Energy losses of test particles in magnetized two-component plasmas are investigated within the framework of the linearized Vlasov-Poisson theory, taking into account the dynamic polarization effects of both the plasma ions and electrons. General expressions of the potential and stopping power are obtained and calculations are performed for protons in a magnetized hydrogen plasma. The influences of the magnetic field, the angle between the proton velocity and magnetic field, and certain plasma parameters on the stopping power are studied. Numerical results show that for low particle velocities and strong magnetic field the dynamic polarization effects of the plasma ions become obvious and contribute mainly to the stopping power.

The master equation is cast in the form of an equality involving the variation, in the course of a transformation, of a quantity playing the role of a generalized potential, weighted with the probability of allowable transformations emanating from different initial states. In the most general case this equality cannot be formulated entirely in terms of thermodynamic variables and state functions. Some conditions under which such a reduction becomes possible are identified and a comparison with fluctuation and work type relationships previously reported in the literature is carried out.

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the $XY$ model on the square lattice to order ${\beta }^{33}$ by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as ${\beta }_c=1.1200\left(1\right)$, which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be $\theta =0.054\left(10\right)$, which is consistent with the renormalization group prediction of $\theta =\frac{1}{16}$.

We consider the thermal Casimir effect in systems of parallel plates coupled to a massless free field theory via quadratic interaction terms which suppress (i) the field on the plates and (ii) the gradient of the field in the plane of the plates. These boundary interactions correspond to (i) the presence of an electrolyte in the plates and (ii) a uniform field of dipoles, in the plates, which are polarizable in the plane of the plates. These boundary interactions lead to Robin-type boundary conditions in the case where there is no field outside the two plates. In the appropriate limit, in both cases Dirichlet boundary conditions are obtained but we show that in case (i) the Dirichlet limit breaks down at short interplate distances and in (ii) it breaks down at large distances. The behavior of the two plate system is also seen to be highly dependent on whether the system is open or closed. In addition we analyze the Casimir force on a third plate placed between two outer plates. The force acting on the central plate is shown to be highly sensitive to whether or not the fluctuating scalar field is present in the region exterior to the two confining plates.

Experiments show that under suitable conditions magnetic particles in ferrofluids and other polar suspensions undergo condensation phase transitions and form dense liquidlike or solidlike phases. The problem of fundamental features and scenarios of the phase transitions is one of the central problems of the physics of these systems. This work deals with the theoretical study of scenarios of condensation phase transitions in ferrofluids, consisting of identical magnetic particles. Our results show that, unlike the classical condensation phase transitions, the appearance of the linear chains precedes the magnetic particle bulk condensation. The effect of the chains on the diagrams of the equilibrium phase transitions is studied.

The voltage-driven dynamics of a stiff polymer through a nanopore are treated with a bend elastic model. In contrast to flexible polymers described by a stretch elasticity, bend elastic chains can be oriented in an external field, here the anchoring field created by the pore atoms. The trajectory of the chain is calculated using the Langevin equation of motion. The dynamical equation is solved by a normal mode analysis of the elastic curve with free ends. Interaction with the pore walls acts to align the chain, and with the electric field induced inside the pore controls the translocation time. Application of a force proportional to the distance of the exit from the end of the pore such as an optical trap slows down the motion, and reduces the chain response to the wall potential and the extension along the pore axis. DNA is a well-known semirigid polymer, and a comparison is made to the molecular dynamics simulation of translocation of DNA through a synthetic nanopore.

A class of nonautonomous nonlinear Schrödinger equations, claiming to be novel integrable systems with rich properties, continues to appear in the literature. All such equations are shown to be not new, but equivalent to the standard autonomous equation, which trivially explains their integrability features.

The adaptive time-stepping algorithm for Brownian simulation of solute diffusion in three-dimensional complex geometries previously developed by the authors of this paper was applied to heterogeneous three-dimensional polymer hydrogel structures. The simulations were performed on reconstructed three-dimensional hydrogels. The obstruction effect from the gel strands on water and diffusion of dendrimers with different sizes were determined by simulations and compared with experimental nuclear magnetic resonance diffusometry data obtained from the same material. It was concluded that obstruction alone cannot explain the observed diffusion rates, but an interaction between the dendrimers and the gel strands should be included in the simulations. The effect of a sticky-wall interaction potential with geometrically distributed residence times on the diffusion rate has been studied. It was found that sticky-wall interaction is a possible explanation for the discrepancy between simulated and experimental diffusion data for dendrimers of different sizes diffusing in hydrogels.

We study the volatility time series of 1137 most traded stocks in the U.S. stock markets for the two-year period 2001–2002 and analyze their return intervals $\tau$, which are time intervals between volatilities above a given threshold $q$. We explore the probability density function of $\tau$, $P_q\left(\tau \right)$, assuming a stretched exponential function, $P_q\left(\tau \right)\sim e^{-{\tau }^{\gamma }}$. We find that the exponent $\gamma$ depends on the threshold in the range between $q=1$ and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how $\gamma$ depends on four essential factors, capitalization, risk, number of trades, and return. We show that $\gamma$ depends on the capitalization, risk, and return but almost does not depend on the number of trades. This suggests that $\gamma$ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of $\tau$, ${\mu }_m\equiv {\mathbf{⟨}{(\tau ∕⟨\tau ⟩)}^m\mathbf{⟩}}^{1∕m}$, in the range of $10<⟨\tau ⟩⩽100$ by a power law, ${\mu }_m\sim {⟨\tau ⟩}^{\delta }$. The exponent $\delta$ is found also to depend on the capitalization, risk, and return but not on the number of trades, and its tendency is opposite to that of $\gamma$. Moreover, we show that $\delta$ decreases with increasing $\gamma$ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.

We study the free-electron gas in an Apollonian network within the tight-binding framework. The scale-free and small-world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities, gaps, and minibands. After an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations, we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum. The fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat. The absence of chiral symmetry of the Apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations.

Inviscid flow within an evaporating sessile drop is analyzed. The field equation $E^2\psi =0$ is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux along the free boundary. Specific results and computations are presented for evaporation corresponding to both uniform flux and purely diffusive gas phase transport into an infinite ambient. Wetting and nonwetting contact angles are considered, with flow patterns in each case being illustrated. The limiting behaviors of small contact angle and droplets of hemispherical shape are treated. All of the above categories are considered for the cases of droplets whose contact lines are either pinned or free to move during evaporation.

A model to calculate the ion-ion pair potentials in hot and dense plasmas is developed based on temperature-dependent density functional theory. The electronic structures, including the energy level and space distributions, are calculated using an average-atom model. The calculated electron space number density is divided into two parts: one is a uniformly distributed electronic sea $\rho \left(r_b\right)$ with a density equal to the total electronic density at the ion sphere boundary, which is redistributed when space overlap occurs between the interacting ions; the left part of the electronic density ${\rho }_i^{2\mathit{nd}}\left(r\right)$ represents the dramatic space variations of the electrons due to the nuclear attraction and the shell structure of the bound states, which maintains unchanged during the interactions between the ions. The pair potential is obtained through space integrations for the energy density functions of electron density. We present molecular dynamics simulations for the ion motion on the basis of the calculated pair potentials in a wide regime of density and temperature. As an example, hot and dense Al and Fe plasmas are simulated to give the equation of state and ion-ion pair distribution function. The results are in agreement with those of other theoretical models.

This paper presents the modeling of microwave $\left(2.45\mathrm{GHz}\right)$ discharges with cylindrical symmetry, produced in the absence of an external magnetic field by ${\mathrm{TM}}_{00}$ surface waves (SW) within either cylindrical or coaxial structures. A stationary, one-dimensional (radial) moment model (including the continuity and the momentum-transfer equations for electrons and positive ions, and the electron mean energy transport equations) is solved self-consistently coupled to Poisson’s equation for the space-charge electrostatic field and the appropriated Maxwell’s equations for the SW electromagnetic field. The model is solved for argon discharges over a broad range of operating conditions: Average electron densities from ${10}^{11}\text{to}3\times {10}^{12}{\mathrm{cm}}^{-3}$ and gas pressures from ${10}^{-2}\text{to}5\text{Torr}$. Results are compared to those of a simplified classical model that disregards charge separation near discharge boundaries, ignoring also the development of electron-plasma resonances caused by the severe electron density gradients within space-charge sheath regions. Simulations show that the presence of a sheath-resonance region has a strong influence on the values of the SW attenuation constant, particularly at low pressures and high electron densities, affecting also the local budget of the discharge power deposition (hence discharge maintenance).

The spectral function for an electron one-component plasma is calculated self-consistently using the $G{W}^{\left(0\right)}$ approximation for the single-particle self-energy. In this way, correlation effects that go beyond the mean-field description of the plasma are contained, i.e., the collisional damping of single-particle states, the dynamical screening of the interaction, and the appearance of collective plasma modes. Second, a nonperturbative analytic solution for the on-shell $G{W}^{\left(0\right)}$ self-energy as a function of momentum is presented. It reproduces the numerical data for the spectral function with a relative error of less than 10% in the regime where the Debye screening parameter is smaller than the inverse Bohr radius, $\kappa <1a_{\mathrm{B}}^{-1}$. In the limit of low density, the nonperturbative self-energy behaves as $n^{1∕4}$, whereas a perturbation expansion leads to the unphysical result of a density-independent self-energy [Fennel and Wilfer, Ann. Phys. (Leipzig) 32, 265 (1974)]. The derived expression will greatly facilitate the calculation of observables in correlated plasmas (transport properties, equation of state) that need the spectral function as an input quantity. This is demonstrated for the shift of the chemical potential, which is computed from the analytical formulas and compared to the $G{W}^{\left(0\right)}$ result. At a plasma temperature of $100\mathrm{eV}$ and densities below ${10}^{21}{\mathrm{cm}}^{-3}$, the two approaches deviate by less than 10% from each other.

Evanescent probe imaging is a powerful characterization technique with subwavelength resolution. In this paper, we present a theoretical and numerical study of the effect of using double negative (DNG) and single negative (SNG) metamaterials in evanescent probe imaging. A sensitivity definition is introduced for evanescent probes and it is shown using quantitative measures that the sensitivity can be increased using DNG material for a target in vacuum and for a buried target. A minimum DNG thickness is required to achieve an improvement in the sensitivity. For a buried target, there is a fundamental limitation on the maximum achievable sensitivity, in addition to a limitation due to the loss of DNG materials. SNG metamaterials have similar improvements over the sensitivity as the DNG materials but there are additional limitations due to the different transmission characteristics of SNG media. To validate the theoretical findings, numerical simulations are presented.

We investigate lattice Boltzmann (LB) modeling of multicomponent diffusion for finite Knudsen numbers. Analytic solutions for binary diffusion in narrow channels, where both molecular and Knudsen diffusion are of importance, are obtained for the standard and higher-order LB methods and validated against the results from the direct simulation Monte Carlo (DSMC) method. The LB methods are shown to reproduce the diffusion slip phenomena. In the DSMC method, while fluid particles are diffusely reflected on a wall, significant component slip and a kinetic boundary layer are observed. It is shown that a higher-order LB method accurately captures the characteristics observed in the DSMC method.

We apply Monte Carlo simulations to count the numbers of solutions of two well-known combinatorial problems: the $N$-queens problem and Latin-square problem. The original system is first converted to a general thermodynamic system, from which the number of solutions of the original system is obtained by using the method of computing the partition function. Collective moves are used to further accelerate sampling: swap moves are used in the $N$-queens problem and a cluster algorithm is developed for the Latin squares. The method can handle systems of ${10}^4\text{degrees}$ of freedom with more than ${10}^{10000}$ solutions.

On the basis of analytical results and molecular dynamics simulations, we clarify the nonequilibrium dynamics of a long-range interacting system in contact with a heat bath. For small couplings with the bath, we show that the system can first be trapped in a Vlasov quasistationary state, then a microcanonical one follows, and finally canonical equilibrium is reached at the bath temperature. We demonstrate that, even out of equilibrium, Hamiltonian reservoirs microscopically coupled with the system and Langevin thermostats provide equivalent descriptions. Our identification of the key parameters determining the quasistationary lifetimes could be exploited to control experimental systems such as the free-electron laser, in the presence of external noise or inherent imperfections.

We consider populations represented by random collections of real-valued points, and explore their statistical resilience to random perturbations—seeking populations whose statistics remain qualitatively unchanged by the action of arbitrary random perturbations of a certain type. Studying a general physical perturbation scheme, we obtain an explicit characterization of statistically resilient populations, show that these objects are fractal, and comprehensively analyze their topological and statistical structures. An application of statistical resilience attained is an alternative explanation of the ubiquity of power-law statistics.

We consider the model of random sequential adsorption, with the depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large-time limit. Numerical Monte Carlo simulations of two-dimensional deposition of disks and one-dimensional deposition of segments are reported for the density-density correlation function and gap-size distribution function, respectively. Analytical considerations supplement numerical results in the one-dimensional case. We investigate the correlation hole—the depletion of correlation functions near contact and, for the present model, their vanishing at contact—that opens up at finite times, as well as its closing and reemergence of the logarithmic divergence of correlation properties at contact in the large-time limit.