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2022-07-14
|
The Damped Wave Equation with Acoustic Boundary Conditions and Non-locally Reacting Surfaces
|
The aim of the paper is to study the problem $$u_{tt}+du_t-c^2\Delta u=0
\qquad \text{in $\mathbb{R}\times\Omega$,}$$ $$\mu v_{tt}- \text{div}_\Gamma
(\sigma \nabla_\Gamma v)+\delta v_t+\kappa v+\rho u_t =0\qquad \text{on
$\mathbb{R}\times \Gamma_1$,}$$ $$v_t =\partial_\nu u\qquad \text{on
$\mathbb{R}\times \Gamma_1$,}$$ $$\partial_\nu u=0 \text{on $\mathbb{R}\times
\Gamma_0$,}$$ $$u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x)\quad \text{in $\Omega$,}$$
$$v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x) \quad \text{on $\Gamma_1$,}$$ where
$\Omega$ is a open domain of $\mathbb{R}^N$ with uniformly $C^r$ boundary
($N\ge 2$, $r\ge 1$), $\Gamma=\partial\Omega$, $(\Gamma_0,\Gamma_1)$ is a
relatively open partition of $\Gamma$ with $\Gamma_0$ (but not $\Gamma_1$)
possibly empty. Here $\text{div}_\Gamma$ and $\nabla_\Gamma$ denote the
Riemannian divergence and gradient operators on $\Gamma$, $\nu$ is the outward
normal to $\Omega$, the coefficients $\mu,\sigma,\delta, \kappa, \rho$ are
suitably regular functions on $\Gamma_1$ with $\rho,\sigma$ and $\mu$ uniformly
positive, $d$ is a suitably regular function in $\Omega$ and $c$ is a positive
constant.
In this paper we first study well-posedness in the natural energy space and
give regularity results. Hence we study asymptotic stability for solutions when
$\Omega$ is bounded, $\Gamma_1$ is connected, $r=2$, $\rho$ is constant and
$\kappa,\delta,d\ge 0$.
|
2207.07047v2
|
2022-12-07
|
Finite-time blow-up to hyperbolic Keller-Segel system of consumption type with logarithmic sensitivity
|
This paper deals with a hyperbolic Keller-Segel system of consumption type
with the logarithmic sensitivity \begin{equation*}
\partial_{t} \rho = - \chi\nabla \cdot \left (\rho \nabla \log c\right),\quad
\partial_{t} c = - \mu c\rho\quad (\chi,\,\mu>0) \end{equation*} in
$\mathbb{R}^d\; (d \ge1)$ for nonvanishing initial data. This system is closely
related to tumor angiogenesis, an important example of chemotaxis. We firstly
show the local existence of smooth solutions corresponding to nonvanishing
smooth initial data. Next, through Riemann invariants, we present some
sufficient conditions of this initial data for finite-time singularity
formation when $d=1$. We then prove that for any $d\ge1$, some nonvanishing
$C^\infty$-data can become singular in finite time. Moreover, we derive
detailed information about the behaviors of solutions when the singularity
occurs. In particular, this information tells that singularity formation from
some initial data is not because $c$ touches zero (which makes $\log c$
diverge) but due to the blowup of $C^1\times C^2$-norm of $(\rho,c)$. As a
corollary, we also construct initial data near any constant equilibrium state
which blows up in finite time for any $d\ge1$. Our results are the extension of
finite-time blow-up results in \cite{IJ21}, where initial data is required to
satisfy some vanishing conditions. Furthermore, we interpret our results in a
way that some kinds of damping or dissipation of $\rho$ are necessarily
required to ensure the global existence of smooth solutions even though initial
data are small perturbations around constant equilibrium states.
|
2212.03758v4
|
2023-02-06
|
Cosmologically Varying Kinetic Mixing
|
The portal connecting the invisible and visible sectors is one of the most
natural explanations of the dark world. However, the early-time dark matter
production via the portal faces extremely stringent late-time constraints. To
solve such tension, we construct the scalar-controlled kinetic mixing varying
with the ultralight CP-even scalar's cosmological evolution. To realize this
and eliminate the constant mixing, we couple the ultralight scalar within
$10^{-33}\text{eV} \lesssim m_0 \ll \text{eV}$ with the heavy doubly charged
messengers and impose the $\mathbb{Z}_2$ symmetry under the dark charge
conjugation. Via the varying mixing, the $\text{keV}-\text{MeV}$ dark photon
dark matter is produced through the early-time freeze-in when the scalar is
misaligned from the origin and free from the late-time exclusions when the
scalar does the damped oscillation and dynamically sets the kinetic mixing. We
also find that the scalar-photon coupling emerges from the underlying physics,
which changes the cosmological history and provides the experimental targets
based on the fine-structure constant variation and the equivalence principle
violation. To ensure the scalar naturalness, we discretely re-establish the
broken shift symmetry by embedding the minimal model into the
$\mathbb{Z}_N$-protected model. When $N \sim 10$, the scalar's mass quantum
correction can be suppressed much below $10^{-33}\text{eV}$.
|
2302.03056v2
|
2023-09-08
|
Minimum-dissipation model for large-eddy simulation in OpenFoam -A study on channel flow, periodic hills and flow over cylinder
|
The minimum-dissipation model is applied to turbulent channel flows up to
$Re_\tau = 2000$, flow past a circular cylinder at $Re=3900$, and flow over
periodic hills at $Re=10595$. Numerical simulations are performed in OpenFOAM
which is based on finite volume methods for discretizing partial differential
equations. We use both symmetry-preserving discretizations and standard
second-order accurate discretization methods in OpenFOAM on structured meshes.
The results are compared to DNS and experimental data.
The results of channel flow mainly demonstrate the static QR model performs
equally well as the dynamic models while reducing the computational cost. The
model constant $C=0.024$ gives the most accurate prediction, and the
contribution of the sub-grid model decreases with the increase of the mesh
resolution and becomes very small (less than 0.2 molecular viscosity) if the
fine meshes are used. Furthermore, the QR model is able to predict the mean and
rms velocity accurately up to $Re_\tau = 2000$ without a wall damping function.
The symmetry-preserving discretization outperforms the standard OpenFOAM
discretization at $Re_\tau=1000$. The results for the flow over a cylinder show
that mean velocity, drag coefficient, and lift coefficient are in good
agreement with the experimental data. The symmetry-preserving scheme with the
QR model predicts the best results. The various comparisons carried out for
flows over periodic hills demonstrate the need to use the symmetry-preserving
discretization or central difference schemes in OpenFOAM in combination with
the minimum dissipation model. The model constant of $C=0.024$ is again the
best one.
|
2309.04415v1
|
2023-11-02
|
Minimum-dissipation model for large-eddy simulation using symmetry-preserving discretization in OpenFOAM
|
The minimum-dissipation model is applied to channel flow up to $Re_\tau =
2000$, flow past a circular cylinder at $Re=3900$, and flow over periodic hills
at $Re=10595$. Numerical simulations were performed in OpenFOAM which is based
on the finite volume methods. We used both symmetry-preserving and standard
second-order accurate discretization methods in OpenFOAM on structured meshes.
The results are compared to DNS and experimental data.
The results of channel flow demonstrate a static QR model performs equally
well as the dynamic models while reducing the computational cost. The model
constant of $C=0.024$ gives the most accurate prediction, and the contribution
of the sub-grid model decreases with the increase of the mesh resolution and
becomes very small (less than 0.2 molecular viscosity) if a fine mesh is used.
Furthermore, the QR model is able to predict the mean and rms velocity
accurately up to $Re_\tau = 2000$ without a wall damping function. The
symmetry-preserving discretization outperforms the standard OpenFOAM
discretization at $Re_\tau=1000$. The results for the flow over a cylinder show
that the mean velocity, drag coefficient, and lift coefficient are in good
agreement with the experimental data and the central difference schemes
conjugated with the QR model predict better results. The various comparisons
carried out for flows over periodic hills demonstrate the need to use central
difference schemes in OpenFOAM in combination with the minimum dissipation
model. The best model constant is again $C=0.024$. The single wind turbine
simulation shows that the QR model is capable of predicting accurate results in
complex rotating scenarios.
|
2311.01360v1
|
2024-01-22
|
Axions and Primordial Magnetogenesis: the Role of Initial Axion Inhomogeneities
|
The relic density of dark matter in the $\Lambda$CDM model restricts the
parameter space for a cosmological axion field, constraining the axion decay
constant, the initial amplitude of the axion field and the axion mass. It is
shown via lattice simulations how the relic density of axion-like particles
with masses close to the one of the QCD axion is affected by axion-gauge field
interactions and by initial axion inhomogeneities. For pre-inflationary axions,
once the Hubble parameter becomes smaller than the axion mass, the latter
starts to oscillate, and part of its energy density is spent producing gauge
fields via parametric resonance. If the gauge fields are dark photons and
Standard Model photons, the energy density of dark photons becomes higher than
the one of the axion, while the high conductivity of the primordial plasma
damps the oscillations of the photon field. Such a scenario allows for the
production of small-scale, primordial magnetic fields, and it is found that the
relic density of axions with a low decay constant are within the bounds set by
the $\Lambda$CDM model, while GUT-scale axions are far too abundant. It is also
shown that initial inhomogeneities of the axion field can change substantially
the gauge field production, boosting or suppressing (depending on the axion
parameters and couplings) the magnetogenesis mechanism with respect to an
homogeneous axion field. It is found that when the axion mass is far lighter
than the QCD axion model and the initial axion field is inhomogeneous, weak but
cosmologically relevant magnetic field seeds can be generated on scales of the
order of $0.1$ kpc.
|
2401.11822v1
|
2024-01-28
|
Perturbation of parabolic equations with time-dependent linear operators: convergence of linear processes and solutions
|
In this work we consider parabolic equations of the form \[
(u_{\varepsilon})_t +A_{\varepsilon}(t)u_{{\varepsilon}} = F_{\varepsilon}
(t,u_{{\varepsilon} }), \] where $\varepsilon$ is a parameter in
$[0,\varepsilon_0)$ and $\{A_{\varepsilon}(t), \ t\in \mathbb{R}\}$ is a family
of uniformly sectorial operators. As $\varepsilon \rightarrow 0^{+}$, we assume
that the equation converges to \[ u_t +A_{0}(t)u_{} = F_{0} (t,u_{}). \] The
time-dependence found on the linear operators $A_{\varepsilon}(t)$ implies that
linear process is the central object to obtain solutions via variation of
constants formula. Under suitable conditions on the family $A_{\varepsilon}(t)$
and on its convergence to $A_0(t)$ when $\varepsilon \rightarrow 0^{+}$, we
obtain a Trotter-Kato type Approximation Theorem for the linear process
$U_{\varepsilon}(t,\tau)$ associated to $A_{\varepsilon}(t)$, estimating its
convergence to the linear process $U_0(t,\tau)$ associated to $A_0(t)$. Through
the variation of constants formula and assuming that $F_{\varepsilon}$
converges to $F_0$, we analyze how this linear process convergence is
transferred to the solution of the semilinear equation. We illustrate the ideas
in two examples. First a reaction-diffusion equation in a bounded smooth
domain, obtaining convergence of the linear process and solution. As a
consequence, we also obtain upper-semicontinuity of the family of pullback
attractors associated to each problem. The second example is a nonautonomous
strongly damped wave equation and we analyze convergence of solution as we
perturb the fractional powers of the associated linear operator.
|
2401.15799v1
|
1999-11-24
|
Damped Lyman alpha absorber and the faint end of the galaxy luminosity function at high redshift
|
We combine predictions for several hierarchical cosmogonies with
observational evidence on damped Lyman alpha systems to establish a
correspondence between the high redshift galaxy population and the properties
of damped Lyman alpha systems. We assume that high redshift galaxies and damped
Lyman alpha systems are hosted by the same dark matter halos and require
consistency between the predicted halo space density, the rate of incidence and
the velocity width distribution of damped Lyman alpha systems, and the observed
galaxy luminosity function at the bright end. We arrive at the following
results: (1) predicted impact parameters between the damped absorption system
and the luminous part of the absorbing galaxy are expected to be very small
(0.3 - 1arcsec) for most galaxies; (2) luminosities of galaxies causing damped
absorption are generally fainter than m_R = 25 and damped Lyman alpha systems
are predicted to sample preferentially the outer regions of galaxies at the
faint end of the galaxy luminosity function at high redshift. Therefore, DLAS
should currently provide the best probe of the progenitors of normal
present-day galaxies.
|
9911447v1
|
2003-03-13
|
An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity
|
This paper introduces an extension of the time-splitting sine-spectral (TSSP)
method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS).
The method is explicit, unconditionally stable and time transversal invariant.
Moreover, it preserves the exact decay rate for the normalization of the wave
function if linear damping terms are added to the NLS. Extensive numerical
tests are presented for cubic focusing nonlinear Schr\"{o}dinger equations in
2d with a linear, cubic or a quintic damping term. Our numerical results show
that quintic or cubic damping always arrests blowup, while linear damping can
arrest blowup only when the damping parameter $\dt$ is larger than a threshold
value $\dt_{\rm th}$. We note that our method can also be applied to solve the
3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics
of a collapsing and exploding Bose-Einstein condensate (BEC).
|
0303158v1
|
2004-11-03
|
Quantum probability applied to the damped harmonic oscillator
|
In this introductory course we sketch the framework of quantum probability in
order to discuss open quantum systems, in particular the damped harmonic
oscillator.
|
0411024v1
|
2006-11-23
|
Path integrals and wavepacket evolution for damped mechanical systems
|
Damped mechanical systems with various forms of damping are quantized using
the path integral formalism. In particular, we obtain the path integral kernel
for the linearly damped harmonic oscillator and a particle in a uniform
gravitational field with linearly or quadratically damped motion. In each case,
we study the evolution of Gaussian wavepackets and discuss the characteristic
features that help us distinguish between different types of damping. For
quadratic damping, we show that the action and equation of motion of such a
system has a connection with the zero dimensional version of a currently
popular scalar field theory. Furthermore we demonstrate that the equation of
motion (for quadratic damping) can be identified as a geodesic equation in a
fictitious two-dimensional space.
|
0611239v1
|
2007-07-05
|
Damping of bulk excitations over an elongated BEC - the role of radial modes
|
We report the measurement of Beliaev damping of bulk excitations in cigar
shaped Bose Einstein condensates of atomic vapor. By using post selection,
excitation line shapes of the total population are compared with those of the
undamped excitations. We find that the damping depends on the initial
excitation energy of the decaying quasi particle, as well as on the excitation
momentum. We model the condensate as an infinite cylinder and calculate the
damping rates of the different radial modes. The derived damping rates are in
good agreement with the experimentally measured ones. The damping rates
strongly depend on the destructive interference between pathways for damping,
due to the quantum many-body nature of both excitation and damping products.
|
0707.0776v1
|
2008-09-22
|
Damping in 2D and 3D dilute Bose gases
|
Damping in 2D and 3D dilute gases is investigated using both the
hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation .
We found that the both methods are good for the Beliaev damping at zero
temperature and Landau damping at very low temperature, however, at high
temperature, the hydrodynamical approach overestimates the Landau damping and
the HFB gives a better approximation. This result shows that the comparison of
the theoretical calculation using the hydrodynamical approach and the
experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056
(1997)) is not proper. For two-dimensional systems, we show that the Beliaev
damping rate is proportional to $k^3$ and the Landau damping rate is
proportional to $ T^2$ for low temperature and to $T$ for high temperature. We
also show that in two dimensions the hydrodynamical approach gives the same
result for zero temperature and for low temperature as HFB, but overestimates
the Landau damping for high temperature.
|
0809.3632v3
|
2008-12-08
|
Landau Damping and Alfven Eigenmodes of Neutron Star Torsion Oscillations
|
Torsion oscillations of the neutron star crust are Landau damped by the
Alfven continuum in the bulk. For strong magnetic fields (in magnetars),
undamped Alfven eigenmodes appear.
|
0812.1570v1
|
2010-09-24
|
Spatial Damping of Propagating Kink Waves in Prominence Threads
|
Transverse oscillations and propagating waves are frequently observed in
threads of solar prominences/filaments and have been interpreted as kink
magnetohydrodynamic (MHD) modes. We investigate the spatial damping of
propagating kink MHD waves in transversely nonuniform and partially ionized
prominence threads. Resonant absorption and ion-neutral collisions (Cowling's
diffusion) are the damping mechanisms taken into account. The dispersion
relation of resonant kink waves in a partially ionized magnetic flux tube is
numerically solved by considering prominence conditions. Analytical expressions
of the wavelength and damping length as functions of the kink mode frequency
are obtained in the Thin Tube and Thin Boundary approximations. For typically
reported periods of thread oscillations, resonant absorption is an efficient
mechanism for the kink mode spatial damping, while ion-neutral collisions have
a minor role. Cowling's diffusion dominates both the propagation and damping
for periods much shorter than those observed. Resonant absorption may explain
the observed spatial damping of kink waves in prominence threads. The
transverse inhomogeneity length scale of the threads can be estimated by
comparing the observed wavelengths and damping lengths with the theoretically
predicted values. However, the ignorance of the form of the density profile in
the transversely nonuniform layer introduces inaccuracies in the determination
of the inhomogeneity length scale.
|
1009.4871v1
|
2012-08-27
|
Optimization of the damped quantum search
|
The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501
(2009)] was analyzed by calculating the highest possible probability of finding
the target state in each iteration. A new damping parameter that depends on the
number of iterations was obtained, this was compared to the critical damping
parameter for different values of target to database size ratio. The result
shows that the range of the new damping parameter as a function of the target
to database size ratio increases as the number of iterations is increased.
Furthermore, application of the new damping parameter per iteration on the
damped quantum search scheme shows a significant improvement on some target to
database size ratio (i.e. greater than or equal to 50% maximum percentage
difference) over the critically damped quantum search.
|
1208.5475v1
|
2013-04-03
|
Damping the zero-point energy of a harmonic oscillator
|
The physics of quantum electromagnetism in an absorbing medium is that of a
field of damped harmonic oscillators. Yet until recently the damped harmonic
oscillator was not treated with the same kind of formalism used to describe
quantum electrodynamics in a arbitrary medium. Here we use the techniques of
macroscopic QED, based on the Huttner--Barnett reservoir, to describe the
quantum mechanics of a damped oscillator. We calculate the thermal and
zero-point energy of the oscillator for a range of damping values from zero to
infinity. While both the thermal and zero-point energies decrease with damping,
the energy stored in the oscillator at fixed temperature increases with
damping, an effect that may be experimentally observable. As the results follow
from canonical quantization, the uncertainty principle is valid for all damping
levels.
|
1304.0977v2
|
2015-05-28
|
Damping factors for head-tail modes at strong space charge
|
This paper suggests how feedback and Landau damping can be taken into account
for transverse oscillations of bunched beam at strong space charge.
|
1505.07704v1
|
2015-06-18
|
Damping of MHD turbulence in partially ionized plasma: implications for cosmic ray propagation
|
We study the damping from neutral-ion collisions of both incompressible and
compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium.
We start from the linear analysis of MHD waves applying both single-fluid and
two-fluid treatments. The damping rates derived from the linear analysis are
then used in determining the damping scales of MHD turbulence. The physical
connection between the damping scale of MHD turbulence and cutoff boundary of
linear MHD waves is investigated. Our analytical results are shown to be
applicable in a variety of partially ionized interstellar medium (ISM) phases
and solar chromosphere. As a significant astrophysical utility, we introduce
damping effects to propagation of cosmic rays in partially ionized ISM. The
important role of turbulence damping in both transit-time damping and
gyroresonance is identified.
|
1506.05585v1
|
2016-02-04
|
Damping Evaluation for Free Vibration of Spherical Structures in Elastodynamic-Acoustic Interaction
|
This paper discusses the free vibration of elastic spherical structures in
the presence of an externally unbounded acoustic medium. In this vibration,
damping associated with the radiation of energy from the confined solid medium
to the surrounding acoustic medium is observed. Evaluating the coupled system
response (solid displacement and acoustic pressure) and characterizing the
acoustic radiation damping in conjunction with the media properties are the
main objectives of this research. In this work, acoustic damping is
demonstrated for two problems: the thin spherical shell and the solid sphere.
The mathematical approach followed in solving these coupled problems is based
on the Laplace transform method. The linear under-damped harmonic oscillator is
the reference model for damping estimation. The damping evaluation is performed
in frequency as well as in time domains; both investigations lead to identical
damping factor expressions.
|
1604.06738v1
|
2017-01-10
|
Magnetic properties in ultra-thin 3d transition metal alloys II: Experimental verification of quantitative theories of damping and spin-pumping
|
A systematic experimental study of Gilbert damping is performed via
ferromagnetic resonance for the disordered crystalline binary 3d transition
metal alloys Ni-Co, Ni-Fe and Co-Fe over the full range of alloy compositions.
After accounting for inhomogeneous linewidth broadening, the damping shows
clear evidence of both interfacial damping enhancement (by spin pumping) and
radiative damping. We quantify these two extrinsic contributions and thereby
determine the intrinsic damping. The comparison of the intrinsic damping to
multiple theoretical calculations yields good qualitative and quantitative
agreement in most cases. Furthermore, the values of the damping obtained in
this study are in good agreement with a wide range of published experimental
and theoretical values. Additionally, we find a compositional dependence of the
spin mixing conductance.
|
1701.02475v1
|
2017-06-14
|
Temperature-dependent Gilbert damping of Co2FeAl thin films with different degree of atomic order
|
Half-metallicity and low magnetic damping are perpetually sought for in
spintronics materials and full Heusler alloys in this respect provide
outstanding properties. However, it is challenging to obtain the well-ordered
half-metallic phase in as-deposited full Heusler alloys thin films and theory
has struggled to establish a fundamentals understanding of the temperature
dependent Gilbert damping in these systems. Here we present a study of the
temperature dependent Gilbert damping of differently ordered as-deposited
Co2FeAl full Heusler alloy thin films. The sum of inter- and intraband electron
scattering in conjunction with the finite electron lifetime in Bloch states
govern the Gilbert damping for the well-ordered phase in contrast to the
damping of partially-ordered and disordered phases which is governed by
interband electronic scattering alone. These results, especially the ultralow
room temperature intrinsic damping observed for the well-ordered phase provide
new fundamental insights to the physical origin of the Gilbert damping in full
Heusler alloy thin films.
|
1706.04670v2
|
2017-09-05
|
Enhancement of space-charge induced damping due to reactive impedances for head-tail modes
|
Landau damping of head-tail modes in bunches due to spreads in the tune shift
can be a deciding factor for beam stability. We demonstrate that the coherent
tune shifts due to reactive impedances can enhance the space-charge induced
damping and change the stability thresholds (here, a reactive impedance implies
the imaginary part of the impedance of both signs). For example, high damping
rates at strong space-charge, or damping of the $k=0$ mode, can be possible. It
is shown and explained, how the negative reactive impedances (causing negative
coherent tune shifts similarly to the effect of space-charge) can enhance the
Landau damping, while the positive coherent tune shifts have an opposite
effect. It is shown that the damping rate is a function of the coherent mode
position in the incoherent spectrum, in accordance with the concept of the
interaction of a collective mode with resonant particles. We present an
analytical model, which allows for quantitative predictions of damping
thresholds for different head-tail modes, for arbitrary space-charge and
coherent tune-shift conditions, as it is verified using particle tracking
simulations.
|
1709.01425v1
|
2018-05-21
|
Critical damping in nonviscously damped linear systems
|
In structural dynamics, energy dissipative mechanisms with non-viscous
damping are characterized by their dependence on the time-history of the
response velocity, mathematically represented by convolution integrals
involving hereditary functions. Combination of damping parameters in the
dissipative model can lead the system to be overdamped in some (or all) modes.
In the domain of the damping parameters, the thresholds between induced
oscillatory and non--oscillatory motion are called critical damping surfaces
(or manifolds, since we can have a lot of parameters). In this paper a general
method to obtain critical damping surfaces for nonviscously damped systems is
proposed. The approach is based on transforming the algebraic equations which
defined implicitly the critical curves into a system of differential equations.
The derivations are validated with three numerical methods covering single and
multiple degree of freedom systems.
|
1805.08022v1
|
2018-11-01
|
Hereditary effects of exponentially damped oscillators with past histories
|
Hereditary effects of exponentially damped oscillators with past histories
are considered in this paper. Nonviscously damped oscillators involve
hereditary damping forces which depend on time-histories of vibrating motions
via convolution integrals over exponentially decaying functions. As a result,
this kind of oscillators are said to have memory. In this work, initialization
for nonviscously damped oscillators is firstly proposed. Unlike the classical
viscously damped ones, information of the past history of response velocity is
necessary to fully determine the dynamic behaviors of nonviscously damped
oscillators. Then, initialization response of exponentially damped oscillators
is obtained to characterize the hereditary effects on the dynamic response. At
last, stability of initialization response is proved and the hereditary effects
are shown to gradually recede with increasing of time.
|
1811.00216v1
|
2019-02-22
|
Strongly Enhanced Gilbert Damping in 3d Transition Metal Ferromagnet Monolayers in Contact with Topological Insulator Bi2Se3
|
Engineering Gilbert damping of ferromagnetic metal films is of great
importance to exploit and design spintronic devices that are operated with an
ultrahigh speed. Based on scattering theory of Gilbert damping, we extend the
torque method originally used in studies of magnetocrystalline anisotropy to
theoretically determine Gilbert dampings of ferromagnetic metals. This method
is utilized to investigate Gilbert dampings of 3d transition metal ferromagnet
iron, cobalt and nickel monolayers that are contacted by the prototypical
topological insulator Bi2Se3. Amazingly, we find that their Gilbert dampings
are strongly enhanced by about one order in magnitude, compared with dampings
of their bulks and free-standing monolayers, owing to the strong spin-orbit
coupling of Bi2Se3. Our work provides an attractive route to tailoring Gilbert
damping of ferromagnetic metallic films by putting them in contact with
topological insulators.
|
1902.08700v1
|
2019-07-01
|
Magnon decay theory of Gilbert damping in metallic antiferromagnets
|
Gilbert damping is a key property governing magnetization dynamics in ordered
magnets. We present a theoretical study of intrinsic Gilbert damping induced by
magnon decay in antiferromagnetic metals through $s$-$d$ exchange interaction.
Our theory delineates the qualitative features of damping in metallic
antiferromagnets owing to their bipartite nature, in addition to providing
analytic expressions for the damping parameters. Magnon-induced intraband
electron scattering is found to predominantly cause magnetization damping,
whereas the N\'eel field is found to be damped via disorder. Depending on the
conduction electron band structure, we predict that magnon-induced interband
electron scattering around band crossings may be exploited to engineer a strong
N\'eel field damping.
|
1907.01045v1
|
2019-08-01
|
The Temperature-dependent Damping of Propagating Slow Magnetoacoustic Waves
|
The rapid damping of slow magnetoacoustic waves in the solar corona has been
extensively studied in previous years. Most studies suggest that thermal
conduction is a dominant contributor to this damping, albeit with a few
exceptions. Employing extreme-ultraviolet (EUV) imaging data from SDO/AIA, we
measure the damping lengths of propagating slow magnetoacoustic waves observed
in several fan-like loop structures using two independent methods. The
dependence of the damping length on temperature has been studied for the first
time. The results do not indicate any apparent decrease in damping length with
temperature, which is in contrast to the existing viewpoint. Comparing with the
corresponding theoretical values calculated from damping due to thermal
conduction, it is inferred that thermal conduction is suppressed in hotter
loops. An alternative interpretation that suggests thermal conduction is not
the dominant damping mechanism, even for short period waves in warm active
region loops, is also presented.
|
1908.00384v1
|
2019-10-14
|
Decay rates for the damped wave equation with finite regularity damping
|
Decay rates for the energy of solutions of the damped wave equation on the
torus are studied. In particular, damping invariant in one direction and equal
to a sum of squares of nonnegative functions with a particular number of
derivatives of regularity is considered. For such damping energy decays at rate
$1/t^{2/3}$. If additional regularity is assumed the decay rate improves. When
such a damping is smooth the energy decays at $1/t^{4/5-\delta}$. The proof
uses a positive commutator argument and relies on a pseudodifferential calculus
for low regularity symbols.
|
1910.06372v3
|
2022-07-01
|
Seismic Response of Yielding Structures Coupled to Rocking Walls with Supplemental Damping
|
Given that the coupling of a framing structure to a strong, rocking wall
enforces a first-mode response, this paper investigates the dynamic response of
a yielding single-degree-of-freedom oscillator coupled to a rocking wall with
supplemental damping (hysteretic or linear viscous) along its sides. The full
nonlinear equations of motion are derived, and the study presents an earthquake
response analysis in term of inelastic spectra. The study shows that for
structures with preyielding period T1<1.0 s the effect of supplemental damping
along the sides of the rocking wall is marginal even when large values of
damping are used. The study uncovers that occasionally the damped response
matches or exceeds the undamped response; however, when this happens, the
exceedance is marginal. The paper concludes that for yielding structures with
strength less than 10% of their weight the use of supplemental damping along
the sides of a rocking wall coupled to a yielding structure is not recommended.
The paper shows that supplemental damping along the sides of the rocking wall
may have some limited beneficial effects for structures with longer preyielding
periods (say T1>1.0 s). Nevertheless, no notable further response reduction is
observed when larger values of hysteretic or viscous damping are used.
|
2207.00641v1
|
2022-11-24
|
Influence of non-local damping on magnon properties of ferromagnets
|
We study the influence of non-local damping on magnon properties of Fe, Co,
Ni and Fe$_{1-x}$Co$_{x}$ ($x=30\%,50\%$) alloys. The Gilbert damping parameter
is typically considered as a local scalar both in experiment and in theoretical
modelling. However, recent works have revealed that Gilbert damping is a
non-local quantity that allows for energy dissipation between atomic sites.
With the Gilbert damping parameters calculated from a state-of-the-art
real-space electronic structure method, magnon lifetimes are evaluated from
spin dynamics and linear response, where a good agreement is found between
these two methods. It is found that non-local damping affects the magnon
lifetimes in different ways depending on the system. Specifically, we find that
in Fe, Co, and Ni the non-local damping decreases the magnon lifetimes, while
in $\rm Fe_{70}Co_{30}$ and Fe$_{50}$Co$_{50}$ an opposite, non-local damping
effect is observed, and our data show that it is much stronger in the former.
|
2211.13486v1
|
2023-03-08
|
Material-Geometry Interplay in Damping of Biomimetic Scale Beams
|
Biomimetic scale-covered substrates are architected meta-structures
exhibiting fascinating emergent nonlinearities via the geometry of collective
scales contacts. In spite of much progress in understanding their elastic
nonlinearity, their dissipative behavior arising from scales sliding is
relatively uninvestigated in the dynamic regime. Recently discovered is the
phenomena of viscous emergence, where dry Coulomb friction between scales can
lead to apparent viscous damping behavior of the overall multi-material
substrate. In contrast to this structural dissipation, material dissipation
common in many polymers has never been considered, especially synergestically
with geometrical factors. This is addressed here for the first time, where
material visco-elasticity is introduced via a simple Kelvin-Voigt model for
brevity and clarity. The results contrast the two damping sources in these
architectured systems: material viscoelasticity, and geometrical frictional
scales contact. It is discovered that although topically similar in effective
damping, viscoelsatic damping follows a different damping envelope than dry
friction, including starkly different effects on damping symmetry and specific
damping capacity.
|
2303.04920v1
|
2009-04-30
|
Wavelength Accuracy of the Keck HIRES Spectrograph and Measuring Changes in the Fine Structure Constant
|
We report on an attempt to accurately wavelength calibrate four nights of
data taken with the Keck HIRES spectrograph on QSO PHL957, for the purpose of
determining whether the fine structure constant was different in the past.
Using new software and techniques, we measured the redshifts of various Ni II,
Fe II, Si II, etc. lines in a damped Ly-alpha system at z=2.309. Roughly half
the data was taken through the Keck iodine cell which contains thousands of
well calibrated iodine lines. Using these iodine exposures to calibrate the
normal Th-Ar Keck data pipeline output we found absolute wavelength offsets of
500 m/s to 1000 m/s with drifts of more than 500 m/s over a single night, and
drifts of nearly 2000 m/s over several nights. These offsets correspond to an
absolute redshift of uncertainty of about Delta z=10^{-5} (Delta lambda= 0.02
Ang), with daily drifts of around Delta z=5x10^{-6} (Delta lambda =0.01 Ang),
and multiday drifts of nearly Delta z=2x10^{-5} (0.04 Ang). The causes of the
wavelength offsets are not known, but since claimed shifts in the fine
structure constant would result in velocity shifts of less than 100 m/s, this
level of systematic uncertainty makes may make it difficult to use Keck HIRES
data to constrain the change in the fine structure constant. Using our
calibrated data, we applied both our own fitting software and standard fitting
software to measure (Delta alpha)/alpha, but discovered that we could obtain
results ranging from significant detection of either sign, to strong null
limits, depending upon which sets of lines and which fitting method was used.
We thus speculate that the discrepant results on (Delta alpha)/alpha reported
in the literature may be due to random fluctuations coming from under-estimated
systematic errors in wavelength calibration and fitting procedure.
|
0904.4725v2
|
2017-12-11
|
Self-acceleration in scalar-bimetric theories
|
We describe scalar-bimetric theories where the dynamics of the Universe are
governed by two separate metrics, each with an Einstein-Hilbert term. In this
setting, the baryonic and dark matter components of the Universe couple to
metrics which are constructed as functions of these two gravitational metrics.
The scalar field, contrary to dark energy models, does not have a potential
whose role is to mimic a late-time cosmological constant. The late-time
acceleration of the expansion of the Universe can be easily obtained at the
background level in these models by appropriately choosing the coupling
functions appearing in the decomposition of the vierbeins for the baryonic and
dark matter metrics. We explicitly show how the concordance model can be
retrieved with negligible scalar kinetic energy. This requires the scalar
coupling functions to show variations of order unity during the accelerated
expansion era. This leads in turn to deviations of order unity for the
effective Newton constants and a fifth force that is of the same order as
Newtonian gravity, with peculiar features. The baryonic and dark matter
self-gravities are amplified although the gravitational force between baryons
and dark matter is reduced and even becomes repulsive at low redshift. This
slows down the growth of baryonic density perturbations on cosmological scales,
while dark matter perturbations are enhanced. In our local environment, the
upper bound on the time evolution of Newton's constant requires an efficient
screening mechanism that both damps the fifth force on small scales and
decouples the local value of Newton constant from its cosmological value. This
cannot be achieved by a quasi-static chameleon mechanism, and requires going
beyond the quasi-static regime and probably using derivative screenings, such
as Kmouflage or Vainshtein screening, on small scales.
|
1712.04520v2
|
1998-03-28
|
Landau damping and the echo effect in a confined Bose-Einstein condensate
|
Low energy collective mode of a confined Bose-Einstein condensate should
demonstrate the echo effect in the regime of Landau damping. This echo is a
signature of reversible nature of Landau damping. General expression for the
echo profile is derived in the limit of small amplitudes of the external
pulses. Several universal features of the echo are found. The existence of echo
in other cases of reversible damping -- Fano effect and Caldeira-Leggett model
-- is emphasized. It is suggested to test reversible nature of the damping in
the atomic traps by conducting the echo experiment.
|
9803351v1
|
2000-07-10
|
Dephasing of Electrons on Helium by Collisions with Gas Atoms
|
The damping of quantum effects in the transport properties of electrons
deposited on a surface of liquid helium is studied. It is found that due to
vertical motion of the helium vapour atoms the interference of paths of
duration $t$ is damped by a factor $\exp - (t/\tau_v)^3$. An expression is
derived for the weak-localization lineshape in the case that damping occurs by
a combination of processes with this type of cubic exponential damping and
processes with a simple exponential damping factor.
|
0007160v1
|
1997-10-07
|
Damping rate of plasmons and photons in a degenerate nonrelativistic plasma
|
A calculation is presented of the plasmon and photon damping rates in a dense
nonrelativistic plasma at zero temperature, following the resummation program
of Braaten-Pisarski. At small soft momentum $k$, the damping is dominated by $3
\to 2$ scattering processes corresponding to double longitudinal Landau
damping. The dampings are proportional to $(\alpha/v_{F})^{3/2} k^2/m$, where
$v_{F}$ is the Fermi velocity.
|
9710260v1
|
2002-12-16
|
Influence of damping on the vanishing of the electro-optic effect in chiral isotropic media
|
Using first principles, it is demonstrated that radiative damping alone
cannot lead to a nonvanishing electro-optic effect in a chiral isotropic
medium. This conclusion is in contrast with that obtained by a calculation in
which damping effects are included using the standard phenomenological model.
We show that these predictions differ because the phenomenological damping
equations are valid only in regions where the frequencies of the applied
electromagnetic fields are nearly resonant with the atomic transitions. We also
show that collisional damping can lead to a nonvanishing electrooptic effect,
but with a strength sufficiently weak that it is unlikely to be observable
under realistic laboratory conditions.
|
0212089v1
|
2005-08-28
|
Simultaneous amplitude and phase damping of a kind of Gaussian states and their separability
|
We give out the time evolution solution of simultaneous amplitude and phase
damping for any continuous variable state. For the simultaneous amplitude and
phase damping of a wide class of two- mode entangled Gaussian states, two
analytical conditions of the separability are given. One is the sufficient
condition of separability. The other is the condition of PPT separability where
the Peres-Horodecki criterion is applied. Between the two conditions there may
exist bound entanglement. The simplest example is the simultaneous amplitude
and phase damping of a two-mode squeezed vacuum state. The damped state is
non-Gaussian.
|
0508209v2
|
2007-08-28
|
Ising Dynamics with Damping
|
We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality.
|
0708.3855v1
|
2008-02-08
|
On the scaling of the damping time for resonantly damped oscillations in coronal loops
|
There is not as yet full agreement on the mechanism that causes the rapid
damping of the oscillations observed by TRACE in coronal loops. It has been
suggested that the variation of the observed values of the damping time as
function of the corresponding observed values of the period contains
information on the possible damping mechanism. The aim of this Letter is to
show that, for resonant absorption, this is definitely not the case unless
detailed a priori information on the individual loops is available.
|
0802.1143v1
|
2008-10-02
|
Critically damped quantum search
|
Although measurement and unitary processes can accomplish any quantum
evolution in principle, thinking in terms of dissipation and damping can be
powerful. We propose a modification of Grover's algorithm in which the idea of
damping plays a natural role. Remarkably, we have found that there is a
critical damping value that divides between the quantum $O(\sqrt{N})$ and
classical O(N) search regimes. In addition, by allowing the damping to vary in
a fashion we describe, one obtains a fixed-point quantum search algorithm in
which ignorance of the number of targets increases the number of oracle queries
only by a factor of 1.5.
|
0810.0470v1
|
2009-07-01
|
Modal approximations to damped linear systems
|
We consider a finite dimensional damped second order system and obtain
spectral inclusion theorems for the related quadratic eigenvalue problem. The
inclusion sets are the 'quasi Cassini ovals' which may greatly outperform
standard Gershgorin circles. As the unperturbed system we take a modally damped
part of the system; this includes the known proportionally damped models, but
may give much sharper estimates. These inclusions are then applied to derive
some easily calculable sufficient conditions for the overdampedness of a given
damped system.
|
0907.0167v1
|
2010-01-14
|
Multi-Error-Correcting Amplitude Damping Codes
|
We construct new families of multi-error-correcting quantum codes for the
amplitude damping channel. Our key observation is that, with proper encoding,
two uses of the amplitude damping channel simulate a quantum erasure channel.
This allows us to use concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction.
|
1001.2356v1
|
2011-09-05
|
Spectral theory of damped quantum chaotic systems
|
We investigate the spectral distribution of the damped wave equation on a
compact Riemannian manifold, especially in the case of a metric of negative
curvature, for which the geodesic flow is Anosov. The main application is to
obtain conditions (in terms of the geodesic flow on $X$ and the damping
function) for which the energy of the waves decays exponentially fast, at least
for smooth enough initial data. We review various estimates for the high
frequency spectrum in terms of dynamically defined quantities, like the value
distribution of the time-averaged damping. We also present a new condition for
a spectral gap, depending on the set of minimally damped trajectories.
|
1109.0930v1
|
2012-06-07
|
From resolvent estimates to damped waves
|
In this paper we show how to obtain decay estimates for the damped wave
equation on a compact manifold without geometric control via knowledge of the
dynamics near the un-damped set. We show that if replacing the damping term
with a higher-order \emph{complex absorbing potential} gives an operator
enjoying polynomial resolvent bounds on the real axis, then the "resolvent"
associated to our damped problem enjoys bounds of the same order. It is known
that the necessary estimates with complex absorbing potential can also be
obtained via gluing from estimates for corresponding non-compact models.
|
1206.1565v1
|
2012-12-03
|
Inviscid limit of stochastic damped 2D Navier-Stokes equations
|
We consider the inviscid limit of the stochastic damped 2D Navier- Stokes
equations. We prove that, when the viscosity vanishes, the stationary solution
of the stochastic damped Navier-Stokes equations converges to a stationary
solution of the stochastic damped Euler equation and that the rate of
dissipation of enstrophy converges to zero. In particular, this limit obeys an
enstrophy balance. The rates are computed with respect to a limit measure of
the unique invariant measure of the stochastic damped Navier-Stokes equations.
|
1212.0509v3
|
2014-01-13
|
NLSE for quantum plasmas with the radiation damping
|
We consider contribution of the radiation damping in the quantum hydrodynamic
equations for spinless particles. We discuss possibility of obtaining of
corresponding non-linear Schrodinger equation (NLSE) for the macroscopic wave
function. We compare contribution of the radiation damping with weakly (or
semi-) relativistic effects appearing in the second order by v/c. The radiation
damping appears in the third order by v/c. So it might be smaller than weakly
relativistic effects, but it gives damping of the Langmuir waves which can be
considerable.
|
1401.2829v1
|
2014-09-26
|
An ultimate storage ring lattice with vertical emittance generated by damping wigglers
|
We discuss the approach of generating round beams for ultimate storage rings
using vertical damping wigglers (with horizontal magnetic field). The vertical
damping wigglers provide damping and excite vertical emittance. This eliminates
the need to generate large linear coupling that is impractical with traditional
off-axis injection. We use a PEP-X compatible lattice to demonstrate the
approach. This lattice uses separate quadrupole and sextupole magnets with
realistic gradient strengths. Intrabeam scattering effects are calculated. The
horizontal and vertical emittances are 22.3 pm and 10.3 pm, respectively, for a
200 mA, 4.5 GeV beam, with a vertical damping wiggler of a total length of 90
meters, peak field of 1.5 T and wiggler period of 100 mm.
|
1409.7452v2
|
2016-08-14
|
Mechanical energy and mean equivalent viscous damping for SDOF fractional oscillators
|
This paper addresses the total mechanical energy of a single degree of
freedom fractional oscillator. Based on the energy storage and dissipation
properties of the Caputo fractional derivatives, the expression for total
mechanical energy in the single degree of freedom fractional oscillator is
firstly presented. The energy regeneration due to the external exciting force
and the energy loss due to the fractional damping force during the vibratory
motion are analyzed. Furthermore, based on the mean energy dissipation of the
fractional damping element in steady-state vibration, a new concept of mean
equivalent viscous damping is suggested and the value of the damping
coefficient is evaluated.
|
1608.04071v1
|
2017-03-01
|
Behaviors of the energy of solutions of two coupled wave equations with nonlinear damping on a compact manifold with boundary
|
In this paper we study the behaviors of the the energy of solutions of
coupled wave equations on a compact manifold with boundary in the case of
indirect nonlinear damping . Only one of the two equations is directly damped
by a localized nonlinear damping term. Under geometric conditions on both the
coupling and the damping regions we prove that the rate of decay of the energy
of smooth solutions of the system is determined from a first order differential
equation .
|
1703.00172v1
|
2017-06-02
|
Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions
|
We consider the damped and driven Navier--Stokes system with stress free
boundary conditions and the damped Euler system in a bounded domain
$\Omega\subset\mathbf{R}^2$. We show that the damped Euler system has a
(strong) global attractor in~$H^1(\Omega)$. We also show that in the vanishing
viscosity limit the global attractors of the Navier--Stokes system converge in
the non-symmetric Hausdorff distance in $H^1(\Omega)$ to the the strong global
attractor of the limiting damped Euler system (whose solutions are not
necessarily unique).
|
1706.00607v1
|
2018-01-20
|
Long time dynamics for weakly damped nonlinear Klein-Gordon equations
|
We continue our study of damped nonlinear Klein-Gordon equations. In our
previous work we considered fixed positive damping and proved a form of the
soliton resolution conjecture for radial solutions. In contrast, here we
consider damping which decreases in time to 0. In the class of radial data we
again establish soliton resolution provided the damping goes to 0 sufficiently
slowly. While our previous work relied on invariant manifold theory, here we
use the Lojasiewicz-Simon inequality applied to a suitable Lyapunov functional.
|
1801.06735v1
|
2018-02-28
|
Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity
|
In our previous two works, we studied the blow-up and lifespan estimates for
damped wave equations with a power nonlinearity of the solution or its
derivative, with scattering damping independently. In this work, we are devoted
to establishing a similar result for a combined nonlinearity. Comparing to the
result of wave equation without damping, one can say that the scattering
damping has no influence.
|
1802.10273v1
|
2018-11-12
|
Choking non-local magnetic damping in exchange biased ferromagnets
|
We investigated the temperature dependence of the magnetic damping in the
exchange biased Pt/ Fe50Mn50 /Fe20Ni80 /SiOx multilayers. In samples having a
strong exchange bias, we observed a drastic decrease of the magnetic damping of
the FeNi with increasing temperature up to the blocking temperature. The
results essentially indicate that the non-local enhancement of the magnetic
damping can be choked by the adjacent antiferromagnet and its temperature
dependent exchange bias. We also pointed out that such a strong temperature
dependent damping may be very beneficial for spintronic applications.
|
1811.04821v1
|
2019-05-23
|
Escaping Locally Optimal Decentralized Control Polices via Damping
|
We study the evolution of locally optimal decentralized controllers with the
damping of the control system. Empirically it is shown that even for instances
with an exponential number of connected components, damping merges all local
solutions to the one global solution. We characterize the evolution of locally
optimal solutions with the notion of hemi-continuity and further derive
asymptotic properties of the objective function and of the locally optimal
controllers as the damping becomes large. Especially, we prove that with enough
damping, there is no spurious locally optimal controller with favorable control
structures. The convoluted behavior of the locally optimal trajectory is
illustrated with numerical examples.
|
1905.09915v1
|
2019-08-22
|
Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equations
|
In this paper, we are interested in analyzing the asymptotic profiles of
solutions to the Cauchy problem for linear structurally damped
$\sigma$-evolution equations in $L^2$-sense. Depending on the parameters
$\sigma$ and $\delta$ we would like to not only indicate approximation formula
of solutions but also recognize the optimality of their decay rates as well in
the distinct cases of parabolic like damping and $\sigma$-evolution like
damping. Moreover, such results are also discussed when we mix these two kinds
of damping terms in a $\sigma$-evolution equation to investigate how each of
them affects the asymptotic profile of solutions.
|
1908.08492v1
|
2019-09-18
|
Global smooth solutions of the damped Boussinesq equations with a class of large initial data
|
The global regularity problem concerning the inviscid Boussinesq equations
remains an open problem. In an attempt to understand this problem, we examine
the damped Boussinesq equations and study how damping affects the regularity of
solutions. In this paper, we consider the global existence to the damped
Boussinesq equations with a class of large initial data, whose $B^{s}_{p,r}$ or
$\dot{B}^{s}_{p,r}$ norms can be arbitrarily large. The idea is splitting the
linear Boussinesq equations from the damped Boussinesq equations, the
exponentially decaying solution of the former equations together with the
structure of the Boussinesq equations help us to obtain the global smooth
solutions.
|
1909.08360v1
|
2020-02-15
|
Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping
|
We introduce a new model of the nonlocal wave equations with a logarithmic
damping mechanism. We consider the Cauchy poroblem for the new model in the
whole space. We study the asymptotic profile and optimal decay and blowup rates
of solutions as time goes to infinity. The damping terms considered in this
paper is not studied so far, and in the low frequency parameters the damping is
rather weakly effective than that of well-studied fractional type of nonlocal
damping. In order to get the optimal estimates in time we meet the so-called
hypergeometric functions with special parameters.
|
2002.06319v1
|
2020-05-13
|
Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping
|
In this paper, we study input-to-state (ISS) issues for damped wave equations
with Dirichlet boundary conditions on a bounded domain of dimension two. The
damping term is assumed to be non-linear and localized to an open subset of the
domain. In a first step, we handle the undisturbed case as an extension of a
previous work, where stability results are given with a damping term active on
the full domain. Then, we address the case with disturbances and provide
input-to-state types of results.
|
2005.06206v3
|
2020-07-25
|
Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping
|
We study the energy decay rate of the Kelvin-Voigt damped wave equation with
piecewise smooth damping on the multi-dimensional domain. Under suitable
geometric assumptions on the support of the damping, we obtain the optimal
polynomial decay rate which turns out to be different from the one-dimensional
case studied in \cite{LR05}. This optimal decay rate is saturated by high
energy quasi-modes localised on geometric optics rays which hit the interface
along non orthogonal neither tangential directions. The proof uses
semi-classical analysis of boundary value problems.
|
2007.12994v2
|
2020-08-12
|
From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation
|
Using a correspondence between the spectrum of the damped wave equation and
non-self-adjoint Schroedinger operators, we derive various bounds on complex
eigenvalues of the former. In particular, we establish a sharp result that the
one-dimensional damped wave operator is similar to the undamped one provided
that the L^1 norm of the (possibly complex-valued) damping is less than 2. It
follows that these small dampings are spectrally undetectable.
|
2008.05176v1
|
2021-08-02
|
Wide-Area Damping Control for Interarea Oscillations in Power Grids Based on PMU Measurements
|
In this paper, a phasor measurement unit (PMU)-based wide-area damping
control method is proposed to damp the interarea oscillations that threaten the
modern power system stability and security. Utilizing the synchronized PMU
data, the proposed almost model-free approach can achieve an effective damping
for the selected modes using a minimum number of synchronous generators.
Simulations are performed to show the validity of the proposed wide-area
damping control scheme.
|
2108.01193v1
|
2021-09-05
|
Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case
|
In this paper, we examine regularity issues for two damped abstract elastic
systems; the damping and coupling involve fractional powers $\mu, \theta$, with
$0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining
the coupling and damping is nondegenerate. This new work is a sequel to the
degenerate case that we discussed recently in \cite{kfl}. First, we prove that
for $1/2 \leq \mu , \theta \leq 1$, the underlying semigroup is analytic. Next,
we show that for $\min(\mu,\theta) \in (0,1/2)$, the semigroup is of certain
Gevrey classes. Finally, some examples of application are provided.
|
2109.02044v1
|
2021-09-28
|
A robust and efficient line search for self-consistent field iterations
|
We propose a novel adaptive damping algorithm for the self-consistent field
(SCF) iterations of Kohn-Sham density-functional theory, using a backtracking
line search to automatically adjust the damping in each SCF step. This line
search is based on a theoretically sound, accurate and inexpensive model for
the energy as a function of the damping parameter. In contrast to usual damped
SCF schemes, the resulting algorithm is fully automatic and does not require
the user to select a damping. We successfully apply it to a wide range of
challenging systems, including elongated supercells, surfaces and
transition-metal alloys.
|
2109.14018v3
|
2021-11-17
|
Spectral asymptotics for the vectorial damped wave equation
|
The eigenfrequencies associated to a scalar damped wave equation are known to
belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand
showed that up to a set of density 0, the eigenfrequencies are confined in a
thinner band determined by the Birkhoff limits of the damping term. In this
article we show that this result is still true for a vectorial damped wave
equation. In this setting the Lyapunov exponents of the cocycle given by the
damping term play the role of the Birkhoff limits of the scalar setting.
|
2111.08982v1
|
2021-12-13
|
Rotons and their damping in elongated dipolar Bose-Einstein condensates
|
We discuss finite temperature damping of rotons in elongated Bose-condensed
dipolar gases, which are in the Thomas-Fermi regime in the tightly confined
directions. The presence of many branches of excitations which can participate
in the damping process, is crucial for the Landau damping and results in
significant increase of the damping rate. It is found, however, that even
rotons with energies close to the roton gap may remain fairly stable in systems
with the roton gap as small as 1nK.
|
2112.06835v2
|
2022-03-03
|
Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint
|
In this paper, we study the direct/indirect stability of locally coupled wave
equations with local Kelvin-Voigt dampings/damping and by assuming that the
supports of the dampings and the coupling coefficients are disjoint. First, we
prove the well-posedness, strong stability, and polynomial stability for some
one dimensional coupled systems. Moreover, under some geometric control
condition, we prove the well-posedness and strong stability in the
multi-dimensional case.
|
2203.01632v1
|
2022-03-12
|
Asymptotic expansion of solutions to the wave equation with space-dependent damping
|
We study the large time behavior of solutions to the wave equation with
space-dependent damping in an exterior domain. We show that if the damping is
effective, then the solution is asymptotically expanded in terms of solutions
of corresponding parabolic equations. The main idea to obtain the asymptotic
expansion is the decomposition of the solution of the damped wave equation into
the solution of the corresponding parabolic problem and the time derivative of
the solution of the damped wave equation with certain inhomogeneous term and
initial data. The estimate of the remainder term is an application of weighted
energy method with suitable supersolutions of the corresponding parabolic
problem.
|
2203.06360v1
|
2022-10-27
|
Sharp polynomial decay for polynomially singular damping on the torus
|
We study energy decay rates for the damped wave equation with unbounded
damping, without the geometric control condition. Our main decay result is
sharp polynomial energy decay for polynomially controlled singular damping on
the torus. We also prove that for normally $L^p$-damping on compact manifolds,
the Schr\"odinger observability gives $p$-dependent polynomial decay, and
finite time extinction cannot occur. We show that polynomially controlled
singular damping on the circle gives exponential decay.
|
2210.15697v3
|
2023-09-26
|
Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam
|
We consider a nonlinear transmission problem for a Bresse beam, which
consists of two parts, damped and undamped. The mechanical damping in the
damped part is present in the shear angle equation only, and the damped part
may be of arbitrary positive length. We prove well-posedness of the
corresponding PDE system in energy space and establish existence of a regular
global attractor under certain conditions on nonlinearities and coefficients of
the damped part only. Moreover, we study singular limits of the problem when
$l\to 0$ or $l\to 0$ simultaneously with $k_i\to +\infty$ and perform numerical
modelling for these processes.
|
2309.15171v2
|
2023-09-27
|
Dispersion and damping of ion-acoustic waves in the plasma with a regularized kappa-distribution
|
The dispersion and damping of ion-acoustic waves in the plasma with a
regularized kappa-distribution are studied. The generalized dispersion relation
and damping rate are derived, which both depend significantly on the parameters
alpha and kappa. The numerical analyses show that the wave frequency and the
damping rate of ion-acoustic waves in the plasma with the regularized
kappa-distribution are both generally less than those in the plasma with the
kappa-distribution, and if kappa is less than a value, the ion-acoustic waves
and their damping rate exist in the plasma with the regularized
kappa-distribution.
|
2309.15885v1
|
2023-11-16
|
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
|
We introduce an autonomous system with closed-loop damping for first-order
convex optimization. While, to this day, optimal rates of convergence are only
achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's
algorithm), we show that our system is the first one featuring a closed-loop
damping while exhibiting a rate arbitrarily close to the optimal one. We do so
by coupling the damping and the speed of convergence of the system via a
well-chosen Lyapunov function. We then derive a practical first-order algorithm
called LYDIA by discretizing our system, and present numerical experiments
supporting our theoretical findings.
|
2311.10053v1
|
2024-02-05
|
Fractional damping induces resonant behavior in the Duffing oscillator
|
The interaction between the fractional order parameter and the damping
parameter can play a relevant role for introducing different dynamical
behaviors in a physical system. Here, we study the Duffing oscillator with a
fractional damping term. Our findings show that for certain values of the
fractional order parameter, the damping parameter, and the forcing amplitude
high oscillations amplitude can be induced. This phenomenon is due to the
appearance of a resonance in the Duffing oscillator only when the damping term
is fractional.
|
2402.02940v1
|
2024-03-13
|
Impact of Decoherence on Average Correlation
|
This article presents a comprehensive study of the impact of decoherence on
the average correlation for pure quantum states. We explore two primary
mechanisms of decoherence: phase damping and amplitude damping, each having
distinct effects on quantum systems. Phase damping, which describes the loss of
quantum coherence without energy loss, primarily affects the phase
relationships between the components of a quantum system while amplitude
damping involves energy dissipation and also affects the state's occupation
probabilities. We show that the average correlation follows a predictable
decaying pattern in both scenarios. Our analysis can be understood in the
context of quantum computing, by focusing on how phase damping influences the
entanglement and correlation between qubits, key factors in quantum
computational efficiency and error correction protocols.
|
2403.10551v1
|
2001-10-29
|
Kinetic equilibrium of iron in the atmospheres of cool dwarf stars II. Weak Fe I lines in the solar spectrum
|
NLTE line formation calculations of FeI in the solar atmosphere are extended
to include weak optical lines. Previously established atomic models are used to
discriminate between different ways of treating collisional interaction
processes. To derive a common solar FeI abundance from both strong and weak
lines, fine-tuning of the microturbulence velocity parameter and the van-der-
Waals damping constants is required. The solar FeI abundances based on all
available f-values are dominated by the large scatter already found for the
stronger lines. In particular the bulk of the data from the work of May et al.
and O'Brian et al. is not adequate for accurate abundance work. Based on
f-values measured by the Hannover and Oxford groups alone, the FeI LTE
abundances are eps(FeI,Sun)=7.57 for the empirical and eps(FeI,Sun) = 7.48 ...
7.51 for the line-blanketed solar model. The solar Fe ionization equilibrium
obtained for different atomic and atmospheric models rules out NLTE atomic
models with a low efficiency of hydrogen collisions. At variance with Paper I,
it is now in better agreement with laboratory FeII f-values for all types of
line-blanketed models. Our final model assumptions consistent with a single
unique solar Fe abundance eps(Fe,Sun) = 7.48 ... 7.51 calculated from NLTE line
formation are (a) a line-blanketed solar model atmosphere, (b) an iron model
atom with hydrogen collision rates 0.5 < S_H < 5 times the standard value to
compensate for the large photoionization cross-sections, (c) a microturbulence
velocity xi = 1.0 kms, (d) van-der-Waals damping parameters decreased by
Delta(log C6) = -0.10...-0.15 as compared to Anstee & O'Mara's calculations,
depending on S_H, (e) FeII f-values as published by Schnabel et al., and (f)
FeI f-values published by the Hannover and Oxford groups.
|
0110605v1
|
2003-11-05
|
Are rotating strange quark stars good sources of gravitational waves?
|
We study the viscosity driven (Jacobi-like) bar mode instability of rapidly
rotating strange stars in general relativity. A triaxial, "bar shaped" compact
star could be an efficient source of continuous wave gravitational radiation in
the frequency range of the forthcoming interferometric detectors. We locate the
secular instability point along several constant baryon mass sequences of
uniformly rotating strange stars described by the MIT bag model. Contrary to
neutron stars, strange stars with T/|W| (the ratio of the rotational kinetic
energy to the absolute value of the gravitational potential energy) much lower
than the corresponding value for the mass-shed limit can be secularly unstable
to bar mode formation if shear viscosity is high enough to damp out any
deviation from uniform rotation. The instability develops for a broad range of
gravitational masses and rotational frequencies of strange quark stars. It
imposes strong constraints on the lower limit of the frequency at the innermost
stable circular orbit around rapidly rotating strange stars. The above results
are robust for all linear self-bound equations of state assuming the growth
time of the instability is faster than the damping timescale. We discuss
astrophysical scenarios where triaxial instabilities (r-mode and viscosity
driven instability) could be relevant in strange stars described by the
standard MIT bag model of normal quark matter. Taking into account actual
values of viscosities in strange quark matter and neglecting the magnetic field
we show that Jacobi-like instability cannot develop in any astrophysicaly
interesting temperature windows. The main result is that strange quark stars
described by the MIT bag model can be accelerated to very high frequency in Low
Mass X-ray binaries if the strange quark mass is ~ 200 MeV or higher.
|
0311128v1
|
2003-11-24
|
Sulphur and zinc abundances in Galactic stars and damped Lyman-alpha systems
|
High resolution spectra of 34 halo population dwarf and subgiant stars have
been obtained with VLT/UVES and used to derive sulphur abundances from the
8694.0, 8694.6 A and 9212.9, 9237.5 A SI lines. In addition, iron abundances
have been determined from 19 FeII lines and zinc abundances from the 4722.2,
4810.5 ZnI lines. The abundances are based on a classical 1D, LTE model
atmosphere analysis, but effects of 3D hydrodynamical modelling on the [S/Fe],
[Zn/Fe] and [S/Zn] ratios are shown to be small. We find that most halo stars
with metallicities in the range -3.2 < [Fe/H] < -0.8 have a near-constant
[S/Fe] = +0.3; a least square fit to [S/Fe] vs. {Fe/H] shows a slope of only
-0.04 +/- 0.01. Among halo stars with -1.2 < [Fe/H] < -0.8 the majority have
[S/Fe] ~ +0.3, but two stars (previously shown to have low [alpha/Fe] ratios)
have [S/Fe] ~ 0. For disk stars with [Fe/H] > -1, [S/Fe] decreases with
increasing [Fe/H]. Hence, sulphur behaves like other typical alpha-capture
elements, Mg, Si and Ca. Zinc, on the other hand, traces iron over three orders
of magnitude in [Fe/H], although there is some evidence for a small systematic
Zn overabundance ([Zn/Fe] ~ +0.1) among metal-poor disk stars and for halo
stars with [Fe/H] < -2.0. Recent measurements of S and Zn in ten damped
Ly-alpha systems (DLAs) with redshifts between 1.9 and 3.4 and zinc abundances
in the range -2.1 < [Zn/H] < -0.15 show an offset relative to the [S/Zn] -
[Zn/H] relation in Galactic stars. Possible reasons for this offset are
discussed, including low and intermittent star formation rates in DLAs.
|
0311529v1
|
2004-12-13
|
Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
|
Dislocation velocities and mobilities are studied by Molecular Dynamics
simulations for edge and screw dislocations in pure aluminum and nickel, and
edge dislocations in Al-2.5%Mg and Al-5.0%Mg random substitutional alloys using
EAM potentials. In the pure materials, the velocities of all dislocations are
close to linear with the ratio of (applied stress)/(temperature) at low
velocities, consistent with phonon drag models and quantitative agreement with
experiment is obtained for the mobility in Al. At higher velocities, different
behavior is observed. The edge dislocation velocity remains dependent solely on
(applied stress)/(temperature) up to approximately 1.0 MPa/K, and approaches a
plateau velocity that is lower than the smallest "forbidden" speed predicted by
continuum models. In contrast, above a velocity around half of the smallest
continuum wave speed, the screw dislocation damping has a contribution
dependent solely on stress with a functional form close to that predicted by a
radiation damping model of Eshelby. At the highest applied stresses, there are
several regimes of nearly constant (transonic or supersonic) velocity separated
by velocity gaps in the vicinity of forbidden velocities; various modes of
dislocation disintegration and destabilization were also encountered in this
regime. In the alloy systems, there is a temperature- and
concentration-dependent pinning regime where the velocity drops sharply below
the pure metal velocity. Above the pinning regime but at moderate stresses, the
velocity is again linear in (applied stress)/(temperature) but with a lower
mobility than in the pure metal.
|
0412324v1
|
2009-12-28
|
Resonant Interactions Between Protons and Oblique Alfvén/Ion-Cyclotron Waves
|
Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves
may play an important role in the heating and acceleration of the fast solar
wind. Although such interactions have been studied extensively for "parallel"
waves, whose wave vectors ${\bf k}$ are aligned with the background magnetic
field ${\bf B}_0$, much less is known about interactions between ions and
oblique A/IC waves, for which the angle $\theta$ between ${\bf k}$ and ${\bf
B}_0$ is nonzero. In this paper, we present new numerical results on resonant
cyclotron interactions between protons and oblique A/IC waves in collisionless
low-beta plasmas such as the solar corona. We find that if some mechanism
generates oblique high-frequency A/IC waves, then these waves initially modify
the proton distribution function in such a way that it becomes unstable to
parallel waves. Parallel waves are then amplified to the point that they
dominate the wave energy at the large parallel wave numbers at which the waves
resonate with the particles. Pitch-angle scattering by these waves then causes
the plasma to evolve towards a state in which the proton distribution is
constant along a particular set of nested "scattering surfaces" in velocity
space, whose shapes have been calculated previously. As the distribution
function approaches this state, the imaginary part of the frequency of parallel
A/IC waves drops continuously towards zero, but oblique waves continue to
undergo cyclotron damping while simultaneously causing protons to diffuse
across these kinetic shells to higher energies. We conclude that oblique A/IC
waves can be more effective at heating protons than parallel A/IC waves,
because for oblique waves the plasma does not relax towards a state in which
proton damping of oblique A/IC waves ceases.
|
0912.5184v1
|
2011-06-14
|
The most metal-poor damped Lyman-alpha systems: Insights into chemical evolution in the very metal-poor regime
|
We present a high spectral resolution survey of the most metal-poor damped
Lyman-alpha absorption systems (DLAs) aimed at probing the nature and
nucleosynthesis of the earliest generations of stars. Our survey comprises 22
systems with iron abundance less than 1/100 solar; observations of seven of
these are reported here for the first time. Together with recent measures of
the abundances of C and O in Galactic metal-poor stars, we reinvestigate the
trend of C/O in the very metal-poor regime and we compare, for the first time,
the O/Fe ratios in the most metal-poor DLAs and in halo stars. We confirm the
near-solar values of C/O in DLAs at the lowest metallicities probed, and find
that their distribution is in agreement with that seen in Galactic halo stars.
We find that the O/Fe ratio in very metal-poor (VMP) DLAs is essentially
constant, and shows very little dispersion, with a mean [<O/Fe>] = +0.39 +/-
0.12, in good agreement with the values measured in Galactic halo stars when
the oxygen abundance is measured from the [O I] 6300 line. We speculate that
such good agreement in the observed abundance trends points to a universal
origin for these metals. In view of this agreement, we construct the abundance
pattern for a typical very metal-poor DLA and compare it to model calculations
of Population II and Population III nucleosynthesis to determine the origin of
the metals in VMP DLAs. Our results suggest that the most metal-poor DLAs may
have been enriched by a generation of metal-free stars; however, given that
abundance measurements are currently available for only a few elements, we
cannot yet rule out an additional contribution from Population II stars.
|
1106.2805v2
|
2012-07-24
|
Doppler Signatures of the Atmospheric Circulation on Hot Jupiters
|
The meteorology of hot Jupiters has been characterized primarily with thermal
measurements, but recent observations suggest the possibility of directly
detecting the winds by observing the Doppler shift of spectral lines seen
during transit. Motivated by these observations, we show how Doppler
measurements can place powerful constraints on the meteorology. We show that
the atmospheric circulation--and Doppler signature--of hot Jupiters splits into
two regimes. Under weak stellar insolation, the day-night thermal forcing
generates fast zonal jet streams from the interaction of atmospheric waves with
the mean flow. In this regime, air along the terminator (as seen during
transit) flows toward Earth in some regions and away from Earth in others,
leading to a Doppler signature exhibiting superposed blueshifted and redshifted
components. Under intense stellar insolation, however, the strong thermal
forcing damps these planetary-scale waves, inhibiting their ability to generate
jets. Strong frictional drag likewise damps these waves and inhibits jet
formation. As a result, this second regime exhibits a circulation dominated by
high-altitude, day-to-night airflow, leading to a predominantly blueshifted
Doppler signature during transit. We present state-of-the-art circulation
models including nongray radiative transfer to quantify this regime shift and
the resulting Doppler signatures; these models suggest that cool planets like
GJ 436b lie in the first regime, HD 189733b is transitional, while planets
hotter than HD 209458b lie in the second regime. Moreover, we show how the
amplitude of the Doppler shifts constrains the strength of frictional drag in
the upper atmospheres of hot Jupiters. If due to winds, the ~2-km/sec blueshift
inferred on HD 209458b may require drag time constants as short as 10^4-10^6
seconds, possibly the result of Lorentz-force braking on this planet's hot
dayside.
|
1207.5639v2
|
2013-01-30
|
Tickling the CMB damping tail: scrutinizing the tension between the ACT and SPT experiments
|
The Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) have
recently provided new, very precise measurements of the cosmic microwave
background (CMB) anisotropy damping tail. The values of the cosmological
parameters inferred from these measurements, while broadly consistent with the
expectations of the standard cosmological model, are providing interesting
possible indications for new physics that are definitely worth of
investigation. The ACT results, while compatible with the standard expectation
of three neutrino families, indicate a level of CMB lensing, parametrized by
the lensing amplitude parameter A_L, that is about 70% higher than expected. If
not a systematic, this anomalous lensing amplitude could be produced by
modifications of general relativity or coupled dark energy. Vice-versa, the SPT
experiment, while compatible with a standard level of CMB lensing, prefers an
excess of dark radiation, parametrized by the effective number of relativistic
degrees of freedom N_eff. Here we perform a new analysis of these experiments
allowing simultaneous variations in both these, non-standard, parameters. We
also combine these experiments, for the first time in the literature, with the
recent WMAP9 data, one at a time. Including the Hubble Space Telescope (HST)
prior on the Hubble constant and information from baryon acoustic oscillations
(BAO) surveys provides the following constraints from ACT: N_eff=3.23\pm0.47,
A_L=1.65\pm0.33 at 68% c.l., while for SPT we have N_eff=3.76\pm0.34,
A_L=0.81\pm0.12 at 68% c.l.. In particular, the A_L estimates from the two
experiments, even when a variation in N_eff is allowed, are in tension at more
than 95% c.l..
|
1301.7343v2
|
2014-12-16
|
Role of the basin boundary conditions in gravity wave turbulence
|
Gravity wave turbulence is studied experimentally in a large wave basin where
irregular waves are generated unidirectionally. The role of the basin boundary
conditions (absorbing or reflecting) and of the forcing properties are
investigated. To that purpose, an absorbing sloping beach opposite to the
wavemaker can be replaced by a reflecting vertical wall. We observe that the
wave field properties depend strongly on these boundary conditions. Quasi-one
dimensional field of nonlinear waves propagate before to be damped by the beach
whereas a more multidirectional wave field is observed with the wall. In both
cases, the wave spectrum scales as a frequency-power law with an exponent that
increases continuously with the forcing amplitude up to a value close to -4,
which is the value predicted by the weak turbulence theory. The physical
mechanisms involved are probably different according to the boundary condition
used, but cannot be easily discriminated with only temporal measurements. We
have also studied freely decaying gravity wave turbulence in the closed basin.
No self-similar decay of the spectrum is observed, whereas its Fourier modes
decay first as a time power law due to nonlinear mechanisms, and then
exponentially due to linear viscous damping. We estimate the linear, nonlinear
and dissipative time scales to test the time scale separation that highlights
the important role of a large scale Fourier mode. By estimation of the mean
energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov
constant is evaluated and found to be compatible with a recent theoretical
value.
|
1412.5144v2
|
2015-02-11
|
Exclusive production of heavy charged Higgs boson pairs in the $p p \to p p H^+ H^-$ reaction at the LHC and a future circular collider
|
We calculate differential cross sections for exclusive production of heavy
charged scalar, weakly interacting particles (charged Higgs bosons, charged
technipions, etc.) via photon-photon exchanges in the $p p \to p p H^+ H^-$
reaction with exact $2 \to 4$ kinematics. We present distributions in
rapidities, transverse momenta, and correlations in azimuthal angles between
the protons and between the charged Higgs bosons. As an example, the integrated
cross section for $\sqrt{s}$ = 14~TeV (LHC) is about 0.1~fb and about 0.9~fb at
the Future Circular Collider (FCC) for $\sqrt{s}$ = 100~TeV when assuming
$m_{H^{\pm}} = 150$~GeV. The results are compared with results obtained within
standard equivalent-photon approximation known from the literature. We discuss
the role of the Dirac and Pauli electromagnetic form factors of the proton. We
have also performed first calculations of cross sections for the exclusive
diffractive Khoze-Martin-Ryskin mechanism. We have estimated limits on the
$g_{h H^+ H^-}$ coupling constant within two-Higgs dublet model based on recent
experimental data from the LHC. The diffractive contribution is, however, much
smaller than the $\gamma \gamma$ one. The $Z \gamma$, $\gamma Z$, and $ZZ$
exchanges give even smaller contributions. Absorption corrections are
calculated for the first time differentially for various distributions. In
general, they lead to a damping of the cross section. The damping depends on
the $M_{H^{+}H^{-}}$ invariant mass and on $t$ four-momentum transfers squared.
In contrast to diffractive processes, the larger the collision energy, the
smaller the effect of absorption. We discuss a possibility to measure the
exclusive production of two charged Higgs bosons with the help of so-called
"forward proton detectors" at the LHC experiments.
|
1502.03323v2
|
2015-07-29
|
The chemistry of the most metal-rich damped Lyman $α$ systems at z$\sim2$ II. Context with the Local Group
|
Using our sample of the most metal-rich damped Lyman $\alpha$ systems (DLAs)
at z$\sim2$, and two literature compilations of chemical abundances in 341 DLAs
and 2818 stars, we present an analysis of the chemical composition of DLAs in
the context of the Local Group. The metal-rich sample of DLAs at z$\sim2$
probes metallicities as high as the Galactic disc and the most metal-rich dwarf
spheroidals (dSphs), permitting an analysis of many elements typically observed
in DLAs (Fe, Zn, Cr, Mn, Si, and S) in comparison to stellar abundances
observed in the Galaxy and its satellites (in particular dSphs). Our main
conclusions are: (1) non-solar [Zn/Fe] abundances in metal-poor Galactic stars
and in dSphs over the full metallicity range probed by DLAs, suggest that Zn is
not a simple proxy for Fe in DLAs and therefore not a suitable indicator of
dust depletion. After correcting for dust depletion, the majority of DLAs have
subsolar [Zn/Fe] similar to dSphs; (2) at [Fe/H]$\sim-0.5$, a constant
[Mn/Fe]$\sim-0.5$ and near-solar [$\alpha$/Fe] (requiring an assumption about
dust depletion) are in better agreement with dwarf galaxies than Galactic disc
stars; (3) [$\alpha$/Zn] is usually solar or subsolar in DLAs. However,
although low ratios of [$\alpha$/Fe] are usually considered more `dwarf-like'
than `Milky Way-like', subsolar [Zn/Fe] in Local Group dwarfs leads to
supersolar [$\alpha$/Zn] in the dSphs, in contrast with the DLAs. Therefore,
whilst DLAs exhibit some similarities with the Local Group dwarf population,
there are also notable differences.
|
1507.08311v1
|
2015-09-01
|
Excitation of surface and volume plasmons in metal nanocluster by fast electrons
|
Surface and volume plasmons excited in a metal cluster by moving electron and
corresponding inelastic scattering spectra are studied based on the
hydrodynamic approach. Along with the bulk losses traditionally taken into
account, the surface and radiative ones are also considered as the physical
mechanisms responsible for the plasmon damping. The second and third mechanisms
are found to be essential for the surface plasmons and depend very differently
on the multipole mode order. The differential equations are obtained which
describe the temporal evolution of every particular mode as that one of a
linear oscillator excited by the given external force, and the electron energy
loss spectra are calculated. The changes in spectrum shape with the impact
parameter and with the electron passage time are analyzed and found to be in
good enough agreement with the data of scanning transmission electron
microscopy (STEM) experiments. It is shown that, in the general case, a
pronounced contribution to the formation of the loss spectrum is given by the
both surface and volume plasmons with low and high multipole indices. In
particular, at long electron passage time, the integral loss spectrum which is
calculated for the free-electron cluster model contains two main peaks: a broad
peak from merging of many high-order multipole resonances of the surface
plasmons and a narrower peak of nearly the same height from merged volume
plasmons excited by the electrons that travel through the central region of the
cluster. Comparatively complex dependences of the calculated excitation
coefficients and damping constants of various plasmons on the order of the
excited multipole result in wide diversity of possible types of the loss
spectrum even for the same cluster material and should be taken into account in
interpretation of corresponding electron energy loss spectroscopy (EELS)
experiments.
|
1509.00405v2
|
2017-11-19
|
Role of Helium-Hydrogen ratio on energetic interchange mode behaviour and its effect on ion temperature and micro-turbulence in LHD
|
In the Large helical device, a change of energetic particle mode is observed
as He concentration is varied in ion-ITB type experiments, having constant
electron density and input heating power but with a clear increase of central
ion temperature in He rich discharges. This activity consists of bursty, but
damped energetic interchange modes (EICs, X Du et al., Phys. Rev. Lett. 114
p.155003 (2015)), whose occurrence rate is dramatically lower in the He-rich
discharges. Mechanisms are discussed for the changes in drive and damping of
the modes with He concentration. These EIC bursts consist of marked changes in
the radial electric field, which is derived from the phase velocity of
turbulence measured with the 2D phase contrast imaging (PCI) system. Similar
bursts are detected in edge fast ion diagnostics. Ion thermal transport by
gyro-Bohm scaling is recognised as a contribution to the change in ion
temperature, though fast ion losses by these EIC modes may also contribute to
the ion temperature dependence on He concentration, most particularly
controlling the height of an "edge-pedestal" in the $T_{i}$ profile. The
steady-state level of fast ions is shown to be larger in Helium rich discharges
on the basis of a compact neutral particle analyser (CNPA), and the fast-ion
component of the diamagnetic stored energy. These events also have an influence
on turbulence and transport. The large velocity shear induced produced during
these events transiently improves confinement and suppresses turbulence, and
has a larger net effect when bursts are more frequent in Hydrogen discharges.
This exactly offsets the increased gyro-Bohm related turbulence drive in
Hydrogen which results in the same time-averaged turbulence level in Hydrogen
as in Helium.
|
1711.07097v2
|
2018-09-02
|
CEPC Conceptual Design Report: Volume 1 - Accelerator
|
The Circular Electron Positron Collider (CEPC) is a large international
scientific project initiated and hosted by China. It is located in a 100-km
circumference underground tunnel. The accelerator complex consists of a linear
accelerator (Linac), a damping ring (DR), the Booster, the Collider and several
transport lines. In the tunnel, space is reserved for a future pp collider,
SPPC. The CEPC center-of-mass energy is 240 GeV, and at that collision energy
will serve as a Higgs factory. The design also allows operation at 91 GeV for a
Z factory and at 160 GeV for a W factory. The heart of the CEPC is a
double-ring collider. It has two interaction points where are located large
detectors. The Booster is in the same tunnel above the Collider. It is a
synchrotron with a 10 GeV injection energy and extraction energy equal to the
beam collision energy. The repetition cycle is 10 seconds. Top-up injection
will be used to maintain constant luminosity. The 10 GeV Linac, injector to the
Booster, built at ground level, accelerates both electrons and positrons. A 1.1
GeV damping ring reduces the positron emittance. Transport lines made of
permanent magnets connect the Linac to the Booster. In addition to particle
physics, the Collider can operate simultaneously as a powerful synchrotron
radiation (SR) light source. It will extend the usable SR spectrum into an
unprecedented energy and brightness range. Two gamma-ray beamlines are included
in the design. Prior to the construction will be a five-year R&D period
(2018-2022). Construction is expected to start in ~2022 and be completed in
~2030. This report is a summary of work accomplished during the past several
years by hundreds of scientists and engineers at home and abroad. The current
volume, Volume I, is on the accelerators. A separate volume, Volume II, will be
on physics and the detectors.
|
1809.00285v1
|
2018-10-10
|
3D Simulations and MLT: II. Onsager's Ideal Turbulence
|
We simulate stellar convection at high Reynolds number (Re$\lesssim$7000)
with causal time stepping but no explicit viscosity. We use the 3D Euler
equations with shock capturing (Colella & Woodward 1984). Anomalous dissipation
of turbulent kinetic energy occurs as an emergent feature of advection
("Onsager damping"), caused by the moderate shocks which terminate the
turbulent kinetic energy spectrum; see also (Perry 2021). In strongly
stratified stellar convection the asymptotic limit for the global damping
length of turbulent kinetic energy is $\ell_d \sim \langle u^3 \rangle /\langle
\epsilon \rangle$. This "dissipative anomaly" (Onsager 1949) fixes the value of
the "mixing length parameter", $\alpha = \ell_{\rm MLT}/H_P
=\overline{\langle\Gamma_1\rangle}$, which is $\sim\, 5/3$ for complete
ionization. The estimate is numerically robust, agrees to within 10% with
estimates from stellar evolution with constant $\alpha$. For weak
stratification $\ell_d$ shrinks to the depth of a thin convective region. Our
flows are filamentary, produce surfaces of separation at boundary layers,
resolve the energy-containing eddies, and develop a turbulent cascade down to
the grid scale which agrees with the $4096^3$ direct numerical simulation of
Kaneda (2003). The cascade converges quickly, and satisfies a power-law
velocity spectrum similar to Kolmogorov (1941). Our flows exhibit
intermittency, anisotropy, and interactions between coherent structures,
features missing from K41 theory. We derive a dissipation rate from Reynolds
stresses which agrees with (i) our flows, (ii) experiment (Warhaft 2002), and
(iii) high Re simulations of the Navier-Stokes equations (Iyer, et al. 2018).
|
1810.04659v4
|
2018-12-10
|
H$_2$/HD molecular data for analysis of quasar spectra in search of varying constants
|
Absorption lines of H$_2$ and HD molecules observed at high redshift in the
line of sight towards quasars are a test ground to search for variation of the
proton-to-electron mass ratio $\mu$. For this purpose, results from
astronomical observations are compared with a compilation of molecular data of
the highest accuracy, obtained in laboratory studies as well as in
first-principles calculations. Aims: A comprehensive line list is compiled for
H$_2$ and HD absorption lines in the Lyman ($B^1\Sigma_u^+$ - $X^1\Sigma_g^+$)
and Werner ($C^1\Pi_u$ - $X^1\Sigma_g^+$) band systems up to the Lyman cutoff
at 912 Angstroms. Molecular parameters listed for each line $i$ are the
transition wavelength $\lambda_i$, the line oscillator strength $f_i$, the
radiative damping parameter of the excited state $\Gamma_i$, and the
sensitivity coefficient $K_i$ for a variation of the proton-to-electron mass
ratio. Methods: The transition wavelengths $\lambda_i$ for the H$_2$ and HD
molecules are determined by a variety of advanced high-precision spectroscopic
experiments involving narrowband vacuum ultraviolet lasers, Fourier-transform
spectrometers, and synchrotron radiation sources. Results for the line
oscillator strengths $f_i$, damping parameters $\Gamma_i$, and sensitivity
coefficients $K_i$ are obtained in theoretical quantum chemical calculations.
Results: A new list of molecular data is compiled for future analyses of cold
clouds of hydrogen absorbers, specifically for studies of $\mu$-variation from
quasar data. The list is applied in a refit of quasar absorption spectra of
B0642$-$5038 and J1237$+$0647 yielding constraints on a variation of the
proton-to-electron mass ratio $\Delta\mu/\mu$ consistent with previous
analyses.
|
1812.03628v2
|
2019-04-26
|
Thermal equilibration in a one-dimensional damped harmonic crystal
|
The features for the unsteady process of thermal equilibration ("the fast
motions") in a one-dimensional harmonic crystal lying in a viscous environment
(e.g., a gas) are under investigation. It is assumed that initially the
displacements of all the particles are zero and the particle velocities are
random quantities with zero mean and a constant variance, thus, the system is
far away from the thermal equilibrium. It is known that in the framework of the
corresponding conservative problem the kinetic and potential energies oscillate
and approach the equilibrium value that equals a half of the initial value of
the kinetic energy. We show that the presence of the external damping
qualitatively changes the features of this process. The unsteady process
generally has two stages. At the first stage oscillations of kinetic and
potential energies with decreasing amplitude, subjected to exponential decay,
can be observed (this stage exists only in the underdamped case). At the second
stage (which always exists), the oscillations vanish, and the energies are
subjected to a power decay. The large-time asymptotics for the energy is
proportional to $t^{-3/2}$ in the case of the potential energy and to
$t^{-5/2}$ in the case the kinetic energy. Hence, at large values of time the
total energy of the crystal is mostly the potential energy. The obtained
analytic results are verified by independent numerical calculations.
|
1904.11902v7
|
2019-11-04
|
The shape of the cosmic ray proton spectrum
|
Recent observations of cosmic ray protons in the energy range
$10^2$--$10^5$~GeV have revealed that the spectrum cannot be described by a
simple power law. A hardening of the spectrum around an energy of order few
hundred~GeV, first observed by the magnetic spectrometers PAMELA and AMS02, has
now been confirmed by several calorimeter detectors (ATIC, CREAM, CALET,
NUCLEON and DAMPE). These new measurements reach higher energy and indicate
that the hardening corresponds to a larger step in spectral index than what
estimated by the magnetic spectrometers. Data at still higher energy (by CREAM,
NUCLEON and DAMPE) show that the proton spectrum undergoes a marked softening
at $E \approx 10^4$~GeV. Understanding the origin of these unexpected spectral
features is a significant challenge for models of the Galactic cosmic rays. An
important open question is whether additional features are present in the
proton spectrum between the softening and the "Knee". Extensive Air Shower
detectors, using unfolding procedures that require the modeling of cosmic ray
showers in the atmosphere, estimated the proton flux below and around the Knee
(at $E \simeq 3$~PeV). These results however have large systematic
uncertainties and are in poor agreement with each other. The measurement in the
PeV energy range, recently presented by IceTop/IceCube, indicates a proton flux
higher than extrapolations of the direct measurements calculated assuming a
constant slope, and therefore requires the existence of an additional spectral
hardening below the Knee. A clarification of this point is very important for
an understanding of the origin of the Galactic cosmic rays, and is also
essential for a precise calculation of the spectra of atmospheric neutrinos in
the energy range ($E \gtrsim 10$~TeV) where they constitute the foreground for
the emerging astrophysical $\nu$ signal.
|
1911.01311v1
|
2021-08-31
|
Toward 100% Spin-Orbit Torque Efficiency with High Spin-Orbital Hall Conductivity Pt-Cr Alloys
|
5d transition metal Pt is the canonical spin Hall material for efficient
generation of spin-orbit torques (SOTs) in Pt/ferromagnetic layer (FM)
heterostructures. However, for a long while with tremendous engineering
endeavors, the damping-like SOT efficiencies (${\xi}_{DL}$) of Pt and Pt alloys
have still been limited to ${\xi}_{DL}$<0.5. Here we present that with proper
alloying elements, particularly 3d transition metals V and Cr, a high
spin-orbital Hall conductivity
(${\sigma}_{SH}{\sim}6.5{\times}10^{5}({\hbar}/2e){\Omega}^{-1}{\cdot} m^{-1}$)
can be developed. Especially for the Cr-doped case, an extremely high
${\xi}_{DL}{\sim}0.9$ in a Pt$_{0.69}$Cr$_{0.31}$/Co device can be achieved
with a moderate Pt$_{0.69}$Cr$_{0.31}$ resistivity of ${\rho}_{xx}{\sim}133
{\mu}{\Omega}{\cdot}cm$. A low critical SOT-driven switching current density of
$J_{c}{\sim}3.2{\times}10^{6} A{\cdot}cm^{-2}$ is also demonstrated. The
damping constant (${\alpha}$) of Pt$_{0.69}$Cr$_{0.31}$/FM structure is also
found to be reduced to 0.052 from the pure Pt/FM case of 0.078. The overall
high ${\sigma}_{SH}$, giant ${\xi}_{DL}$, moderate ${\rho}_{xx}$, and reduced
${\alpha}$ of such a Pt-Cr/FM heterostructure makes it promising for versatile
extremely low power consumption SOT memory applications.
|
2108.13857v3
|
2022-04-06
|
Universal Relations for Neutron Star F-Mode and G-Mode Oscillations
|
Among the various oscillation modes of neutron stars, f- and g- modes are the
most likely to be ultimately observed in binary neutron star mergers. The
f-mode is known to correlate in normal neutron stars with their tidal
deformability, moment of inertia and quadrupole moment. Using a piecewise
polytropic parameterization scheme to model the uncertain hadronic high-density
EOS and a constant sound-speed scheme to model pure quark matter, we refine
this correlation and show that these universal relations also apply to both
self-bound stars and hybrid stars containing phase transitions. We identify a
novel 1-node branch of the f-mode that occurs in low-mass hybrid stars in a
narrow mass range just beyond the critical mass necessary for a phase
transition to appear. This 1-node branch shows the largest, but still small,
deviations from the universal correlation we have found. The g-mode frequency
only exists in matter with a non-barotropic equation of state involving
temperature, chemical potential or composition, or a phase transition in
barotropic matter. The g-mode therefore could serve as a probe for studying
phase transitions in hybrid stars. In contrast with the f-mode, discontinuity
g-mode frequencies depend strongly on properties of the transition (the density
and the magnitude of the discontinuity) at the transition. Imposing causality
and maximum mass constraints, the g-mode frequency in hybrid stars is found to
have an upper bound of about 1.25 kHz. However, if the sound speed c_s in the
inner core at densities above the phase transition density is restricted to
c_s^2 < c^2/3, the g-mode frequencies can only reach about 0.8 kHz, which are
significantly lower than f-mode frequencies, 1.3-2.8 kHz. Also, g-mode
gravitational wave damping times are extremely long, >10^4 s (10^2 s) in the
inner core with c_s^2< c^{2/3} (c^2), in comparison with the f-mode damping
time, 0.1-1 s.
|
2204.03037v2
|
2022-09-26
|
Partially dissipative systems in the critical regularity setting, and strong relaxation limit
|
Many physical phenomena may be modelled by first order hyperbolic equations
with degenerate dissipative or diffusive terms. This is the case for example in
gas dynamics, where the mass is conserved during the evolution, but the
momentum balance includes a diffusion (viscosity) or damping (relaxation) term,
or, in numerical simulations, of conservation laws by relaxation schemes. Such
so-called partially dissipative systems have been first pointed out by S.K.
Godunov in a short note in Russian in 1961. Much later, in 1984, S. Kawashima
highlighted in his PhD thesis a simple criterion ensuring the existence of
global strong solutions in the vicinity of a linearly stable constant state.
This criterion has been revisited in a number of research works. In particular,
K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing
a Lyapunov functional allowing to refine Kawashima's results and to establish
global existence results in some situations that were not covered before. These
notes originate essentially from the PhD thesis of T. Crin-Barat that was
initially motivated by an earlier observation of the author in a Chapter of the
handbook coedited by Y. Giga and A. Novotn{\'y}. Our main aim is to adapt the
method of Beauchard and Zuazua to a class of symmetrizable quasilinear
hyperbolic systems (containing the compressible Euler equations), in a critical
regularity setting that allows to keep track of the dependence with respect to
e.g. the relaxation parameter. Compared to Beauchard and Zuazua's work, we
exhibit a 'damped mode' that will have a key role in the construction of global
solutions with critical regularity, in the proof of optimal time-decay
estimates and, last but not least, in the study of the strong relaxation limit.
For simplicity, we here focus on a simple class of partially dissipative
systems, but the overall strategy is rather flexible, and adaptable to much
more involved situations.
|
2209.12734v1
|
2023-05-09
|
Lower semicontinuity of pullback attractors for a non-autonomous coupled system of strongly damped wave equations
|
The aim of this paper is to study the robustness of the family of pullback
attractors associated to a non-autonomous coupled system of strongly damped
wave equations, given by the following evolution system $$\left\{
\begin{array}{lr} u_{tt} - \Delta u + u + \eta(-\Delta)^{1/2}u_t +
a_{\epsilon}(t)(-\Delta)^{1/2}v_t = f(u), &(x, t) \in\Omega\times (\tau,
\infty),\\ v_{tt} - \Delta v + \eta(-\Delta)^{1/2}v_t -
a_{\epsilon}(t)(-\Delta)^{1/2}u_t = 0, &(x, t) \in\Omega\times (\tau,
\infty),\end{array}\right.$$ subject to boundary conditions $$u = v = 0, \; (x,
t) \in\partial\Omega\times (\tau, \infty),$$ and initial conditions $$u(\tau,
x) = u_0(x), \ u_t(\tau, x) = u_1(x), \ v(\tau, x) = v_0(x), \ v_t(\tau, x) =
v_1(x), \ x \in \Omega, \ \tau\in\mathbb{R},$$ where $\Omega$ is a bounded
smooth domain in $\mathbb{R}^n$, $n \geq 3$, with the boundary $\partial\Omega$
assumed to be regular enough, $\eta > 0$ is a constant, $a_{\epsilon}$ is a
H\"{o}lder continuous function satisfying uniform boundedness conditions, and
$f\in C^1(\mathbb{R})$ is a dissipative nonlinearity with subcritical growth.
This problem is a modified version of the well known Klein-Gordon-Zakharov
system. Under suitable hyperbolicity conditions, we obtain the gradient-like
structure of the limit pullback attractor associated with this evolution
system, and we prove the continuity of the family of pullback attractors at
$\epsilon = 0$.
|
2305.05724v3
|
2023-06-23
|
Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces
|
In this paper, we investigate the stability of the 2-dimensional (2D)
Taylor-Couette (TC) flow for the incompressible Navier-Stokes equations. The
explicit form of velocity for 2D TC flow is given by $u=(Ar+\frac{B}{r})(-\sin
\theta, \cos \theta)^T$ with $(r, \theta)\in [1, R]\times \mathbb{S}^1$ being
an annulus and $A, B$ being constants. Here, $A, B$ encode the rotational
effect and $R$ is the ratio of the outer and inner radii of the annular region.
Our focus is the long-term behavior of solutions around the steady 2D TC flow.
While the laminar solution is known to be a global attractor for 2D channel
flows and plane flows, it is unclear whether this is still true for rotating
flows with curved geometries. In this article, we prove that the 2D
Taylor-Couette flow is asymptotically stable, even at high Reynolds number
($Re\sim \nu^{-1}$), with a sharp exponential decay rate of
$\exp(-\nu^{\frac13}|B|^{\frac23}R^{-2}t)$ as long as the initial perturbation
is less than or equal to $\nu^\frac12 |B|^{\frac12}R^{-2}$ in Sobolev space.
The powers of $\nu$ and $B$ in this decay estimate are optimal. It is derived
using the method of resolvent estimates and is commonly recognized as the
enhanced dissipative effect. Compared to the Couette flow, the enhanced
dissipation of the rotating Taylor-Couette flow not only depends on the
Reynolds number but also reflects the rotational aspect via the rotational
coefficient $B$. The larger the $|B|$, the faster the long-time dissipation
takes effect. We also conduct space-time estimates describing inviscid-damping
mechanism in our proof. To obtain these inviscid-damping estimates, we find and
construct a new set of explicit orthonormal basis of the weighted
eigenfunctions for the Laplace operators corresponding to the circular flows.
These provide new insights into the mathematical understanding of the 2D
Taylor-Couette flows.
|
2306.13562v1
|
2023-08-14
|
Temperature Evolution of Magnon Propagation Length in Tm$_3$Fe$_5$O$_{12}$ Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping
|
The magnon propagation length ($\langle\xi\rangle$) of a ferro/ferrimagnet
(FM) is one of the key factors that controls the generation and propagation of
thermally-driven spin current in FM/heavy metal (HM) bilayer based
spincaloritronic devices. Theory predicts that for the FM layer,
$\langle\xi\rangle$ is inversely proportional to the Gilbert damping ($\alpha$)
and the square root of the effective magnetic anisotropy constant ($K_{\rm
eff}$). However, direct experimental evidence of this relationship is lacking.
To experimentally confirm this prediction, we employ a combination of
longitudinal spin Seebeck effect (LSSE), transverse susceptibility, and
ferromagnetic resonance experiments to investigate the temperature evolution of
$\langle\xi\rangle$ and establish its correlation with the effective magnetic
anisotropy field, $H_K^{\rm eff}$ ($\propto K_{\rm eff}$) and $\alpha$ in
Tm$_3$Fe$_5$O$_{12}$ (TmIG)/Pt bilayers. We observe concurrent drops in the
LSSE voltage and $\langle\xi\rangle$ below 200$^\circ$K in TmIG/Pt bilayers
regardless of TmIG film thickness and substrate choice and attribute it to the
noticeable increases in $H_K^{\rm eff}$ and $\alpha$ that occur within the same
temperature range. From the TmIG thickness dependence of the LSSE voltage, we
determined the temperature dependence of $\langle\xi\rangle$ and highlighted
its correlation with the temperature-dependent $H_K^{\rm eff}$ and $\alpha$ in
TmIG/Pt bilayers, which will be beneficial for the development of rare-earth
iron garnet-based efficient spincaloritronic nanodevices.
|
2308.07236v3
|
2023-09-19
|
Impact of strain on the SOT-driven dynamics of thin film Mn$_3$Sn
|
Mn$_3$Sn, a metallic antiferromagnet with an anti-chiral 120$^\circ$ spin
structure, generates intriguing magneto-transport signatures such as a large
anomalous Hall effect, spin-polarized current with novel symmetries, anomalous
Nernst effect, and magneto-optic Kerr effect. When grown epitaxially as
MgO(110)[001]$\parallel$ Mn$_3$Sn($0\bar{1}\bar{1}0$)[0001], Mn$_3$Sn
experiences a uniaxial tensile strain, which changes the bulk six-fold
anisotropy landscape to a perpendicular magnetic anisotropy with two stable
states. In this work, we investigate the field-assisted spin orbit-torque
(SOT)-driven response of the order parameter in single-domain Mn$_3$Sn with
uniaxial tensile strain. We find that for a non-zero external magnetic field,
the order parameter can be switched between the two stable states if the
magnitude of the input current is between two field-dependent critical
currents. Below the lower critical current, the order parameter exhibits a
stationary state in the vicinity of the initial stable state. On the other
hand, above the higher critical current, the order parameter shows oscillatory
dynamics which could be tuned from the 100's of megahertz to the gigahertz
range. We obtain approximate expressions of the two critical currents and find
them to agree very well with the numerical simulations for experimentally
relevant magnetic fields. We also obtain unified functional form of the
switching time versus the input current for different magnetic fields. Finally,
we show that for lower values of Gilbert damping ($\alpha \leq 2\times
10^{-3}$), the critical currents and the final steady states depend
significantly on the damping constant. The numerical and analytic results
presented in our work can be used by both theorists and experimentalists to
understand the SOT-driven order dynamics in PMA Mn$_3$Sn and design future
experiments and devices.
|
2309.10246v2
|
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