Diffusion Damping Research Articles

Asymptotic analysis for a shear beam model with thermoelastic diffusion damping

Asymptotic analysis for a shear beam model with thermoelastic diffusion damping

The stabilizing effect of temperature and magnetic field on a 2D magnetic Bénard fluids

In this paper we study the stability of a special magnetic Bénard system near equilibrium, where there exists Laplacian magnetic diffusion and temperature damping but the velocity equation involves no dissipation. Without any velocity dissipation, the fluid velocity is governed by the two-dimensional incompressible Euler equation, whose solution can grow rapidly in time. However, when the fluid is coupled with the magnetic field and temperature through the magnetic Bénard system, we show that the solution is stable. Our results mathematically illustrate that the magnetic field and temperature have the effect of enhancing dissipation and contribute to stabilize the fluid.

Angular correlations of cosmic microwave background spectrum distortions from photon diffusion

ABSTRACT During cosmic recombination, charged particles bind into neutral atoms and the mean free path of photons rapidly increases, resulting in the familiar diffusion damping of primordial radiation temperature variations. An additional effect is a small photon spectrum distortion, because photons arriving from a particular sky direction were originally in thermal equilibrium at various spatial locations with different temperatures; the combination of these different blackbody temperature distributions results in a spectrum with a Compton y-distortion. Using the approximation that photons had zero mean free path prior to their second-to-last scattering, we derive an expression for the resulting y-distortion, and compute the angular correlation function of the diffusion y-distortion and its cross-correlation with the square of the photon temperature fluctuation. Detection of the cross-correlation is within reach of existing arcminute-resolution microwave background experiments such as the Atacama Cosmology Telescope and the South Pole Telescope.

Blow‐up and energy decay for a class of wave equations with nonlocal Kirchhoff‐type diffusion and weak damping

The purpose of this paper is to study the following equation driven by a nonlocal integro‐differential operator : with homogeneous Dirichlet boundary condition and initial data, where is the Gagliardo seminorm, and with , is the space dimension. By virtue of a differential inequality technique, an upper bound of the blow‐up time is obtained with a bounded initial energy if and some additional conditions are satisfied. For , in particular, the blow‐up result with high initial energy also is showed by constructing a new control functional and combining energy inequalities with the concavity argument. Moreover, an estimate for the lower bound of the blow‐up time is investigated. Finally, the energy decay estimate is proved as well. These results improve and complement some recent works.

Boundedness and asymptotic behavior in a quasilinear chemotaxis system for alopecia areata

In this paper, we study the following chemotaxis system with generalized volume-filling effect ut=∇⋅(D1(u)∇u)−χ1∇⋅(S1(u)∇w)+w−μ1uη1,(x,t)∈Ω×(0,∞),vt=∇⋅(D2(v)∇v)−χ2∇⋅(S2(v)∇w)+w+ruv−μ2vη2,(x,t)∈Ω×(0,∞),0=Δw+u+v−w,(x,t)∈Ω×(0,∞),under homogeneous Neumann boundary conditions in a smoothly bounded domain Ω⊂Rn(n≥1), which describes the spatio-temporal dynamics of alopecia areata lesions, where χ1, χ2, r, μ1, μ2 are positive parameters and η1,η2≥2. When the functions Di and Si(i=1,2) belong to C2 fulfilling Di(s)≥(s+1)αi, 0≤S(s)≤sβi with αi∈R and βi≥0 for all s≥0, we study the global existence and boundedness of classical solutions for the above system under some suitable conditions, and find that either the higher-order nonlinear diffusion or strong logistic damping can prevent blow-up of classical solutions for the problem. In addition, when ηi=2 and 0≤Si(s)≤s(s+1)βi−1 with 0≤βi<1 or 0≤Si(s)≤sβi with βi≥1 for all s≥0 and i=1,2, if the chemosensitivity χ1 and χ2 are appropriately mild and some other parameter conditions hold, the globally bounded solution will stabilize to the constant coexistence equilibrium as the time goes to infinity. Our results not only extend the previous ones of Tao & Xu (2022), but also involve some new conclusions.

Determination of pressure from nonlinear equations of nonhomogeneous non-newtonian fluids

In this paper, the initial-boundary problem for a system of nonlinear equations modified by p-laplacian diffusion and nonlinear damping term, in which describe the motion of a non-homogeneous (with unknown and non constant density ) incompressible viscoelastic non-Newtonian fluids is considered. Usually, a pressure does not include in the definition of weak generalized solution to equations of hydrodynamics for incompressible fluids, because weak solutions consider in the solenoidal space due to the incompressibility (continuity) equation. In the classical hydrodynamic equations, after determining a velocity and a density, a pressure can be determined by using the theorem of a representation of the space L2(Ω) into the direct sum of two orthogonal subspaces. The recovering of a pressure from the nonlinear equations of hydrodynamics modified by p-laplacian and nonlinear damping term requires a new approches. Here, under a suitable conditions on the data of the problem, a pressure has been uniquelly determined from the initial-boundary value problem for the system of nonlinear modified equations describing the motion of nonhomogeneous (with unknown and non constant density ) incompressible viscoelastic non-Newtonian fluids. The main functional spaces and necessary axuillary conclusions are introduced. A space of generalized weak solutions is identified. The pressure uniquelly recovered by using the known de-Ram lemma.

Theory of sound attenuation in amorphous solids from nonaffine motions

We present a theoretical derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory takes into account the nonaffine displacements in transverse waves and is able to predict both the ubiquitous low-energy diffusive damping ∼k 2, as well as a novel contribution to the Rayleigh damping ∼k 4 at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevin-type) damping in particle motion (which arises from anharmonicity), and to the nonaffine correction to the static shear modulus, whereas the Rayleigh damping emerges in the limit of low anharmonicity, consistent with previous observations and macroscopic models. Importantly, the k 4 Rayleigh contribution derived here does not arise from harmonic disorder or elastic heterogeneity effects and it is the dominant mechanism for sound attenuation in amorphous solids as recently suggested by molecular simulations.

New paradigm for glassy-like anomalies in solids from fundamental symmetries

Glasses and disordered materials are known to display anomalous features in the density of states, in the specific heat and in thermal transport. Nevertheless, in recent years, the question whether these properties are really anomalous (and peculiar of disordered systems) or rather more universal than previously thought, has emerged. New experimental and theoretical observations have questioned the origin of the boson peak (BP) and the linear in T specific heat exclusively from disorder and two-level systems (TLS). The same properties have been indeed observed in ordered or minimally disordered compounds and in incommensurate structures for which the standard explanations are not applicable. Using the formal analogy between phason modes (e.g., in quasicrystals and incommensurate lattices) and diffusions, and between amplitude modes and optical phonons, we suggest the existence of a more universal physics behind these properties. In particular, we strengthen the idea that linear in T specific heat is linked to low energy diffusive modes resulting from fundamental symmetries, and that a BP excess can be induced in crystals either by gapped optical-like modes and/or by anharmonic diffusive (Akhiezer) damping.

Modulated longitudinal gates on encoded spin qubits via curvature couplings to a superconducting cavity

We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a gate voltage variation. For a two-qubit ($n$-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal $\sigma_z$-coupling, offering gate times of 10s of ns even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse $\sigma_x$-coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron exchange-only qubit or a double quantum dot singlet-triplet qubit). This approach allows always-on, exchange-only qubits, for example, to stay on their "sweet spots" during gate operations, minimizing the charge noise and eliminating an always-on static longitudinal qubit-qubit coupling. We calculate the main gate errors due to the (1) diffusion (Johnson) noise and (2) damping of the resonator, the (3) $1/f$-charge noise qubit gate dephasing and $1/f$-noise on the longitudinal coupling, (4) qubit dephasing and ac-Stark frequency shifts via photon fluctuations in the resonator, and (5) spin-dependent resonator frequency shifts (via a "dispersive-like" static curvature coupling), most of them associated with the non-zero qubit energy curvature (quantum capacitance). Using spin-echo-like error suppression at optimal regimes, gate infidelities of $10^{-2}-10^{-3}$ can be achieved with experimentally existing parameters. The proposed schemes seem suitable for remote spin-to-spin entanglement of two spin-qubits or a cluster of spin-qubits: an important resource of quantum computing.

Generalized sedeonic equations of hydrodynamics

We present a generalization of the equations of hydrodynamics based on the noncommutative algebra of space-time sedeons. It is shown that for vortex-less flow the system of Euler and continuity equations is represented as a single nonlinear sedeonic second-order wave equation for scalar and vector potentials, which is naturally generalized on viscous and vortex flows. As a result we obtained the closed system of four equations describing the diffusion damping of translational and vortex motions. The main peculiarities of the obtained equations are illustrated on the basis of the plane wave solutions describing the propagation of sound waves.

Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials.

The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity, etc. The old Debye model of vibrational spectra at low energy gives the vibrational density of states (VDOS) as proportional to the frequency squared, but in many materials the spectrum departs from this law which results in a peak upon normalizing the VDOS by frequency squared, which is known as the "boson peak." A description of the VDOS of solids (both crystals and glasses) is presented starting from first principles. Without using any assumptions whatsoever of disorder in the material, it is shown that the boson peak in the VDOS of both ordered crystals and glasses arises naturally from the competition between elastic mode propagation and diffusive damping. The theory explains the recent experimental observations of boson peak in perfectly ordered crystals, which cannot be explained based on previous theoretical frameworks. The theory also explains, for the first time, how the vibrational spectrum changes with the atomic density of the solid, and explains recent experimental observations of this effect.

Damping Characteristics of Horizontal Laplacian Diffusion Filters

Horizontally diffusive computational damping terms are frequently employed in 3D atmospheric simulation models to enhance stability and to suppress small-scale noise. In configuring these filters, it is desirable that damping effects are concentrated on the smaller-scale disturbances close to the grid scale and that the dissipation is spatially isotropic. On Cartesian meshes, the isotropy of the damping can vary greatly depending on the numerical formulation of the horizontal filter. The most isotropic behavior appears to result from recursive application of a 2D Laplacian that combines both along-axis and diagonal contributions. Also, the recursive application of 1D Laplacians in each coordinate direction provides better isotropy than the recursive application of the 2D Laplacian represented with a five-point operator. Increased isotropy also permits a larger maximum diffusivity, which may be beneficial in certain filter applications. On hexagonal and triangular meshes, Laplacian operators exhibit excellent isotropy, owing to the more isotropic nature of the meshes. However, previous research has established that straightforward application of the Laplacian may yield a diffusion operator that damps both resolved physical modes and unresolved high-wavenumber (aliased) modes, but it does not converge to the proper analytic behavior. Special averaging is then required to recover an accurate representation for the Laplacian. A consequence of this averaging is that the resulting filters do not act on the aliased modes (the checkerboard mode in particular) and thus employing the unaveraged diffusion operators may be preferable. The damping characteristics and stability constraints are derived for both the unaveraged and averaged Laplacian filters for C-grid staggering on these meshes.

Impact of Lateral Mixing in the Ocean on El Nino in a Suite of Fully Coupled Climate Models

AbstractWe examine the dependence of the amplitude of the El Nino‐Southern Oscillation (ENSO) on the mixing coefficient parameterizing the lateral mixing of tracers (ARedi) The value of this coefficient is very uncertain, ranging in Earth System Models between a few hundred and a few thousand m2 s−1, with some observational estimates showing even higher values. A suite of simulations is made with two spatially varying distributions of ARedi derived from satellite observations as well as four simulations where a spatially constant ARedi is varied over a factor of 6. Surprisingly, larger values of ARedi result in stronger ENSO variability despite the higher mixing coefficients producing more efficient lateral diffusive damping of anomalies. This is because lateral mixing also warms the cold tongue, increasing vertical temperature gradients and decreasing horizontal temperature gradients. Larger vertical temperature gradients make sea surface temperatures more responsive to atmospheric forcing, while smaller horizontal temperature gradients shift the location of convection and make the atmosphere more responsive to sea surface temperature anomalies. The last effect holds across simulations as well as within individual simulations and thus also helps to explain interdecadal variability in ENSO amplitude. By contrast, a previously proposed anticorrelation between the amplitude interannual and annual variability does not hold across simulations, although it does hold within simulations. The propagation of thermocline depth anomalies is relatively insensitive to the value of ARedi. Properly specifying the lateral mixing along the equator (including distinguishing the impacts of subgridscale turbulence and tropical instability waves) appears essential to simulating ENSO.

On the origin of nonlocal damping in plasmonic monomers and dimers

The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with time-dependent density functional theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic architectures: metal–dielectric interfaces, metal–dielectric–metal gaps, spherical nanoparticles and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective–diffusive GNOR theory, describes well the enhanced losses and plasmon broadening predicted by ab initio calculations in few-nm particles or few-to-sub-nm gaps. Through the evaluation of a local effective dielectric function, it is shown that absorptive losses appear dominantly close to the metal surface, in agreement with TDDFT and the mechanism of Landau damping due to generation of electron–hole pairs near the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies.

Modeling the Effect of Curvature on the Collective Behavior of Cells Growing New Tissue

The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue’s evolution. Understanding the cellular basis of this control is highly significant for bioscaffold tissue engineering, the evolution of bone microarchitecture, wound healing, and tumor growth. Although previous models have proposed geometrical relationships between tissue growth and curvature, the role of cell density and cell vigor remains poorly understood. We propose a cell-based mathematical model of tissue growth to investigate the systematic influence of curvature on the collective crowding or spreading of tissue-synthesizing cells induced by changes in local tissue surface area during the motion of the interface. Depending on the strength of diffusive damping, the model exhibits complex growth patterns such as undulating motion, efficient smoothing of irregularities, and the generation of cusps. We compare this model with in vitro experiments of tissue deposition in bioscaffolds of different geometries. By including the depletion of active cells, the model is able to capture both smoothing of initial substrate geometry and tissue deposition slowdown as observed experimentally.

Disformal transformations on the CMB

In this work we study the role of disformal transformation on cosmological backgrounds and its relation to the speed of sound for tensor modes. A speed different from one for tensor modes can arise in several contexts, such as Galileons theories or massive gravity, nevertheless the speed is very constrained to be one by observations of gravitational wave emission. It has been shown that in inflation a disformal transformation allows to set the speed for tensor modes to one without making changes to the curvature power spectrum. Here we show that this invariance does not hold when considering the CMB anisotropy power spectrum. It turns out that the after doing the transformation there is an imprint on the acoustic peaks and the diffusion damping. This has interesting consequences; here we explore quartic galileon theories which allow a modified speed for tensor modes. For these theories the transformation can be used to constraint the parameter space in different regimes.

Solving the small-scale structure puzzles with dissipative dark matter

Small-scale structure is studied in the context of dissipative dark matter, arising for instance in models with a hidden unbroken Abelian sector, so that dark matter couples to a massless dark photon. The dark sector interacts with ordinary matter via gravity and photon-dark photon kinetic mixing. Mirror dark matter is a theoretically constrained special case where all parameters are fixed except for the kinetic mixing strength, ϵ. In these models, the dark matter halo around spiral and irregular galaxies takes the form of a dissipative plasma which evolves in response to various heating and cooling processes. It has been argued previously that such dynamics can account for the inferred cored density profiles of galaxies and other related structural features. Here we focus on the apparent deficit of nearby small galaxies (``missing satellite problem"), which these dissipative models have the potential to address through small-scale power suppression by acoustic and diffusion damping. Using a variant of the extended Press-Schechter formalism, we evaluate the halo mass function for the special case of mirror dark matter. Considering a simplified model where Mbaryons ∝ Mhalo, we relate the halo mass function to more directly observable quantities, and find that for ϵ ≈ 2 × 10−10 such a simplified description is compatible with the measured galaxy luminosity and velocity functions. On scales Mhalo ≲ 108 M⊙, diffusion damping exponentially suppresses the halo mass function, suggesting a nonprimordial origin for dwarf spheroidal satellite galaxies, which we speculate were formed via a top-down fragmentation process as the result of nonlinear dissipative collapse of larger density perturbations. This could explain the planar orientation of satellite galaxies around Andromeda and the Milky Way.

Planck constraints on scalar-tensor cosmology and the variation of the gravitational constant

Cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background (CMB) obtained from the Planck 2015 results are presented. We consider the harmonic attractor model, in which the scalar field has a harmonic potential with curvature ($\beta$) in the Einstein frame and the theory relaxes toward the Einstein gravity with time. Analyzing the {\it TT}, {\it EE}, {\it TE} and lensing CMB data from Planck by the Markov chain Monte Carlo method, we find that the present-day deviation from the Einstein gravity (${\alpha_0}^2$) is constrained as ${\alpha_0}^2<2.5\times10^{-4-4.5\beta^2}\ (95.45\% {\rm\ C.L.})$ and ${\alpha_0}^2<6.3\times10^{-4-4.5\beta^2}\ (99.99\%\ {\rm C.L.})$ for $0<\beta<0.4$. The time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{\rm rec}/G_0<1.0056\ (95.45\% {\rm\ C.L.})$ and $G_{\rm rec}/G_0<1.0115\ (99.99 \%{\rm\ C.L.})$. We also find that the constraints are little affected by extending to nonflat cosmological models because the diffusion damping effect revealed by Planck breaks the degeneracy of the projection effect.

Idealized Quasi-Biennial Oscillations in an Ensemble of Dry GCM Dynamical Cores

Abstract The paper demonstrates that quasi-biennial oscillation (QBO)-like oscillations can be simulated in an ensemble of dry GCM dynamical cores that are driven by a simple Held–Suarez temperature relaxation and low-level Rayleigh friction. The tropical stratospheric circulations of four dynamical cores, which are options in NCAR’s Community Atmosphere Model, version 5 (CAM5), are intercompared. These are the semi-Lagrangian (SLD) and Eulerian (EUL) spectral transform, finite-volume (FV), and spectral element (SE) dynamical cores. The paper investigates how the model design choices impact the wave generation, propagation, and dissipation mechanisms in the equatorial region. SLD, EUL, and SE develop spontaneous QBO-like oscillations in the upper equatorial stratosphere, whereas FV does not sustain the oscillation. Transformed Eulerian-mean (TEM) analyses reveal that resolved waves are the dominant drivers of the QBOs. However, the Eliassen–Palm flux divergence is strongly counteracted by the TEM momentum budget residual, which represents the forcing by diffusion and thermal damping. Interestingly, a reversed Brewer–Dobson circulation accelerates the downward propagation of the SLD’s QBO, whereas the EUL’s and SE’s QBOs are slowed by a mean ascent. Waves are abundant in the SLD’s, EUL’s, and SE’s tropical atmosphere despite the absence of moist convection as a typical wave trigger. Dynamic instabilities are suggested as a wave-triggering mechanism in the troposphere and wave-dissipation process in the stratosphere. In particular, there are indications that the increased occurrences of strongly negative instability indicators in SLD, EUL, and SE are related to more vigorous wave activities and higher magnitudes of the resolved wave forcing in comparison to FV.

Evidence for tropospheric wind shear excitation of high-phase-speed gravity waves reaching the mesosphere using the ray-tracing technique

Abstract. Sources and propagation characteristics of high-frequency gravity waves observed in the mesosphere using airglow emissions from Gadanki (13.5° N, 79.2° E) and Hyderabad (17.5° N, 78.5° E) are investigated using reverse ray tracing. Wave amplitudes are also traced back, including both radiative and diffusive damping. The ray tracing is performed using background temperature and wind data obtained from the MSISE-90 and HWM-07 models, respectively. For the Gadanki region, the suitability of these models is tested. Further, a climatological model of the background atmosphere for the Gadanki region has been developed using nearly 30 years of observations available from a variety of ground-based (MST radar, radiosondes, MF radar) and rocket- and satellite-borne measurements. ERA-Interim products are utilized for constructing background parameters corresponding to the meteorological conditions of the observations. With the reverse ray-tracing method, the source locations for nine wave events could be identified to be in the upper troposphere, whereas for five other events the waves terminated in the mesosphere itself. Uncertainty in locating the terminal points of wave events in the horizontal direction is estimated to be within 50–100 km and 150–300 km for Gadanki and Hyderabad wave events, respectively. This uncertainty arises mainly due to non-consideration of the day-to-day variability in the tidal amplitudes. Prevailing conditions at the terminal points for each of the 14 events are provided. As no convection in and around the terminal points is noticed, convection is unlikely to be the source. Interestingly, large (~9 m s−1km−1) vertical shears in the horizontal wind are noticed near the ray terminal points (at 10–12 km altitude) and are thus identified to be the source for generating the observed high-phase-speed, high-frequency gravity waves.