A symmetrical E-shaped metamaterial is investigated in this paper. Numerical simulations disclose the two electromagnetic resonances and the superwide negative-refractive band of this structure. The distributions of the induced current in the E-shaped copper wires show that these two electromagnetic resonances originate from the current flowing in the different C-shaped rings. The retrieved negative-refractive band is superwide, and the negative refraction with high transmission occurs in the different bands. The metamaterial with two or even more electromagnetic resonances offers an opportunity for the realization of wide-band negative refraction.

Conditions under which the evolution equations of a multivariate system can be cast in a variational form are identified. A kinetic potential generating both the deterministic part of the evolution and the probabilistic properties in a suitably defined set of variables is derived and compared to the thermodynamic potentials. The results are illustrated on the kinetics of phase transitions involving intermediate metastable phases and chemical reactions giving rise to two or more intermediate species.

We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, “sense” the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.

The Fokker-Planck equation for the probability $f\left(r,t\right)$ to find a random walker at position $r$ at time $t$ is derived for the case that the probability to make jumps depends nonlinearly on $f\left(r,t\right)$. The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in the absence of drift and external fields a scaling solution, describing anomalous diffusion, is possible only if the nonlinearity in the jump probability is of the power law type $\left[\sim f^{\eta }\left(r,t\right)\right]$, in which case the generalized Fokker-Planck equation reduces to the porous media equation. Monte Carlo simulations are shown to confirm the theoretical results.

We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of the DNA, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We find that in three dimensions the heat capacity acquires a logarithmic dependence on reduced temperature.

The mechanism of charge transport in the imidazolium-based ionic liquid 1,3-dimethylimidazolium dimethylphosphate is analyzed by combining broadband dielectric spectroscopy (BDS) and pulsed field gradient nuclear magnetic resonance (PFG NMR). The dielectric spectra are dominated—on the low-frequency side—by electrode polarization effects while, for higher frequencies, charge transport in a disordered matrix is the underlying physical mechanism. Using the Einstein and Einstein-Smoluchowski equations enables one to determine—in excellent agreement with direct measurements by PFG NMR—the diffusion coefficient of the charge carriers. By that, it becomes possible to extract from the dielectric spectra separately the number density and the mobilities of the charge carriers and the type of their thermal activation. It is shown that the observed Vogel-Fulcher-Tammann (VFT) dependence of the dc conductivity can be traced back to a similar temperature dependence of the mobility while for the number density an Arrhenius-type thermal activation is found. Extrapolating the latter to room temperature indicates that nearly all charge carriers are participating in the conduction process.

We investigate the effects of clay proportion and nanoscale dispersion in the dielectric response of poly(vinyl alcohol)-bentonite nanocomposites. The dielectric study was performed using the thermally stimulated depolarization current technique, covering the temperature range of the secondary and high-temperature relaxation processes. Important changes in the secondary relaxations are observed at low clay contents in comparison with neat poly(vinyl alcohol) (PVA). The high-temperature processes show a complex peak, which is a combination of the glass-rubber transition and the space-charge relaxations. The analysis of these processes shows the existence of two segmental relaxations for the nanocomposites. Dielectric results were complemented by calorimetric experiments using differential scanning calorimetry. Morphologic characterization was performed by x-ray diffraction (XRD) and transmission electron microscopy (TEM). TEM and XRD results show a mixture of intercalated and exfoliated clay dispersion in a trend that promotes the exfoliated phase as the bentonite content diminishes. Dielectric and morphological results indicate the existence of polymer-clay interactions through the formation of hydrogen bounds and promoted by the exfoliated dispersion of the clay. These interactions affect not only the segmental dynamics, but also the secondary local dynamics of PVA.

We consider a generalized discrete ${\varphi }^4$ model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is integrable. Namely, this problem originally expressed as a three-point map can be reduced to a two-point map, from which the exact moving solutions can be derived iteratively. It was also found that these high-speed kinks can be stable and robust against perturbations introduced in the initial conditions.

The three-dimensional finite-difference time-domain (3D-FDTD) method is developed and implemented in the case of oblique incidence in order to study biperiodic structures that are finished according to the third direction. The perfectly matched layer (PML) is adapted to the developed algorithm. The electromagnetic fields of Maxwell’s equations in the main grid and in the PML media are transferred from the $E\text{−}H$ domain to the mapped $P\text{−}Q$ domain. The modified Maxwell’s equations are implemented by the split-field method (SFM). Several tests are made and presented in order to verify and demonstrate the accuracy of our codes. The obtained results are in good agreement with published ones obtained by other methods. The originality of this paper comes, first from the fact that it brings a complete development of the used algorithm, and second, from the study of the spectral response of a radar dome based on annular aperture arrays perforated into a perfect conductor plate.

A Monte Carlo (MC) simulation in the isobaric-multithermal (MuTh) ensemble has been carried out for a bulk Lennard-Jones fluid system that consists of 108 particles. The MuTh weight factor which we determined turned out to be reliable for the temperature and pressure range from $\left(T^{\ast },P^{\ast }\right)=\left(T_0^{\ast },P_0^{\ast }\right)=\left(2.09,7.25\right)$ to $\left(T^{\ast },P^{\ast }\right)=\left(0.417,1.45\right)$ along $P^{\ast }/T^{\ast }=P_0^{\ast }/T_0^{\ast }$. Thermodynamic quantities calculated from the MuTh MC production run by the reweighting techniques showed the discontinuous change, which is the feature of the first-order phase transition. The radial distribution functions suggest that the transition takes place between liquid and solid states. Two distinct local maxima were observed in the obtained contour representations of the probability distribution at $T^{\ast }=1.04$ and $P^{\ast }=3.63$, which is the phase transition point along $P^{\ast }/T^{\ast }=P_0^{\ast }/T_0^{\ast }$.

We describe an efficient technique for measuring the effective interaction potential for pairs of colloidal particles. The particles to be tested are confined in an extended optical trap, also known as a line tweezer, that is projected with the holographic optical trapping technique. Their diffusion along the line reflects not only their intrinsic interactions with each other, but also the influence of the line’s potential energy landscape and interparticle interactions mediated by scattered light. We demonstrate that measurements of the particles’ trajectories at just two laser powers can be used to correct explicitly for optically induced forces and that statistically optimal analysis for optically induced forces yields autocalibrated measurements of the particles’ intrinsic interactions with remarkably few statistically independent measurements of the particles’ separation.

The present study puts an end to the ongoing controversy regarding volume versus surface nucleation in freezing aerosols: Our study on nanosized aerosol particles demonstrates that current state of the art measurements of droplet ensembles cannot distinguish between the two mechanisms. The reasons are inherent experimental uncertainties as well as approximations used to analyze the kinetics. The combination of both can lead to uncertainties in the rate constants of two orders of magnitude, with important consequences for the modeling of atmospheric processes.

Formation of rafts and other domains in cell membranes is considered as wetting of proteins by lipids. The membrane is modeled as a continuous elastic medium. Thermodynamic functions of the lipid films that wet proteins are calculated using a mean-field theory of liquid crystals as adapted to biomembranes. This approach yields the conditions necessary for a macroscopic wetting film to form; its thickness could also be determined. It is shown that films of macroscopic thicknesses form around large (tens nanometers in diameter) lipid-protein aggregates; only thin adsorption films form around single proteins or small complexes. The means by which wetting films can facilitate the merger of these aggregates is considered. It is shown that a wetting film prevents a protein from leaving an aggregate. Using experimentally derived values of elastic moduli and spontaneous curvatures as well as height mismatch between aggregates and bulk membrane, we obtained numerical results, which can be compared with the experimental data.

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices’ statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. We construct other examples of integrable dynamics of Toda type on the square lattice, as well as on the triangular lattice, as nonlinear symmetries of the discrete Laplace equations on square and triangular lattices. We also construct the $\tau$-function formulations and Darboux-Bäcklund transformations of these dynamics.

In this paper we examine numerically the properties, especially the scaling properties, of an isolated crescent singularity similar to that of a developable cone. The desired isolated crescent region is produced by applying six potential forces to an elastic sheet in a controlled way, for which no central pushing force is required. Two types of length scales of the crescent are identified and shown to scale differently with the thickness and the separation of potentials. It is found that in one direction, the width of the crescent scales with both thickness and separation to the 1/2 power. In the other direction, the radius of curvature of the crescent scales with thickness to the 1/3 power and separation to the 2/3 power, in agreement with previous observation for the crescent size of a developable cone. We expect our findings of the double features of the crescent singularity to have importance in understanding the puzzling scaling behavior of the crescent.

We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of $⟨\text{exp}\left(-\beta W\right)⟩$ to its theoretical mean value, where $W$ is the work done on the test system and $\beta$ is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.