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The Lambda-Cold Dark Matter (LCDM) model agrees with most of the cosmological observations, but has some hindrances from observed data at smaller scales such as galaxies. Recently, Berezhiani and Khoury (2015) proposed a new theory involving interacting superfluid dark matter with three model parameters, which explains galactic dynamics with great accuracy. In the present work, we study the cosmological behaviour of this model in the linear regime of cosmological perturbations. In particular, we compute both analytically and numerically the matter linear growth factor and obtain new bounds for the model parameters which are significantly stronger than previously found. These new constraints come from the fact that structures within the superfluid dark matter framework grow quicker than in LCDM, and quite rapidly when the DM-baryon interactions are strong., Comment: 16 pages, 6 figures

In single-molecule force spectroscopy, the rupture force Fmax required for mechanical unfolding of a biomolecule or for pulling a ligand out of a binding site depends on the pulling speed V and, in the linear Bell-Evans regime, Fmax ∼ ln(V). Recently, it has been found that non-equilibrium work W is better than Fmax in describing relative ligand binding affinity, but the dependence of W on V remains unknown. In this paper, we developed an analytical theory showing that in the linear regime, W ∼ c1 ln(V) + c2 ln2(V), where c1 and c2 are constants. This quadratic dependence was also confirmed by all-atom steered molecular dynamics simulations of protein-ligand complexes. Although our theory was developed for ligand unbinding, it is also applicable to other processes, such as mechanical unfolding of proteins and other biomolecules, due to its universality.

This article determines the fluid motion underlying coupled linear internal and surface waves in a deep-water two-fluid-layer model (with the lower layer being of infinite depth). A detailed Eulerian description of the wave-field kinematics for coupled linear travelling waves is achieved using phase-plane analysis. The qualitative motion of individual fluid particles is elucidated through analysis of the relevant nonlinear dynamical systems from the Lagrangian viewpoint.

International audience; The search space of full-waveform inversion (FWI) can be extended via a relaxation of the wave equation to increase the linear regime of the inversion. This wave-equation relaxation is implemented by solving jointly (in a least-squares sense) the wave equation weighted by a penalty parameter and the observation equation such that the reconstructed wavefields closely match the data, hence preventing cycle skipping at receivers. Then, the subsurface parameters are updated by minimizing the temporal and spatial source extension generated by the wave-equation relaxation to push back the data-assimilated wavefields toward the physics. This extended formulation of FWI has been efficiently implemented in the frequency domain with the augmented Lagrangian method in which the overdetermined systems of the data-assimilated wavefields can be solved separately for each frequency with linear-algebra methods and the sensitivity of the optimization to the penalty parameter is mitigated through the action of the Lagrange multipliers. Applying this method in the time domain is, however, hampered by two main issues: the computation of data-assimilated wavefields with explicit time-stepping schemes and the storage of the Lagrange multipliers capturing the history of the source residuals in the state space. These two issues are solved by recognizing that the source residuals on the right side of the extended wave equation, when formulated in a form suitable for explicit time stepping, are related to the extended data residuals through an adjoint equation. This relationship first allows us to relate the extended data residuals to the reduced data residuals through a normal equation in the data space. Once the extended data residuals have been estimated by solving (exactly or approximately) this normal equation, the data-assimilated wavefields are computed with explicit time-stepping schemes by cascading an adjoint and a forward simulation. Second, the relationship between the source and the data residuals allows us to project the Lagrange multipliers tied to the wave-equation constraint in the data space at the expense of additional adjoint simulations. This leads to a formulation of the extended FWI that is very similar to that of the classic reduced-space FWI. The computational cost of the extended FWI is two times that of the classic reduced-space FWI, and the storage requirement is the same. Applications to different synthetic benchmarks involving large contrasts confirm the resilience of the method to cycle skipping even when the quadratic problem for the extended data residuals is solved approximately with one inner iteration of a steepest-descent method.

We study the spatiotemporal evolution of an evaporating liquid film sheared by a gas considering both inertial and thermal instabilities, the latter arising from a combination of evaporation and Marangoni effects. The shearing gas is modeled by imposing a constant shear stress applied along the liquid's interface. Following in the footsteps of Joo et al. [S. W. Joo et al., J. Fluid Mech. 230, 117 (1991)], long-wave theory is used to derive a Benney-like equation governing the temporal volution of the liquid interface under the effects of inertia, hydrostatic pressure, surface tension, thermocapillarity, evaporation, and gas shear. Linear stability theory is used to investigate the temporal and spatiotemporal characteristics of the flow, where it is found that the evaporation of the film promotes absolute instabilities and can cause convective-absolute transitions of the perturbations. It is also found that a strong enough counterflowing shearing gas can suppress the inertial instability, commonly known as the H mode, affirming similar conclusions found by previous studies for a strongly confined isothermal film. Additionally, our temporal stability analysis indicates that the thinning of the film reduces the phase speed of thermal perturbations, due to the increasing dominance of viscosity. However, our spatiotemporal analysis shows that the thinning of the film actually results in the growth of additional modes with higher group velocities resulting in faster contamination of the flow field. Moreover, the interface evolution equation is solved numerically to (i) simulate the film's interface evolution subject to finite perturbations and (ii) compare to the results of the linear stability analysis. We find qualitative agreement between the temporal dynamics of the linear and nonlinear instabilities. Our subsequent numerical nonlinear spatiotemporal stability analysis demonstrates that for weaker thermal instabilities, the wave-front dynamics are imposed by the nonlinearly saturated wave packet, while for stronger thermal instabilities, the wave-front dynamics are dictated by the linear dispersion relationship. We also study the effects of the dimensionless parameters on the rupture location and the time it takes for the fluid film to rupture. Finally, the shear stress's effect on the rupture mechanics of the film is studied using self-similarity analysis, where we identify the fate of the evolution equation's solutions.

Using experimental data on the electric pulse heating of a niobium wire, we showed for the first time that a linear relationship between the flux and force—the fundamental assumption of the linear regime in thermodynamics—is fulfilled at a rate of temperature change of dT/dτ ≈ 5 × 107 K/s.

Experimental thermograms obtained on samples of different shapes and sizes under spontaneous cooling, pulsed resistive heating, or laser surface heating of the solid phase of high-temperature metals are analyzed. It is shown that all the thermograms can be ascribed to a linear thermodynamic regime. A linear dependence of the entropy production density on the rate of variation of the temperature is found on analyzing the thermograms. This means that the rate of variation in the temperature can be regarded as an additional variable for the entropy production density in the linear regime and can be used for representing properties measured in a nonstationary thermal regime.

The aim of this paper is to investigate physical characteristics of spherical stars for an observer moving relative to matter distribution in linear regime. We impose shear-free condition to explore numerical solution of the field equations for five well-known compact stars (PSR J1614-2230, PSR J1903+0327, Vela X-1, SMC X-1, Cen X-3) and examine their physical behavior. It is found that all considered compact stars are stable. We conclude that all expected physical features are present related to stellar fluid configuration.

International audience; We investigate the influence of gravity and heat loss on the long-time nonlinear dynamics of premixed flames. We show that even when their influence remains weak in the linear regime they can significantly modify the long-time behavior. We suggest that the presence of such a large-scale stabilizing effect could be responsible for the creation of new cells on the front and the appearance of the strong persistent patterns observed in several recent experimental and numerical studies. It could also explain some statistical anomalies observed in the topology of flame fronts.

Quantum dots (QDs) are model systems for studying quantum thermoelectric behaviour because of their ability to control and measure the effects of electron-energy filtering and quantum confinement on thermoelectric properties. In this chapter, we will discuss the thermoelectric properties of QDs. It starts with a discussion of thermoelectric coefficients in quantum limits in the linear regime, followed by the discussions on the Wiedemann–Franz law, figure of merit and nonlinear responses. At the end, we will briefly look into the applications for using thermoelectric properties of QDs.

We show that Maxwell's demon-like nonreciprocity can be supported in a class of non-Hermitian gyrotropic metasurfaces in the linear regime. The proposed metasurface functions as a transmission-only Maxwell's demon operating at a pair of photon energies. Based on multiple scattering theory, we construct a dual-dipole model to explain the underlying mechanism that leads to the antisymmetric nonreciprocal transmission. The results may inspire new designs of compact nonreciprocal devices for photonics., 6 pages, 5 figures

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

We study the effect of magnetic field on the properties of a high mobility gated two-dimensional electron gas in a field effect transistor with the Hall bar geometry. When approaching the current saturation when the drain side of the channel becomes strongly depleted, we see a number of unusual effects related to the magnetic field induced re-distribution of the electron density in the conducting channel. The experimental results obtained in the non-linear regime have been interpreted based on the results obtained in the linear regime by a simple theoretical model, which describes quite well our observations., 6 pages, 8 figures

It is a commonly accepted creed that in typical situations the rate of entropy production is non-negative. We show that this assertion is not entirely correct if a time-dependent, external perturbation is not compensated by a rapid enough decay of the response function. This is demonstrated for three variants of the Drude model to describe electrical conduction in noble metals, namely the classical free electron gas, the Drude-Sommerfeld model, and the Extended Drude-Sommerfeld model. The analysis is concluded with a discussion of potential experimental verifications and ramifications of negative entropy production rates., 6+4 pages, 10 figures

Specimens are collected from $N$ different sources. Each specimen has probability $p$ of being contaminated, independently of the other specimens. Suppose we can repeatedly take small portions from several specimens, mix them together, and test the mixture for contamination, so that if the test turns positive, then at least one of the samples in the mixture is contaminated. In this paper we consider a binary search scheme for determining all contaminated specimens. More precisely, we study the number $T(N)$ of tests required in order to find all the contaminated specimens, if this search scheme is applied. We derive recursive and, in some cases, explicit formulas for the expectation, the variance, and the characteristic function of $T(N)$. Also, we determine the asymptotic behavior of the moments of $T(N)$ as $N \to \infty$ and from that we obtain the limiting distribution of $T(N)$ (appropriately normalized), which turns out to be normal., 27 pages, 2 tables

In this paper, we analyze the real-time infection data of COVID-19 epidemic for nine nations. Our analysis is up to 7 April 2020. For China and South Korea, who have already flattened their infection curves, the number of infected individuals (I(t)) exhibits power-law behavior before flattening of the curve. Italy has transitioned to the power-law regime for some time. For the other six nations—USA, Spain, Germany, France, Japan, and India—a power-law regime is beginning to appear after exponential growth. We argue that the transition from an exponential regime to a power-law regime may act as an indicator for flattening of the epidemic curve. We also argue that long-term community transmission and/or the transmission by asymptomatic carriers traveling long distances may be inducing the power-law growth of the epidemic.

Observations of barrier coasts around the world suggest that some systems do not conform to the O'Brien-Jarret law. Here we explain this by investigating how resonance and bottom friction affect the response of tidal inlets to variations in basin geometry. Therefore, we develop a morphodynamic barrier coast model that is based on the stability concept of Escoffier for the morphological evolution of the inlets, coupled with an idealized hydrodynamic model that describes the water motion in the outer sea, inlets, and arbitrarily shaped back-barrier basin. We find that the total tidal prism through all inlets is predominantly determined by the (cross-shore) width of the basin and identify three regimes for this. First, a linear regime for narrow basins (i.e., basin width (Formula presented.) tidal wavelength) where a larger basin leads to a linear increase in total tidal prism. Second, a resonant regime for basins with a width around the resonant condition in which the total tidal prism reaches a peak. This resonance condition is a quarter tidal wavelength for basins without friction, which shifts to narrower basins as friction becomes stronger, down to 0.15 tidal wavelength. Third, a dissipative regime for wide basins (i.e., the cross-shore basin dimension or basin width (Formula presented.) resonant condition) with sufficiently strong bottom friction in which the total tidal prism does not change for wider basins, because the tidal wave completely dissipates in the basin.

In a model presented in Yang et al. [Phys. Rev. B 99, 024418 (2019)] it was stated that in the linear regime spin selectivity cannot be measured when using two contacts configuration, and that the results observed when studying the chiral-induced spin-selectivity effect are not consistent with this statement. Here we claim that the results cited clearly indicate nonlinearity and therefore the spin selectivity observed is valid observation.

Recent experimental advances probing coherent phonon and electron transport in nanoscale devices at contact have motivated theoretical channel-based analyses of conduction based on the nonequilibrium Green's function formalism. The transmission through each channel has been known to be bounded above by unity, yet actual transmissions in typical systems often fall far below these limits. Building upon recently derived radiative heat transfer limits and a unified formalism characterizing heat transport for arbitrary bosonic systems in the linear regime, we propose new bounds on conductive heat transfer. In particular, we demonstrate that our limits are typically far tighter than the Landauer limits per channel and are close to actual transmission eigenvalues by examining a model of phonon conduction in a 1-dimensional chain. Our limits have ramifications for designing molecular junctions to optimize conduction., Comment: 10 pages, 2 figures, 2 appendices

The wave is one of the fundamental phenomena occurring in physics. Locally acting forces produce perturbations that propagate in space and time. Their dynamics shows features that allow general classifications of a wide variety of phenomena and, in the linear regime, general relations among the dynamic variables can be formulated.

The kinetics of oxidation of palladium is investigated in this study. The effects of temperature and pressure on the oxide growth of palladium are discussed. A study of the linear regime of palladium oxidation data is examined, and regression analysis is utilized to analyze the oxidation of palladium. Comparison of the oxidation kinetics of palladium is made with that of ruthenium, rhodium and silver.

International audience; We present an experimental and numerical investigation of the Darrieus- Landau instability in a quasi two-dimensional Hele-Shaw cell. Experiments and Lattice-Boltzmann numerical simulations are compared with Darrieus- Landau analytical theory, showing an excellent agreement for the exponential growth rate of the instability in the linear regime. The negative growth rate – second solution of the dispersion relation – was also measured numerically for the first time to the authors’ knowledge. Experiments and numerical simulations were then carried out beyond the cutoff wavelength, providing good agreement even in the unexplored regime where Darrieus-Landau is supplanted by diffusive stabilization. Lastly, the non-linear evolution involving the merging of crests on the experimental flame front is also successfully recovered using both the Michelson-Sivashinsky equation integration and the Lattice-Boltzmann simulation.

The cavity mediated spin current between two ferrite samples has been reported by Bai et. al. [Phys. Rev. Lett. 118, 217201 (2017)]. This experiment was done in the linear regime of the interaction in the presence of external drive. In the current paper we develop a theory for the spin current in the nonlinear domain where the external drive is strong so that one needs to include the Kerr nonlinearity of the ferrite materials. In this manner the nonlinear polaritons are created and one can reach both bistable and multistable behavior of the spin current. The system is driven into a far from equilibrium steady state which is determined by the details of driving field and various interactions. We present a variety of steady state results for the spin current. A spectroscopic detection of the nonlinear spin current is developed, revealing the key properties of the nonlinear polaritons. The transmission of a weak probe is used to obtain quantitative information on the multistable behavior of the spin current. The results and methods that we present are quite generic and can be used in many other contexts where cavities are used to transfer information from one system to another, e.g., two different molecular systems., Comment: 8 pages, 8 figures

Building on the celebrated works by Toupin (1963) on non-linear elastic dielectric materials and by Noll (1967) on the theory of material uniformity, we use the method of linear perturbations to obtain a generalised form of the equations of piezoelectricity in the linear regime, i.e., below the ferroelectric threshold. More specifically, in their most general form, the piezoelectric constitutive equations that we obtain include an anelastic strain and an anelastic polarisation, both arising from the intrinsic inhomogeneity of the body and according to the theory of material uniformity. These are distinct from the irreversible strain and polarisation that occur at values of stress and electric field above the ferroelectric threshold. Some of the known standard forms of the piezoelectricity equations are retrieved as particular cases.

Calculations of thermoelectric transport coefficients including quantum effects are performed on superlattices using the Buttiker approximation. The results are compared to the Boltzmann transport equation with minibands present, and to an incoherent transport model. Comparisons are performed in the linear regime for the electrical conductivity, Seebeck and Lorenz coefficients. We show that at superlattice periods smaller than the typical electron mean free path, the former model and the calculations including quantum effects are in agreement. However, for longer superlattices the incoherent model is shown to be more correct.

We present a simple model that is able to demonstrate that degradation on the morphology of a conducting Large Area Field Emitter (LAFE) may cause a kinked behavior on the corresponding ordinary Fowler-Nordheim (FN) plot, even operating at cold field electron emission (CFE) regime at finite temperature. The simulated FN plot, which is shown to be formed by two clear linear regimes, presented also saturation at high applied field limit. Importantly, we observed a nearly linear regime, even after the degradation has been started, in which spurious values of the slope characterization parameter were achieved. This feature is a strong evidence that the change in the morphology of the LAFE, during the increasing of the applied field, can lead to an unorthodox field emission. Our results show that the effective scaled barrier field, extracted from the simulated FN plot in our model, is consistent with that found in recent experiments reported in literature. Such results are a partial history and probably justify the connection between the general mechanism of LAFE's degradation and unorthodox field emission. Finally, the consequences of initial local FEF distributions on the transition from the latter nearly linear behavior to the saturation regime are discussed.

Based on the inversion characteristic of the truncated Airy pulse in linear regime with third-order dispersion (TOD), we discuss the related dynamics of the truncated Airy pulse in a nonlinear femtosecond optical system. The influence of the initial total power and the Airy pulse width on the nonlinear effect is studied in detail. The results show that when the initial total power is less than one kilowatt, the inversion characteristics of the truncated Airy pulse with several femtosecond width can be observed, and increasing TOD coefficient will lead to tight-focusing of the truncated Airy pulse near the reversed distance. The interaction between the truncated Airy pulses is also studied. These properties are useful for manipulating pulse propagation in fiber system.

We propose a scheme to realize a topological insulator with optical-passive elements, and analyze the effects of Kerr-nonlinearities in its topological behavior. In the linear regime, our design gives rise to an optical spectrum with topological features and where the bandwidths and bandgaps are dramatically broadened. The resulting edge modes cover a very wide frequency range. We relate this behavior to the fact that the effective Hamiltonian describing the system's amplitudes is long-range. We also develop a method to analyze the scheme in the presence of a Kerr medium. We assess robustness and stability of the topological features, and predict the presence of chiral squeezed fluctuations at the edges in some parameter regimes., Comment: 18 pages, 9 figures

We will consider the effects of compressibility and viscosity on the early dynamics of the Richtmyer–Meshkov instability (RMI). In particular, we will combine theory, scaling, and high resolution simulation of RMI to probe the details of the initial compression and the subsequent viscous damping as a shock interacts with a density discontinuity. We will propose a refinement of the classic 1D model for the linear regime of RMI that, for small initial perturbation wavelengths, more accurately reproduces the 2D dynamics of a fully resolved numerical simulation.