmic weight are introduced.
2305.05124v1
2023-05-19
Cold damping of levitated optically coupled nanoparticles
Methods for controlling the motion of single particles, optically levitated in vacuum, have developed rapidly in recent years. The technique of cold damping makes use of feedback-controlled, electrostatic forces to increase dissipation without introducing additional thermal fluctuations. This process has been instrumental in the ground-state cooling of individual electrically charged nanoparticles. Here we show that the same method can be applied to a pair of nanoparticles, coupled by optical binding forces. These optical binding forces are about three orders of magnitude stronger than typical Coulombic inter-particle force and result in a coupled motion of both nanoparticles characterized by a pair of normal modes. We demonstrate cold damping of these normal modes, either independently or simultaneously, to sub-Kelvin temperatures at pressures of 5x10^{-3} mbar. Experimental observations are captured by a theoretical model which we use to survey the parameter space more widely and to quantify the limits imposed by measurement noise and time delays. Our work paves the way for the study of quantum interactions between meso-scale particles and the exploration of multiparticle entanglement in levitated optomechanical systems.
2305.11809v1
2023-05-25
Damping of three-dimensional waves on coating films dragged by moving substrates
Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsen the product quality. In this article, we investigate the stability of a thin liquid film dragged by a vertical substrate moving against gravity, a flow configuration found in a variety of coating processes. The receptivity of the liquid film to three-dimensional disturbances is discussed with Direct Numerical Simulations (DNS), an in-house non-linear Integral Boundary Layer (IBL) film model, and Linear Stability Analysis (LSA). The thin film model, successfully validated with the DNS computations, implements a pseudo-spectral approach for the capillary terms that allows for investigating non-periodic surface tension dominated flows. The combination of these numerical tools allows for describing the mechanisms of capillary and non-linear damping, and identifying the instability threshold of the coating processes. The results show that transverse modulations can be beneficial for the damping of two-dimensional waves within the range of operational conditions considered in this study, typical of air-knife and slot-die coating.
2305.16139v3
2023-06-12
Realizable Eddy Damped Markovian Anisotropic Closure for Turbulence and Rossby Wave Interactions
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure but unlike the EDQNM is guaranteed to be realizable in the presence of transient waves. Jack Herring's important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and Lagrangian statistical dynamical closure theories, and the statistical dynamics of the interaction of turbulence with topography. The impact of Herring's work is described and placed in the context of related developments. Some of the further works that have built on Herring's foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence are put into perspective by comparing related developments in strong interaction quantum filed theory.
2306.06921v1
2023-06-18
Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential
We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in other words, compact Riemannian manifolds with boundary conformally embedded in a product of the Euclidean line and a transversal manifold. With an additional assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove that the knowledge of a certain partial Cauchy data set determines time-dependent damping coefficient and potential uniquely.
2306.10442v2
2023-06-26
Blow-up result for a weakly coupled system of wave equations with a scale-invariant damping, mass term and time derivative nonlinearity
We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms. The latter are specifically of great interest from both physical and mathematical points of view since they allow the speeds of propagation to be time-dependent ones. However, we assume in this work that both waves are propagating with the same speeds. Employing this fact together with other hypotheses on the aforementioned parameters (mass and damping coefficients), we obtain a new blow-up region for the system under consideration, and we show a lifespan estimate of the maximal existence time.
2306.14768v1
2023-06-26
Revisiting the damped quantum harmonic oscillator
We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for describing a finite temperature reservoir. We recover in this way a number of well-known and some, perhaps, less familiar results. An example of the latter is an ab initio proof that the oscillator relaxes to the mean-force Gibbs state. We find that special care is necessary when comparing the damped oscillator with its undamped counterpart as the former has two distinct natural frequencies, one associated with short time evolution and the other with longer times.
2306.15013v1
2023-06-27
SPDER: Semiperiodic Damping-Enabled Object Representation
We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.
2306.15242v1
2023-07-03
Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order $O(t^{-2})$ for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.
2307.00975v3
2023-07-05
Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in space and a modified implicit exponential Euler scheme in time. The presence of the super-linearly growing damping in the underlying model brings challenges into the error analysis. To address these difficulties, we first achieve upper mean-square error bounds, and then obtain mean-square convergence rates of the considered numerical solution. This is done without requiring the moment bounds of the full approximations. The main result shows that, in dimension one, the scheme admits a convergence rate of order $\tfrac12$ in space and order $1$ in time. In dimension two, the error analysis is more subtle and can be done at the expense of an order reduction due to an infinitesimal factor. Numerical experiments are performed and confirm our theoretical findings.
2307.01975v1
2023-07-12
Decoherence effects on lepton number violation from heavy neutrino-antineutrino oscillations
We study decoherence effects and phase corrections in heavy neutrino-antineutrino oscillations (NNOs), based on quantum field theory with external wave packets. Decoherence damps the oscillation pattern, making it harder to resolve experimentally. Additionally, it enhances lepton number violation (LNV) for processes in symmetry-protected low-scale seesaw models by reducing the destructive interference between mass eigenstates. We discuss a novel time-independent shift in the phase and derive formulae for calculating decoherence effects and the phase shift in the relevant regimes, which are the no dispersion regime and transverse dispersion regime. We find that the phase shift can be neglected in the parameter region under consideration since it is small apart from parameter regions with large damping. In the oscillation formulae, decoherence can be included by an effective damping parameter. We discuss this parameter and present averaged results, which apply to simulations of NNOs in the dilepton-dijet channel at the HL-LHC. We show that including decoherence effects can dramatically change the theoretical prediction for the ratio of LNV over LNC events.
2307.06208v1
2023-07-23
Visco-elastic damped wave models with time-dependent coefficient
In this paper, we study the following Cauchy problem for linear visco-elastic damped wave models with a general time-dependent coefficient $g=g(t)$: \begin{equation} \label{EqAbstract} \tag{$\star$} \begin{cases} u_{tt}- \Delta u + g(t)(-\Delta)u_t=0, &(t,x) \in (0,\infty) \times \mathbb{R}^n, \\ u(0,x)= u_0(x),\quad u_t(0,x)= u_1(x), &x \in \mathbb{R}^n. \end{cases} \end{equation} We are interested to study the influence of the damping term $g(t)(-\Delta)u_t$ on qualitative properties of solutions to \eqref{EqAbstract} as decay estimates for energies of higher order and the parabolic effect. The main tools are related to WKB-analysis. We apply elliptic as well as hyperbolic WKB-analysis in different parts of the extended phase space.
2307.12340v1
2023-07-24
Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature
It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the $H\_3$ Hamiltonian of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in $H\_3$, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.
2307.12705v1
2023-08-01
Regularity for the Timoshenko system with fractional damping
We study, the Regularity of the Timoshenko system with two fractional dampings $(-\Delta)^\tau u_t$ and $(-\Delta)^\sigma \psi_t$; both of the parameters $(\tau, \sigma)$ vary in the interval $[0,1]$. We note that ($\tau=0$ or $\sigma=0$) and ($\tau=1$ or $\sigma=1$) the dampings are called frictional and viscous, respectively. Our main contribution is to show that the corresponding semigroup $S(t)=e^{\mathcal{B}t}$, is analytic for $(\tau,\sigma)\in R_A:=[1/2,1]\times[ 1/2,1]$ and determine the Gevrey's class $\nu>\dfrac{1}{\phi}$, where $\phi=\left\{\begin{array}{ccc} \dfrac{2\sigma}{\sigma+1} &{\rm for} & \sigma\leq \tau,\\\\ \dfrac{2\tau}{\tau+1} &{\rm for} & \tau\leq \sigma. \end{array}\right.$ \quad and \quad $(\tau,\sigma)\in R_{CG}:= (0,1)^2$.
2308.00573v2
2023-08-16
Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system
A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for low ones. This allows to derive a sharp description of the space-time decay of solutions for large time. However, such analysis relies heavily on the use of the Fourier transform that we avoid here, developing the "physical space version" of the hyperbolic hypocoercivity approach introduced by Beauchard and Zuazua, to prove new asymptotic results in the linear and nonlinear settings. The new physical space version of the hyperbolic hypocoercivity approach allows to recover the natural heat-like time-decay of solutions under sharp rank conditions, without employing Fourier analysis or $L^1$ assumptions on the initial data. Taking advantage of this Fourier-free framework, we establish new enhanced time-decay estimates for initial data belonging to weighted Sobolev spaces. These results are then applied to the nonlinear compressible Euler equations with linear damping. We also prove the logarithmic stability of the nonlinearly damped $p$-system.
2308.08280v1
2023-09-06
Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System
In this work, we present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. Our method relies on a semiclassical dynamical system derived from an extended classical Hamiltonian, where the phase-space variables are given by expectation values of observables and quantum dispersions. The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems (OQS), and the description of dissipation in quantum mechanics. By employing the Bateman's dual model as the initial classical framework, and undergoing quantization, we demonstrate that our description aligns exceptionally well with the well-established Lindblad master equation. Furthermore, our approach exhibits robustness and broad applicability in the context of OQS, rendering it a versatile and powerful tool for studying various phenomena. We intend to contribute to the advancement of quantum physics by providing an effective means of quantizing the damped harmonic oscillator and shedding light on the behavior of open quantum systems.
2309.02689v1
2023-09-09
Secondary cosmic-ray nuclei in the model of Galactic halo with nonlinear Landau damping
We employ our recent model of the cosmic-ray (CR) halo by Chernyshov et al. (2022) to compute the Galactic spectra of stable and unstable secondary nuclei. In this model, confinement of the Galactic CRs is entirely determined by the self-generated Alfvenic turbulence whose spectrum is controlled by nonlinear Landau damping. We analyze the physical parameters affecting propagation characteristics of CRs, and estimate the best set of free parameters providing accurate description of available observational data. We also show that agreement with observations at lower energies may be further improved by taking into account the effect of ion-neutral damping which operates near the Galactic disk.
2309.04772v1
2023-09-20
On the damping of tidally driven oscillations
Expansions in the oscillation modes of tidally perturbed bodies provide a useful framework for representing tidally induced flows. However, recent work has demonstrated that such expansions produce inaccurate predictions for secular orbital evolution when mode damping rates are computed independently. We explore the coupling of collectively driven modes by frictional and viscous dissipation, in tidally perturbed bodies that are both non-rotating and rigidly rotating. This exploration leads us to propose an alternative approach to treating the damping of tidally driven oscillations that accounts for dissipative mode coupling, but which does not require any information beyond the eigenfunctions and eigenfrequencies of adiabatic modes.
2309.11502v1
2023-09-25
Linearly implicit exponential integrators for damped Hamiltonian PDEs
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the Hamiltonian function and portioning out the nonlinearly of consecutive time steps. They require only a solution of one linear system at each time step. Therefore they are computationally more advantageous than implicit integrators. We also construct an exponential version of the well-known one-step Kahan's method by polarizing the quadratic vector field. These integrators are applied to one-dimensional damped Burger's, Korteweg-de-Vries, and nonlinear Schr{\"o}dinger equations. Preservation of the dissipation rate of linear and quadratic conformal invariants and the Hamiltonian is illustrated by numerical experiments.
2309.14184v2
2023-10-12
Plasmon dispersion and Landau damping in the nonlinear quantum regime
We study the dispersion properties of electron plasma waves, or plasmons, which can be excited in quantum plasmas in the nonlinear regime. In order to describe nonlinear electron response to finite amplitude plasmons, we apply the Volkov approach to non-relativistic electrons. For that purpose, we use the Schr\"odinger equation and describe the electron population of a quantum plasma as a mixture of quantum states. Within the kinetic framework that we are able to derive from the Volkov solutions, we discuss the role of the wave amplitude on the nonlinear plasma response. Finally, we focus on the quantum properties of nonlinear Landau damping and study the contributions of multi-plasmon absorption and emission processes.
2310.08544v1
2023-10-29
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
In this article we investigate the asymptotic profile of solutions for the Cauchy problem of the nonlinear damped beam equation with two variable coefficients: \[ \partial_t^2 u + b(t) \partial_t u - a(t) \partial_x^2 u + \partial_x^4 u = \partial_x \left( N(\partial_x u) \right). \] In the authors' previous article [17], the asymptotic profile of solutions for linearized problem ($N \equiv 0$) was classified depending on the assumptions for the coefficients $a(t)$ and $b(t)$ and proved the asymptotic behavior in effective damping cases. We here give the conditions of the coefficients and the nonlinear term in order that the solution behaves as the solution for the heat equation: $b(t) \partial_t u - a(t) \partial_x^2 u=0$ asymptotically as $t \to \infty$.
2310.18878v1
2023-11-09
Landau Damping in an Electron Gas
Material science methods aim at developing efficient computational schemes for describing complex many-body effects and how they are revealed in experimentally measurable properties. Bethe-Salpeter equation in the self-consistent Hartree-Fock basis is often used for this purpose, and in this paper we employ the real-frequency diagrammatic Monte Carlo framework for solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function (and, ultimately, for the system's polarization) to study the effect of electron-hole Coulomb scattering on Landau damping in the homogeneous electron gas. We establish how this damping mechanism depends on the Coulomb parameter $r_s$ and changes with temperature between the correlated liquid and thermal gas regimes. In a broader context of dielectric response in metals, we also present the full polarization and the typical dependence of the exchange-correlation kernel on frequency at finite momentum and temperature within the same computational framework.
2311.05611v2
2023-11-11
On asymptotic properties of solutions to $σ$-evolution equations with general double damping
In this paper, we would like to consider the Cauchy problem for semi-linear $\sigma$-evolution equations with double structural damping for any $\sigma\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in [0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2 \in (\sigma/2,\sigma]$, which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.
2311.06660v1
2023-11-14
Enhanced classical radiation damping of electronic cyclotron motion in the vicinity of the Van Hove singularity in a waveguide
We study the damping process of electron cyclotron motion and the resulting emission in a waveguide using the classical Friedrichs model without relying on perturbation analysis such as Fermi's golden rule. A classical Van Hove singularity appears at the lower bound (or cut-off frequency) of the dispersion associated with each of the electromagnetic field modes in the waveguide. In the vicinity of the Van Hove singularity, we found that not only is the decay process associated with the resonance pole enhanced (amplification factor ~ $10^4$) but the branch-point effect is also comparably enhanced. As a result, the timescale on which most of the decay occurs is dramatically shortened. Further, this suggests that the non-Markovian branch point effect should be experimentally observable in the vicinity of the Van Hove singularity. Our treatment yields a physically-acceptable solution without the problematic runaway solution that is well known to appear in the traditional treatment of classical radiation damping based on the Abraham-Lorentz equation.
2311.08121v3
2023-11-18
The temperature dependent Boltzmann equation beyond local equilibrium assumption
In this manuscript, we present a temperature dependent Boltzmann equation for the particles transport through a environmental reservoir, where the temperature refers to the equilibrium temperature of reservoir, a new damping force and a inverse damping relaxation time are derived based on the classical Boltzmann equation, which have obvious influence on the external force and the relaxation time of transport particles. For comparison, we also define a non-equilibrium temperature for the transport particle by its distribution function out of equilibrium, which is different from the equilibrium temperature of reservoir. There exist heat transfer between the transport particle and the reservoir, because the whole transport particles are in non-equilibrium state. Finally, we illustrate them by an example of one-dimensional transport procedure, the damping force and the non-equilibrium temperature defined by us are shown numerically.
2311.11028v1
2023-12-13
Integrating Superregenerative Principles in a Compact, Power-Efficient NMR/NQR Spectrometer: A Novel Approach with Pulsed Excitation
We present a new approach to Nuclear Quadrupole Resonance (NQR)/Nuclear Magnetic Resonance (NMR) spectroscopy, the Damp-Enhanced Superregenerative Nuclear Spin Analyser (DESSA). This system integrates Superregenerative principles with pulsed sample excitation and detection, offering significant advancements over traditional Super-Regenerative Receivers (SRRs). Our approach overcomes certain limitations associated with traditional Super-Regenerative Receivers (SRRs) by integrating direct digital processing of the oscillator response delay time (T$_d$) and an electronic damp unit to regulate the excitation pulse decay time (T$_e$). The essence is combining pulsed excitation with a reception inspired by, but distinct from, conventional SRRs. The damp unit allows a rapid termination of the oscillation pulse and the initiation of detection within microseconds, and direct digital processing avoids the need for a second lower frequency which is used for quenching in a traditional SRRs, thereby avoiding the formation of sidebands. We demonstrate the effectiveness of DESSA on a \ch{NaClO3} sample containing the isotope Chlorine-35 where it accurately detects the NQR signal with sub-kHz resolution.
2312.08491v1
2023-12-26
Dynamical polarization function, plasmons, their damping and collective effects in semi-Dirac bands
We have calculated the dynamical polarization, plasmons and damping rates in semi-Dirac bands (SDB's) with zero band gap and half-linear, half-parabolic low-energy spectrum. The obtained plasmon dispersions are strongly anisotropic and demonstrate some crucial features of both two-dimensional electron gas and graphene. Such gapless energy dispersions lead to a localized area of undamped and low-damped plasmons in a limited range of the frequencies and wave vectors. The calculated plasmon branches demonstrate an increase of their energies for a finite tilting of the band structure and a fixed Fermi level which could be used as a signature of a specific tilted spectrum in a semi-Dirac band.
2312.16117v1
2024-01-09
Coherent errors in stabilizer codes caused by quasistatic phase damping
Quantum error correction is a key challenge for the development of practical quantum computers, a direction in which significant experimental progress has been made in recent years. In solid-state qubits, one of the leading information loss mechanisms is dephasing, usually modelled by phase flip errors. Here, we introduce quasistatic phase damping, a more subtle error model which describes the effect of Larmor frequency fluctuations due to 1/f noise. We show how this model is different from a simple phase flip error model, in terms of multi-cycle error correction. Considering the surface code, we provide numerical evidence for an error threshold, in the presence of quasistatic phase damping and readout errors. We discuss the implications of our results for spin qubits and superconducting qubits.
2401.04530v2
2024-01-19
Composite learning backstepping control with guaranteed exponential stability and robustness
Adaptive backstepping control provides a feasible solution to achieve asymptotic tracking for mismatched uncertain nonlinear systems. However, input-to-state stability depends on high-gain feedback generated by nonlinear damping terms, and closed-loop exponential stability with parameter convergence involves a stringent condition named persistent excitation (PE). This paper proposes a composite learning backstepping control (CLBC) strategy based on modular backstepping and high-order tuners to compensate for the transient process of parameter estimation and achieve closed-loop exponential stability without the nonlinear damping terms and the PE condition. A novel composite learning mechanism that maximizes the staged exciting strength is designed for parameter estimation, such that parameter convergence can be achieved under a condition of interval excitation (IE) or even partial IE that is strictly weaker than PE. An extra prediction error is employed in the adaptive law to ensure the transient performance without nonlinear damping terms. The exponential stability of the closed-loop system is proved rigorously under the partial IE or IE condition. Simulations have demonstrated the effectiveness and superiority of the proposed method in both parameter estimation and control compared to state-of-the-art methods.
2401.10785v1
2024-01-23
Model-Free $δ$-Policy Iteration Based on Damped Newton Method for Nonlinear Continuous-Time H$\infty$ Tracking Control
This paper presents a {\delta}-PI algorithm which is based on damped Newton method for the H{\infty} tracking control problem of unknown continuous-time nonlinear system. A discounted performance function and an augmented system are used to get the tracking Hamilton-Jacobi-Isaac (HJI) equation. Tracking HJI equation is a nonlinear partial differential equation, traditional reinforcement learning methods for solving the tracking HJI equation are mostly based on the Newton method, which usually only satisfies local convergence and needs a good initial guess. Based upon the damped Newton iteration operator equation, a generalized tracking Bellman equation is derived firstly. The {\delta}-PI algorithm can seek the optimal solution of the tracking HJI equation by iteratively solving the generalized tracking Bellman equation. On-policy learning and off-policy learning {\delta}-PI reinforcement learning methods are provided, respectively. Off-policy version {\delta}-PI algorithm is a model-free algorithm which can be performed without making use of a priori knowledge of the system dynamics. NN-based implementation scheme for the off-policy {\delta}-PI algorithms is shown. The suitability of the model-free {\delta}-PI algorithm is illustrated with a nonlinear system simulation.
2401.12882v1
2024-01-30
The nonlinear dynamic behavior of a Rubber-Layer Roller Bearing (RLRB) for vibration isolation
In this paper, we study the dynamic behavior of a Rubber-Layer Roller Bearing (RLRB) interposed between a spring-mass elemental superstructure and a vibrating base. Thanks to the viscoelastic rolling contact between the rigid rollers and the rubber layers, the RLRB is able to provide a nonlinear damping behavior. The effect of the RLRB geometric and material parameters is investigated under periodic base excitation, showing that both periodic and aperiodic responses can be achieved. Specifically, since the viscoelastic damping is non-monotonic (bell shaped), there exist systemdynamic conditions involving the decreasing portion of the damping curve in which a strongly nonlinear behavior is experienced. In the second part of the paper, we investigate the effectiveness of the nonlinear device in terms of seismic isolation. Focusing on the mean shock of the Central Italy 2016 earthquake, we opportunely tune the material and geometrical RLRB parameters, showing that a significant reduction of both the peak and root-mean-square value of the inertial force acting on the superstructure is achieved, compared to the best performance of a linear base isolation system.
2401.16880v1
2024-01-30
Poynting-Robertson damping of laser beam driven lightsails
Lightsails using Earth-based lasers for propulsion require passive stabilization to stay within the beam. This can be achieved through the sail's scattering properties, creating optical restoring forces and torques. Undamped restoring forces produce uncontrolled oscillations, which could jeopardize the mission, but it is not obvious how to achieve damping in the vacuum of space. Using a simple two-dimensional model we show that the Doppler effect and relativistic aberration of the propelling laser beam create damping terms in the optical forces and torques. The effect is similar to the Poynting-Robertson effect causing loss of orbital momentum of dust particles around stars, but can be enhanced by design of the sail's geometry.
2401.16924v1
2024-02-29
The Equation of Motion for Taut-Line Buzzers
Equations of motion are developed for the oscillatory rotation of a disk suspended between twisted strings kept under tension by a hanging mass, to which additional forces may be applied. In the absence of forcing, damped harmonic oscillations are observed to decay with an exponential time envelope for two different string types. This is consistent with damping caused by string viscosity, rather than air turbulence, and may be quantified in terms of a quality factor. To test the proposed equation of motion and model for viscous damping within the string, we measure both the natural oscillation frequency and the quality factor for widely varied values of string length, string radius, disk moment of inertia, and hanging mass. The data are found to scale in good accord with predictions. A variation where rotational kinetic energy is converted back and forth to spring potential energy is also discussed.
2402.19285v1
2024-03-08
A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping
In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the Nonlinear Schr\"odinger Equation (NLSE) as a guide strategy, even in the presence of damping. A three-dimensional diagram is used to illustrate stable parameter regions for damped stationary solitons. Moreover, an analysis of the influence of the number of oscillators in the system, and a numerical investigation regarding the stability of solitonic behavior is done. Through numerical analyses, it is observed that the developed algorithm not only has the capability to locate the highest amplitudes in the chain of oscillators, but also to control the intensity at which these amplitudes are located according to design requirements. The outcomes of the proposed methodology elucidate the impact that the coupling stiffness has on the stabilization of the NLSE, as well as the influence of the number of oscillators on the continuity hypothesis. The developed algorithm holds potential for practical applications in mechanical engineering since the NLSE is used as a design line rather than as a consequence of the phenomenon description.
2403.05176v1
2024-03-08
Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
When orbiting hotter stars, hot Jupiters are often highly inclined relative to their host star equator planes. By contrast, hot Jupiters orbiting cooler stars are more aligned. Prior attempts to explain this correlation between stellar obliquity and effective temperature have proven problematic. We show how resonance locking -- the coupling of the planet's orbit to a stellar gravity mode (g mode) -- can solve this mystery. Cooler stars with their radiative cores are more likely to be found with g-mode frequencies increased substantially by core hydrogen burning. Strong frequency evolution in resonance lock drives strong tidal evolution; locking to an axisymmetric g mode damps semi-major axes, eccentricities, and as we show for the first time, obliquities. Around cooler stars, hot Jupiters evolve into spin-orbit alignment and avoid engulfment. Hotter stars lack radiative cores, and therefore preserve congenital spin-orbit misalignments. We focus on resonance locks with axisymmetric modes, supplementing our technical results with simple physical interpretations, and show that non-axisymmetric modes also damp obliquity.
2403.05616v1
2024-03-10
Linear-in-temperature resistivity and Planckian dissipation arise in a stochastic quantization model of Cooper pairs
We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.
2403.09710v1
1995-10-04
Microlensing By a Prolate All-Macho Halo
It is widely believed that dark matter halos are flattened, that is closer to oblate than prolate. The evidence cited is based largely on observations of galaxies which do not look anything like our own and on numerical simulations which use ad hoc initial conditions. Given what we believe to be a ``reasonable doubt'' concerning the shape of dark Galactic halo we calculate the optical depth and event rate for microlensing of stars in the LMC assuming a wide range of models that include both prolate and oblate halos. We find, in agreement with previous analysis, that the optical depth for a spherical (E0) halo and for an oblate (E6) halo are roughly the same, essentially because two competing effects cancel approximately. However the optical depth for an E6 prolate halo is reduced by ~35%. This means that an all-Macho prolate halo with reasonable parameters for the Galaxy is consistent with the published microlensing event rate.
9510023v1
1997-04-25
Constraints on the density perturbation spectrum from primordial black holes
We re-examine the constraints on the density perturbation spectrum, including its spectral index $n$, from the production of primordial black holes. The standard cosmology, where the Universe is radiation dominated from the end of inflation up until the recent past, was studied by Carr, Gilbert and Lidsey; we correct two errors in their derivation and find a significantly stronger constraint than they did, $n \lesssim 1.25$ rather than their 1.5. We then consider an alternative cosmology in which a second period of inflation, known as thermal inflation and designed to solve additional relic over-density problems, occurs at a lower energy scale than the main inflationary period. In that case, the constraint weakens to $n \lesssim 1.3$, and thermal inflation also leads to a `missing mass' range, $10^{18} g \lesssim M \lesssim 10^{26} g$, in which primordial black holes cannot form. Finally, we discuss the effect of allowing for the expected non-gaussianity in the density perturbations predicted by Bullock and Primack, which can weaken the constraints further by up to 0.05.
9704251v1
1998-02-26
Inversion of polarimetric data from eclipsing binaries
We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the Backus-Gilbert method to control the resolution and stability of the recovered solution, and to make quantitative estimates of the maximum accuracy possible. Using this method we confirm that the limb polarization can indeed be recovered, and demonstrate this with simulated data, thus determining the level of observational accuracy required to achieve a given accuracy of reconstruction. This allows us to set out an optimal observational strategy, and to critcally assess the claimed detection of limb polarization in the Algol system. The use of polarization in stars has been proposed as a diagnostic tool in microlensing surveys by Simmons et al. (1995), and we discuss the extension of this work to the case of microlensing of extended sources.
9802334v1
1998-09-04
Cluster-Cluster Strong Lensing: Expectations and Detection Methods
We calculate the all-sky number of galaxy clusters that are expected to be gravitationally lensed by foreground massive clusters. We describe the redshift and number distributions of clusters using a Press-Schechter analysis, and model the foreground lensing clusters as singular isothermal spheres. If Omega_m=0.3 and Omega_Lambda=0.7, we expect ~ 30 cluster-cluster strong lensing events that involve foreground X-ray luminous clusters with total mass greater than 7.5 x 10^14 h^-1 M_sun, or X-ray luminosity L_x (2-10 keV) 8 x 10^44 h^-2 ergs s^-1, and background clusters with total mass greater than 10^14 h^-1 M_sun. The number expected in an open universe with Omega_m = 0.3 is less than \~ 4. Because of uncertainty in sigma_8, the root-mean-square density fluctuations in spheres of radius 8 h^-1 Mpc, the exact number of such lensing events is uncertain by a factor of about 5. We examine methods to detect cluster-cluster lensing events based on optical, X-ray, and Sunyaev-Zel'dovich effect observations.
9809062v3
2000-04-14
Source Reconstruction as an Inverse Problem
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically subject to some bias, they can invert data without requiring one to assume a particular model for the source. The Backus-Gilbert method in particular concentrates on the tradeoff between resolution and stability, and allows one to select an optimal compromise between them. We use these tools to analyse the problem of reconstructing features of the source star in a microlensing event, show that it should be possible to obtain useful information about the star with reasonably obtainable data, and note that the quality of the reconstruction is more sensitive to the number of data points than to the quality of individual ones.
0004200v1
2000-04-18
Galaxy Cluster Baryon Fractions, Cluster Surveys and Cosmology
The properties of nearby galaxy clusters limit the range of cosmological parameters consistent with our universe. We describe the limits which arise from studies of the intracluster medium (ICM) mass fraction fICM and consideration of the possible sources of systematic error: Omega_M<0.44h_{50}^{-1/2} at 95% confidence. We emphasize that independent of Type Ia supernovae (SNe Ia) observations, this cluster study, taken together with published cosmic microwave background (CMB) anisotropy studies, indicates a non-zero quintessence or dark energy component Omega_Q>0. We then discuss future galaxy cluster surveys which will probe the abundance of galaxy clusters to intermediate and high redshift. We investigate the sensitivity of these surveys to the cosmological density parameter Omega_M and the equation of state parameter w of any quintessence component. In particular, we show that cluster survey constraints from a proposed large solid angle X-ray survey are comparable in precision and complementary in nature to constraints expected from future CMB anisotropy and SNe Ia studies.
0004244v1
2000-05-11
Measurement of [OIII] Emission in Lyman Break Galaxies
Measurements of [OIII] emission in Lyman Break galaxies (LBGs) at z>3 are presented. Four galaxies were observed with narrow-band filters using the Near-IR Camera on the Keck I 10-m telescope. A fifth galaxy was observed spectroscopically during the commissioning of NIRSPEC, the new infrared spectrometer on Keck II. The emission-line spectrum is used to place limits on the metallicity. Comparing these new measurements with others available from the literature, we find that strong oxygen emission in LBGs may suggest sub-solar metallicity for these objects. The [OIII]5007 line is also used to estimate the star formation rate (SFR) of the LBGs. The inferred SFRs are higher than those estimated from the UV continuum, and may be evidence for dust extinction.
0005254v1
2001-03-02
Clusters in the Precision Cosmology Era
Over the coming decade, the observational samples available for studies of cluster abundance evolution will increase from tens to hundreds, or possibly to thousands, of clusters. Here we assess the power of future surveys to determine cosmological parameters. We quantify the statistical differences among cosmologies, including the effects of the cosmic equation of state parameter w, in mock cluster catalogs simulating a 12 sq. deg Sunyaev-Zeldovich Effect survey and a deep 10^4 sq. deg X-ray survey. The constraints from clusters are complementary to those from studies of high-redshift Supernovae (SNe), CMB anisotropies, or counts of high-redshift galaxies. Our results indicate that a statistical uncertainty of a few percent on both Omega_m and w can be reached when cluster surveys are used in combination with any of these other datasets.
0103049v1
2002-07-05
New Tests of the Cluster Entropy Floor Hypothesis
Recent efforts to account for the observed X-ray luminosity - temperature relation of galaxy clusters has led to suggestions that the ICM has an apparent ``entropy floor'' at or above the level of 300 keV cm^2. Here, we propose new tests based on the thermal Sunyaev-Zeldovich effect and on the cluster gas mass - temperature trend (from X-ray data) to probe the level of excess entropy in the ICM. We show that these new tests lend further support to the case for a high entropy floor in massive clusters.
0207147v1
2003-06-18
Kinematic Masses of Super Star Clusters in M82 from High-Resolution Near-Infrared Spectroscopy
Using high-resolution (R~22,000) near-infrared (1.51 -- 1.75 microns) spectra from Keck Observatory, we measure the kinematic masses of two super star clusters in M82. Cross-correlation of the spectra with template spectra of cool evolved stars gives stellar velocity dispersions of sigma_r=15.9 +/- 0.8 km/s for MGG-9 and sigma_r=11.4 +/- 0.8 km/s for MGG-11. The cluster spectra are dominated by the light of red supergiants, and correlate most closely with template supergiants of spectral types M0 and M4.5. We fit King models to the observed profiles of the clusters in archival HST/NICMOS images to measure the half-light radii. Applying the virial theorem, we determine masses of 1.5 +/- 0.3 x 10^6 M_sun for MGG-9 and 3.5 +/- 0.7 x 10^5 M_sun for MGG-11. Population synthesis modelling suggests that MGG-9 is consistent with a standard initial mass function, whereas MGG-11 appears to be deficient in low-mass stars relative to a standard IMF. There is, however, evidence of mass segregation in the clusters, in which case the virial mass estimates would represent lower limits.
0306373v1
2003-09-10
The CMB Quadrupole in a Polarized Light
The low quadrupole of the cosmic microwave background (CMB), measured by COBE and confirmed by WMAP, has generated much discussion recently. We point out that the well-known correlation between temperature and polarization anisotropies of the CMB further constrains the low multipole anisotropy data. This correlation originates from the fact that the low-multipole polarization signal is sourced by the CMB quadrupole as seen by free electrons during the relatively recent cosmic history. Consequently, the large-angle temperature anisotropy data make restrictive predictions for the large-angle polarization anisotropy, which depend primarily on the optical depth for electron scattering after cosmological recombination, tau. We show that if current cosmological models for the generation of large angle anisotropy are correct and the COBE/WMAP data are not significantly contaminated by non-CMB signals, then the observed C_te amplitude on the largest scales is discrepant at the 99.8% level with the observed C_tt for the concordance LCDM model with tau=0.10. Using tau=0.17, the preferred WMAP model-independent value, the discrepancy is at the level of 98.5%.
0309281v2
2003-10-11
Statistics of Giant Arcs in Galaxy Clusters
We study the expected properties and statistics of giant arcs produced by galaxy clusters in a LambdaCDM universe and investigate how the characteristics of CDM clusters determine the properties of the arcs they generate. Due to the triaxiality and substructure of CDM halos, the giant arc cross section for individual clusters varies by more than an order of magnitude as a function of viewing angle. In addition, the shallow density cusps and triaxiality of CDM clusters cause systematic alignments of giant arcs which should be testable with larger samples from forthcoming lensing surveys. We compute the predicted statistics of giant arcs for the LambdaCDM model and compare to results from previous surveys. The predicted arc statistics are in excellent agreement with the numbers of giant arcs observed around low redshift (0.2 < z < 0.6) clusters from the EMSS sample, however there are hints of a possible excess of arcs observed around high redshift z > 0.6 clusters. This excess, if real, appears to be due to the presence of highly massive or concentrated clusters at high redshifts.
0310306v1
2004-01-23
Gravitational Lensing of the Microwave Background by Galaxy Clusters
Galaxy clusters will distort the pattern of temperature anisotropies in the microwave background via gravitational lensing. We create lensed microwave background maps using clusters drawn from numerical cosmological simulations. A distinctive dipole-like temperature fluctuation pattern is formed aligned with the underlying microwave temperature gradient. For a massive cluster, the characteristic angular size of the temperature distortion is a few arcminutes and the characteristic amplitude a few micro-Kelvin. We demonstrate a simple technique for estimating the lensing deflection induced by the cluster; microwave background lensing measurements have the potential to determine the mass distribution for some clusters with good accuracy on angular scales up to a few arcminutes. Future high-resolution and high-sensitivity microwave background maps will have the capability to detect lensing by clusters; we discuss various systematic limitations on probing cluster masses using this technique.
0401519v2
2004-04-15
Is the slope of the intrinsic Baldwin effect constant?
We investigate the relationship between emission-line strength and continuum luminosity in the best-studied nearby Seyfert 1 galaxy NGC5548. Our analysis of 13 years of ground-based optical monitoring data reveals significant year-to-year variations in the observed H-beta emission-line response in this source. More specifically, we confirm the result of Gilbert and Peterson (2003) of a non-linear relationship between the continuum and H-beta emission-line fluxes. Furthermore, we show that the slope of this relation is not constant, but rather decreases as the continuum flux increases. Both effects are consistent with photoionisation model predictions of a luminosity-dependent response in this line.
0404296v1
2005-08-04
Gravitino, Axino, Kaluza-Klein Graviton Warm and Mixed Dark Matter and Reionisation
Stable particle dark matter may well originate during the decay of long-lived relic particles, as recently extensively examined in the cases of the axino, gravitino, and higher-dimensional Kaluza-Klein (KK) graviton. It is shown that in much of the viable parameter space such dark matter emerges naturally warm/hot or mixed. In particular, decay produced gravitinos (KK-gravitons) may only be considered cold for the mass of the decaying particle in the several TeV range, unless the decaying particle and the dark matter particle are almost degenerate. Such dark matter candidates are thus subject to a host of cosmological constraints on warm and mixed dark matter, such as limits from a proper reionisation of the Universe, the Lyman-alpha forest, and the abundance of clusters of galaxies.. It is shown that constraints from an early reionsation epoch, such as indicated by recent observations, may potentially limit such warm/hot components to contribute only a very small fraction to the dark matter.
0508141v2
1999-08-10
Magnetic relaxation in a classical spin chain as model for nanowires
With decreasing particle size, different mechanisms dominate the thermally activated magnetization reversal in ferromagnetic particles. We investigate some of these mechanisms for the case of elongated, single-domain nanoparticles which we describe by a classical Heisenberg spin chain driven by an external magnetic field. For sufficiently small system size the magnetic moments rotate coherently. With increasing size a crossover to a reversal due to soliton-antisoliton nucleation sets in. For even larger systems many of these soliton-antisoliton pairs nucleate at the same time. These effects give rise to a complex size dependence of the energy barriers and characteristic time scales of the relaxation. We study these quantities using Monte Carlo simulations as well as a direct integration of the Landau-Lifshitz-Gilbert equation of motion with Langevin dynamics and we compare our results with asymptotic solutions for the escape rate following from the Fokker-Planck equation. Also, we investigate the crossover from coherent rotation to soliton-antisoliton nucleation and multi-droplet nucleation, especially its dependence on the system size, the external field and the anisotropy of the system.
9908150v1
2000-07-17
Fine-grid Simulations of Thermally Activated Switching in Nanoscale Magets
Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve magnetization patterns within nanomagnets and uses the Fast Multipole method to calculate dipole-dipole interactions efficiently. The thermal fluctuations play an essential part in the reversal process whenever the applied field is less than the zero-temperature coercive field. In this situation pillar-shaped nanomagnets are found to reverse through a local curling mode that involves the formation and propagation of a domain wall. Tapering the ends of the pillars to reduce pole-avoidance effects changes the energies involved but not the fundamental process. The statistical distribution of switching times is well described by the independent nucleation and subsequent growth of regions of reversed magnetization at both ends of the pillar.
0007279v1
2001-01-31
Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an external magnetic field less than the coercive value. The distribution of switching times is compared to a simple analytic theory that describes reversal with nucleation at the ends of the nanomagnets. Results are also presented for arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a separation of 300 nm, where the field from neighboring pillars is only $\sim$ 1 Oe, the interactions have a significant effect on the switching of the magnets.
0101477v2
2001-05-04
On a common circle: natural scenes and Gestalt rules
To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.
0105097v1
2002-10-11
Fluctuations and Dissipation of Coherent Magnetization
A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The model reproduces the Gilbert-Brown form of the equation in the classical limit. The magnetic moment is linearly coupled to a reservoir of bosonic degrees of freedom. Use of generalized coherent states makes the semiclassical limit more transparent within a path-integral formulation. A general fluctuation-dissipation theorem is derived. The magnitude of the magnetic moment also fluctuates beyond the Gaussian approximation. We discuss how the approximate stochastic description of the thermal field follows from our result. As an example, we go beyond the linear-response method and show how the thermal fluctuations become anisotropy-dependent even in the uniaxial case.
0210273v2
2002-11-18
Field dependence of magnetization reversal by spin transfer
We analyse the effect of the applied field (Happl) on the current-driven magnetization reversal in pillar-shaped Co/Cu/Co trilayers, where we observe two different types of transition between the parallel (P) and antiparallel (AP) magnetic configurations of the Co layers. If Happl is weaker than a rather small threshold value, the transitions between P and AP are irreversible and relatively sharp. For Happl exceding the threshold value, the same transitions are progressive and reversible. We show that the criteria for the stability of the P and AP states and the experimentally observed behavior can be precisely accounted for by introducing the current-induced torque of the spin transfer models in a Landau-Lifschitz-Gilbert equation. This approach also provides a good description for the field dependence of the critical currents.
0211371v1
2003-10-18
NMR Investigation of the Organic Conductor lambda-(BETS)2FeCl4
The two-dimensional organic conductor lambda-(BETS)2FeCl4 has an unusual phase diagram as a function of temperature and magnetic field that includes a paramagnetic metal (PM) phase, an antiferromagnetic insulating (AFI) phase, and a field-induced superconducting phase [S. Uji, H. Kobayashi, L. Balicas, and James S. Brooks, Adv. Mater. 14, 243 (2002), and cited references]. Here, we report a preliminary investigation of the PM and AFI phases at 9.0 T over the temperature range 2.0-180 K that uses proton NMR measurements of the spectrum, the spin-lattice relaxation rate (1/T1), and the spin echo decay rate (1/T2). The sample is asmall single crystal whose mass is approximately 3 micrograms (approximately 2E16 protons). Its small size creates several challenges that include detecting small signals and excluding parasitic proton signals that are not from the sample [H. N. Bachman and I. F. Silvera, J. Mag. Res. 162, 417 (2003)]. These strategies and other techniques used to obtain viable signals are described.
0310433v1
2004-04-22
Non-collinear magnetic structures: a possible cause for current induced switching
Current induced switching in Co/Cu/Co trilayers is described in terms of ab-initio determined magnetic twisting energies and corresponding sheet resistances. In viewing the twisting energy as an energy flux the characteristic time thereof is evaluated by means of the Landau-Lifshitz-Gilbert equation using ab-initio parameters. The obtained switching times are in very good agreement with available experimental data. In terms of the calculated currents, scalar quantities since a classical Ohm's law is applied, critical currents needed to switch magnetic configurations from parallel to antiparallel and vice versa can unambiguously be defined. It is found that the magnetoresistance viewed as a function of the current is essentially determined by the twisting energy as a function of the relative angle between the orientations of the magnetization in the magnetic slabs, which in turn can also explain in particular cases the fact that after having switched off the current the system remains in the switched magnetic configuration. For all ab-initio type calculations the fully relativistic Screened Korringa-Kohn-Rostoker method and the corresponding Kubo-Greenwood equation in the context of density functional theory are applied.
0404534v1
2004-06-21
Basic considerations for magnetization dynamics in the combined presence of spin-transfer torques and thermal fluctuations
This article reviews basic theoretical features of Gilbert magnetization dynamics of a single domain magnetic film in the presence of Slonczewski spin-transfer torques, with and without thermal fluctuations taken into account. Rather than showing results of detailed numerical calculations, the discussion here is restricted to basic analytical results and conclusions which can mostly be derived from simply the form of the equations of motion, as well as elementary considerations based on classical stability analysis and the fluctuation-dissipation theorem. The presents work describes how interesting features of spin-transfer may be viewed as arising from non-equilibrium thermodynamics that are a direct consequence of the nonreciprocal nature of spin-transfer torques. The present article discusses fairly general results for spin-torque induced instability without thermal fluctuations, as well as the case of thermally activated magnetization reversal in uniaxial devices in the combined presence of external fields, thermal fluctuations, and spin-transfer torques. The results will be discussed and briefly compared and contrasted with that of prior work.
0406486v1
2004-06-24
Thermal Effects on the Magnetic Field Dependence of Spin Transfer Induced Magnetization Reversal
We have developed a self-aligned, high-yield process to fabricate CPP (current perpendicular to the plane) magnetic sensors of sub 100 nm dimensions. A pinned synthetic antiferromagnet (SAF) is used as the reference layer which minimizes dipole coupling to the free layer and field induced rotation of the reference layer. We find that the critical currents for spin transfer induced magnetization reversal of the free layer vary dramatically with relatively small changes the in-plane magnetic field, in contrast to theoretical predictions based on stability analysis of the Gilbert equations of magnetization dynamics including Slonczewski-type spin-torque terms. The discrepancy is believed due to thermal fluctuations over the time scale of the measurements. Once thermal fluctuations are taken into account, we find good quantitative agreement between our experimental results and numerical simulations.
0406574v1
2004-07-23
Micromagnetic understanding of current-driven domain wall motion in patterned nanowires
In order to explain recent experiments reporting a motion of magnetic domain walls (DW) in nanowires carrying a current, we propose a modification of the spin transfer torque term in the Landau-Lifchitz-Gilbert equation. We show that it explains, with reasonable parameters, the measured DW velocities as well as the variation of DW propagation field under current. We also introduce coercivity by considering rough wires. This leads to a finite DW propagation field and finite threshold current for DW propagation, hence we conclude that threshold currents are extrinsic. Some possible models that support this new term are discussed.
0407628v2
2004-08-07
Hysteresis multicycles in nanomagnet arrays
We predict two new physical effects in arrays of single-domain nanomagnets by performing simulations using a realistic model Hamiltonian and physical parameters. First, we find hysteretic multicycles for such nanomagnets. The simulation uses continuous spin dynamics through the Landau-Lifshitz-Gilbert (LLG) equation. In some regions of parameter space, the probability of finding a multicycle is as high as ~0.6. We find that systems with larger and more anisotropic nanomagnets tend to display more multicycles. This result demonstrates the importance of disorder and frustration for multicycle behavior. We also show that there is a fundamental difference between the more realistic vector LLG equation and scalar models of hysteresis, such as Ising models. In the latter case, spin and external field inversion symmetry is obeyed but in the former it is destroyed by the dynamics, with important experimental implications.
0408158v1
2004-12-03
High frequency magnetic permeability of nanocomposite film
The high frequency magnetic permeability of nanocomposite film consisting of the single-domain spherical ferromagnetic particles in the dielectric matrix is studied. The permeability is assumed to be determined by rotation of the ferromagnetic inclusion magnetic moments around equilibrium direction in AC magnetic field. The composite is modeled by a cubic array of ferromagnetic particles. The magnetic permeability tensor is calculated by solving the Landau-Lifshits-Gilbert equation accounting for the dipole interaction of magnetic particles. The permeability tensor components are found as functions of the frequency, temperature, ferromagnetic inclusions density and magnetic anisotropy. The obtained results show that nanocomposite films could have rather high value of magnetic permeability in the microwave range.
0412073v1
2005-01-07
Dielectric resonances of ordered passive arrays
The electrical and optical properties of ordered passive arrays, constituted of inductive and capacitive components, are usually deduced from Kirchhoff's rules. Under the assumption of periodic boundary conditions, comparable results may be obtained via an approach employing transfer matrices. In particular, resonances in the dielectric spectrum are demonstrated to occur if all eigenvalues of the transfer matrix of the entire array are unity. The latter condition, which is shown to be equivalent to the habitual definition of a resonance in impedance for an array between electrodes, allows for a convenient and accurate determination of the resonance frequencies, and may thus be used as a tool for the design of materials with a specific dielectric response. For the opposite case of linear arrays in a large network, where periodic boundary condition do not apply, several asymptotic properties are derived. Throughout the article, the derived analytic results are compared to numerical models, based on either Exact Numerical Renormalisation or the spectral method.
0501137v1
2005-07-27
"Stochastic Modeling of Coercivity " - A Measure of Non-equilibrium State
A typical coercivity versus particle size curve for magnetic nanoparticles has been explained by using the Gilbert equation followed by the corresponding Fokker Plank equation. Kramer's treatment has been employed to explain the increase in coercivity in the single domain region. The single to multi-domain transformation has been assumed to explain the decrease in coercive field beyond a certain particle size. The justification for using Langevin theory of paramagnetism (including anisotropy energy) to fit the M vs H curve is discussed. The super-symmetric Hamiltonian approach is used to find out the relaxation time for the spins (making an angle greater than $90^0$ with applied field) at domain wall. The main advantage of our technique is that we can easily take into account the time of measurement as we usually do in realistic measurement.
0507640v1
2005-09-13
Synchronization of spin-transfer oscillators driven by stimulated microwave currents
We have simulated the non-linear dynamics of networks of spin-transfer oscillators. The oscillators are magnetically uncoupled but electrically connected in series. We use a modified Landau-Lifschitz- Gilbert equation to describe the motion of each oscillator in the presence of the oscillations of all the others. We show that the oscillators of the network can be synchronized not only in frequency but also in phase. The coupling is due to the microwave components of the current induced in each oscillator by the oscillations in all the other oscillators. Our results show how the emitted microwave power of spin-transfer oscillators can be considerably enhanced by current-induced synchronization in an electrically connected network. We also discuss the possible application of our synchronization mechanism to the interpretation of the surprisingly narrow microwave spectrum in some isolated spin-transfer oscillators.
0509326v2
2005-11-04
Synchronized Magnetization Oscillations in F/N/F Nanopillars
Current-induced magnetization dynamics in a trilayer structure composed of two ferromagnetic free layers and a nonmagnetic spacer is examined. Both free layers are treated as a monodomain magnetic body with an uniform agnetization. The dynamics of the two magnetizations is modeled by modified Landau-Lifshitz-Gilbert equations with spin-transfer torque terms. By solving the equations simultaneously, we discuss their various solutions in detail. We show that there exists the synchronous motion of two magnetizations among the various solutions; the magnetizations are resonantly coupled via spin-transfer torques and perform precessional motions with the same period. The condition to excite the synchronous motion depends on the difference between the intrinsic frequencies of the two ferromagnetic free layers as well as the magnitude of current.
0511095v1
2006-01-27
Dynamics of thin-film spin-flip transistors with perpendicular source-drain magnetizations
A "spin-flip transistor" is a lateral spin valve consisting of ferromagnetic source drain contacts to a thin-film normal-metal island with an electrically floating ferromagnetic base contact on top. We analyze the \emph{dc}-current-driven magnetization dynamics of spin-flip transistors in which the source-drain contacts are magnetized perpendicularly to the device plane by magnetoelectronic circuit theory and the macrospin Landau-Lifshitz-Gilbert equation. Spin flip scattering and spin pumping effects are taken into account. We find a steady-state rotation of the base magnetization at GHz frequencies that is tuneable by the source-drain bias. We discuss the advantages of the lateral structure for high-frequency generation and actuation of nanomechanical systems over recently proposed nanopillar structures.
0601630v1
2007-03-17
Large-amplitude coherent spin waves exited by spin-polarized current in nanoscale spin valves
We present spectral measurements of spin-wave excitations driven by direct spinpolarized current in the free layer of nanoscale Ir20Mn80/Ni80Fe20/Cu/Ni80Fe20 spin valves. The measurements reveal that large-amplitude coherent spin wave modes are excited over a wide range of bias current. The frequency of these excitations exhibits a series of jumps as a function of current due to transitions between different localized nonlinear spin wave modes of the Ni80Fe20 nanomagnet. We find that micromagnetic simulations employing the Landau-Lifshitz-Gilbert equation of motion augmented by the Slonczewski spin torque term (LLGS) accurately describe the frequency of the current-driven excitations including the mode transition behavior. However LLGS simulations give qualitatively incorrect predictions for the amplitude of excited spin waves as a function of current.
0703458v2
2001-12-11
A Data Mining Framework for Optimal Product Selection in Retail Supermarket Data: The Generalized PROFSET Model
In recent years, data mining researchers have developed efficient association rule algorithms for retail market basket analysis. Still, retailers often complain about how to adopt association rules to optimize concrete retail marketing-mix decisions. It is in this context that, in a previous paper, the authors have introduced a product selection model called PROFSET. This model selects the most interesting products from a product assortment based on their cross-selling potential given some retailer defined constraints. However this model suffered from an important deficiency: it could not deal effectively with supermarket data, and no provisions were taken to include retail category management principles. Therefore, in this paper, the authors present an important generalization of the existing model in order to make it suitable for supermarket data as well, and to enable retailers to add category restrictions to the model. Experiments on real world data obtained from a Belgian supermarket chain produce very promising results and demonstrate the effectiveness of the generalized PROFSET model.
0112013v1
2005-02-22
The QuarkNet/Grid Collaborative Learning e-Lab
We describe a case study that uses grid computing techniques to support the collaborative learning of high school students investigating cosmic rays. Students gather and upload science data to our e-Lab portal. They explore those data using techniques from the GriPhyN collaboration. These techniques include virtual data transformations, workflows, metadata cataloging and indexing, data product provenance and persistence, as well as job planners. Students use web browsers and a custom interface that extends the GriPhyN Chiron portal to perform all of these tasks. They share results in the form of online posters and ask each other questions in this asynchronous environment. Students can discover and extend the research of other students, modeling the processes of modern large-scale scientific collaborations. Also, the e-Lab portal provides tools for teachers to guide student work throughout an investigation. http://quarknet.uchicago.edu/elab/cosmic
0502089v1
2006-10-11
Properties of codes in rank metric
We study properties of rank metric and codes in rank metric over finite fields. We show that in rank metric perfect codes do not exist. We derive an existence bound that is the equivalent of the Gilbert--Varshamov bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes satisfying GV. We derive the probability distribution of minimum rank distance for random and random $\F{q}$-linear codes. We give an asymptotic equivalent of their average minimum rank distance and show that random $\F{q}$-linear codes are on GV bound for rank metric. We show that the covering density of optimum codes whose codewords can be seen as square matrices is lower bounded by a function depending only on the error-correcting capability of the codes. We show that there are quasi-perfect codes in rank metric over fields of characteristic 2.
0610057v1