The extended optical theorem is generalized for scalar acoustical beams of arbitrary character with any angle of incidence interacting with an object of arbitrary geometric shape and size, and placed randomly in the beam's path with any scattering angle. Analytical expressions for the extinction, absorption, and scattering cross sections are derived, and the connections with the axial (i.e., along the direction of wave propagation) torque and radiation force calculations are discussed. As examples to illustrate the analysis for a viscoelastic object, the extinction, absorption, and scattering cross sections are provided for an infinite plane progressive wave, infinite nondiffracting Bessel beams, a zero-order spherical quasi-Gaussian beam, and a Bessel-Gauss vortex beam emanating from a finite circular aperture, which reduces to a finite high-order Bessel beam, a finite zero-order Bessel beam, and a finite piston radiator vibrating uniformly with appropriate selection of beam parameters. The similarity with the asymptotic quantum inelastic cross sections is also mentioned.

Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

We establish experimentally the flow patterns of induced-charge electro-osmosis around immobilized metallic spheres in aqueous electrolyte. The ac field modifies local electrolyte concentration and causes quadrupolar flows with inward velocities being smaller than the outward ones. At high fields, the flow becomes irregular, with vortices smaller than the size of the sphere. Janus metallodielectric spheres create dipolar flows and pump the fluid from the dielectric toward the metallic part. The experimentally determined far-field flows decay with distance as $r^{-3}$.

We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the computationally tractable model of two-dimensional (2D) magnetohydrodynamics in a periodic box. In the absence of any external magnetic forcing, the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing, the system behaves as 2D magnetohydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied, a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point, the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade.

The x-ray laser-matter interaction for a low-$Z$ material, carbon, is studied with a particle-in-cell code that solves the photoionization and x-ray transport self-consistently. Photoionization is the dominant absorption mechanism and nonthermal photoelectrons are produced with energy near the x-ray photon energy. The photoelectrons ionize the target rapidly via collisional impact ionization and field ionization, producing a hot plasma column behind the laser pulse. The radial size of the heated region becomes larger than the laser spot size due to the kinetic nature of the photoelectrons. The plasma can have a temperature of more than 10 000 K ($>1\mathrm{eV}$), an energy density greater than ${10}^4$ $\mathrm{J}/{\mathrm{cm}}^3$, an ion-ion Coulomb coupling parameter $\Gamma \ge 1$, and electron degeneracy $\Theta \ge 1$, i.e., strongly coupled warm dense matter. By increasing the laser intensity, the plasma temperature rises nonlinearly from tens of eV to hundreds of eV, bringing it into the high energy density matter regime. The heating depth and temperature are also controllable by changing the photon energy of the incident laser light.

Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from equilibrium. In particular, the probabilities for observing the reversible efficiency and the least likely efficiency are identical to those of the same machine working under the time-reversed driving. For time-symmetric drivings, this reversible and the least probable efficiency coincide.

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

A walker is a droplet bouncing on a liquid surface and propelled by the waves that it generates. This macroscopic wave-particle association exhibits behaviors reminiscent of quantum particles. This article presents a toy model of the coupling between a particle and a confined standing wave. The resulting two-dimensional iterated map captures many features of the walker dynamics observed in different configurations of confinement. These features include the time decomposition of the chaotic trajectory in quantized eigenstates and the particle statistics being shaped by the wave. It shows that deterministic wave-particle coupling expressed in its simplest form can account for some quantumlike behaviors.

We here present a simple fitting-parameter-free theory of the Leidenfrost effect (droplet levitation above a superheated plate) covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. The geometry of this film is found to be in excellent quantitative agreement with the interferometric measurements of Burton et al. [Phys. Rev. Lett. 109, 074301 (2012)]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632 (2003)] as far as the effect of plate superheat is concerned and highlight the relative role of evaporation, gravity, and capillarity in the vapor film. To further substantiate these findings, a treatment of the problem by matched asymptotic expansions is also presented.

The accurate prediction and control of the interaction of liquids with hot surfaces is paramount in numerous areas, including cooling applications. We present results illustrating the effect of ambient pressure on the temperature required for a droplet to levitate over a hot surface, i.e., the Leidenfrost temperature. In the present study the dependence of wetting and levitating temperatures on ambient pressure in a range of subatmospheric pressures is reported. Experimental data indicate that the Leidenfrost temperature decreases with decreasing pressure at subatmospheric pressures. A physical approach for the dependence of Leidenfrost temperature on ambient pressure, based on an analogy with saturation pressure dependence, is proposed. Furthermore, previous literature data for pressures above atmospheric are also included in the analysis to support and validate the proposed approach. In addition, the effect of substrate material, substrate roughness, and type of fluid on the Leidenfrost temperature is discussed.

The swimming velocity and rate of dissipation of a linear chain consisting of two or three little spheres and a big sphere is studied on the basis of low Reynolds number hydrodynamics. The big sphere is treated as a passive cargo, driven by the tail of little spheres via hydrodynamic and direct elastic interaction. The fundamental solution of Stokes equations in the presence of a sphere with a no-slip boundary condition, as derived by Oseen, is used to model the hydrodynamic interactions between the big sphere and the little spheres.

We study the Dean instability in curved channels using the lattice Boltzmann model for generalized metrics. For this purpose, we first improve and validate the method by measuring the critical Dean number at the transition from laminar to vortex flow for a streamwise curved rectangular channel, obtaining very good agreement with the literature values. Taking advantage of the easy implementation of arbitrary metrics within our model, we study the fluid flow through a double-curved channel, using ellipsoidal coordinates, and study the transition to vortex flow in dependence of the two perpendicular curvature radii of the channel. We observe transitions not only to two-cell vortex flow but also to four-cell and even six-cell vortex flow, and we find that the critical Dean number at the transition to two-cell vortex flow exhibits a minimum when the two curvature radii are approximately equal.

The energy spectral density $E\left(k\right)$, where $k$ is the spatial wave number, is a well-known diagnostic of homogeneous turbulence and magnetohydrodynamic turbulence. However, in most of the curves plotted by different authors, some systematic kinks can be observed at $k=9$, 15, and 19. We claim that these kinks have no physical meaning and are in fact the signature of the method that is used to estimate $E\left(k\right)$ from a three-dimensional spatial grid. In this paper we give another method in order to get rid of the spurious kinks and to estimate $E\left(k\right)$ much more accurately.

We study close-to-equilibrium properties of a one-dimensional symmetric inclusion process (SIP) with finite size by coupling it to two particle reservoirs at the two boundaries with slightly different chemical potentials. The boundaries introduce irreversibility and induce a weak particle current in the system. We calculate the McLennan ensemble for the SIP, which corresponds to the entropy production, and the first-order nonequilibrium correction for the stationary state. We find that the first-order correction is a product measure and is exactly consistent with the local equilibrium measure corresponding to the steady-state density profile in the finite-size SIP, without the need to be in the thermodynamic limit. This provides a novel example for microscopic extensions of the McLennan formula and the interpretation of first-order nonequilibrium correction as entropy production.

Recent developments in theoretical aspects of spin noise and relaxation and their interrelationship reveal a modified spin density, distinct from the density matrix, as the necessary object to describe fluctuations in spin systems. These fluctuations are to be viewed as an intrinsic quantum mechanical property of such systems immersed in random magnetic environments and are observed as “spin noise” in the absence of any radio frequency excitation. With the prospect of ultrafast digitization, the role of spin noise in real-time parameter extraction for (NMR) spin systems, and the advantage over standard techniques, is of essential importance, especially for systems containing a small number of spins. In this article we outline prospects for harnessing the recent dynamical theory in terms of spin-noise measurement, with attention to real-time properties.

We consider the motion of an aspherical inelastic particle of dumbbell type bouncing repeatedly on a horizontal flat surface. The coefficient of restitution of such a particle depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision whose variance is considerable, even for small eccentricity. Assuming random angular orientation of the particle at the instant of contact we characterize the measured coefficient of restitution as a fluctuating quantity and obtain a wide probability density function including a finite probability for negative values of the coefficient of restitution. This may be understood from the partial exchange of translational and rotational kinetic energy.

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtain scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in dividing the surface in bins of size $\varepsilon$ and using only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class are found. The binning method allows the accurate determination of the height distributions of the ballistic models in both growth and steady-state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2 + 1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in $2+1$ dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.

The statistical methods exploiting the “Correlation-Functions” or the “Differential-Critical-Region” are both suitable for describing phase transformation kinetics ruled by nucleation and growth. We present a critical analysis of these two approaches, with particular emphasis to transformations ruled by diffusional growth which cannot be described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. In order to bridge the gap between these two methods, the conditional probability functions entering the “Differential-Critical-Region” approach are determined in terms of correlation functions. The formulation of these probabilities by means of cluster expansion is also derived, which improves the accuracy of the computation. The model is applied to 2D and 3D parabolic growths occurring at constant value of either actual or phantom-included nucleation rates. Computer simulations have been employed for corroborating the theoretical modeling. The contribution to the kinetics of phantom overgrowth is estimated and it is found to be of a few percent in the case of constant value of the actual nucleation rate. It is shown that for a parabolic growth law both approaches do not provide a closed-form solution of the kinetics. In this respect, the two methods are equivalent and the longstanding overgrowth phenomenon, which limits the KJMA theory, does not admit an exact analytical solution.

The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ${\zeta }_n$ from the structure functions $S_n\left(r\right)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio $|S_n\left(r\right)/S_3\left(r\right)|$ against the separation $r$ in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots $S_n\left(r\right)$ against $S_3\left(r\right)$, with the assumption $S_3\left(r\right)\sim r$. Using our method for the particular case of $S_2\left(r\right)$ we obtain the result that the exponent ${\zeta }_2$ decreases as the Taylor-Reynolds number increases, with ${\zeta }_2\to 0.679\pm 0.013$ as $R_{\lambda }\to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.