We study a three-dimensional system of a rectangular waveguide resonator with an inserted thin ferrite disk. The interplay of reflection and transmission at the disk interfaces together with a material gyrotropy effect, gives rise to a rich variety of wave phenomena. We analyze the wave propagation based on full Maxwell-equation numerical solutions of the problem. We show that the power-flow lines of the microwave-cavity field interacting with a ferrite disk, in the proximity of its ferromagnetic resonance, form whirlpool-like electromagnetic vortices. Such vortices are characterized by the dynamical symmetry breaking. The role of ohmic losses in waveguide walls and dielectric and magnetic losses in a disk are the subjects of our investigations.

Pendry et al. have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight– (homogeneous) layer approximation of the ideal continuous medium. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.

The Saupe ordering matrix of a banana-shaped mesogenic molecule as a solute in a common nematic calamitic solvent has been determined by ${}^2\mathrm{H}$-NMR spectroscopy as a function of temperature. The temperature dependence of the Saupe ordering matrix element associated with the principal molecular axis is consistent with a glassy behavior in the reorientational motion of this particular solute molecule. The Haller expression, appropriately modified, provides a good fit to the experimental data.

We have investigated the smectic-$C_{\alpha }^{*}$–smectic-$C^{*}$ $\left(\mathrm{Sm}{C}_{\alpha }^{*}\text{−}\mathrm{Sm}{C}^{*}\right)$ transition in a series of binary mixtures with resonant x-ray diffraction, differential optical reflectivity, and heat capacity measurements. Results show that the phases are separated by a first-order transition that ends at a critical point. We report the observation of such a critical point. We have proposed the appropriate order parameter and obtained values of two critical exponents associated with this transition. The values of the critical exponents suggest that long-range interactions are present in the $\mathrm{Sm}{C}_{\alpha }^{*}\text{−}\mathrm{Sm}{C}^{*}$ critical region.

We have developed an efficient method for the atomistic determination of the conductance of a biological ion channel model by applying an external field to the conducting ions only. The underlying theory is discussed and demonstrated in a simple test system consisting of two ions in a box of water. Finally, the theory is applied to the experimentally determined structure of the KcsA potassium channel from which a conductance in reasonable agreement with the experimental result is predicted.

The population balance equation (PBE) for growth by attachment of a monomeric unit is described in the discrete domain by an infinite set of differential equations. Transforming the discrete problem into the continuous domain produces a series expansion which is usually truncated past the first term. We study the effect of this truncation and we show that by including the second-order term one obtains a Fokker-Planck approximation of the continuous PBE whose first and second moments are exact. We use this truncation to study the asymptotic behavior of the variance of the size distribution with growth rate that is a power-law function of the particle mass with exponent $a$. We obtain analytic expressions for the variance and show that its asymptotic behavior is different in the regimes $a<1∕2$ and $a>1∕2$. These conclusions are corroborated by Monte Carlo simulations.

We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and $XY$ models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.

This paper addresses the geometric random packing and void fraction of polydisperse particles. It is demonstrated that the bimodal packing can be transformed into a continuous particle-size distribution of the power law type. It follows that a maximum packing fraction of particles is obtained when the exponent (distribution modulus) of the power law function is zero, which is to say, the cumulative finer fraction is a logarithmic function of the particle size. For maximum geometric packings composed of sieve fractions or of discretely sized particles, the distribution modulus is positive (typically $0<\alpha <0.37$). Furthermore, an original and exact expression is derived that predicts the packing fraction of the polydisperse power law packing, and which is governed by the distribution exponent, size width, mode of packing, and particle shape only. For a number of particle shapes and their packing modes (close, loose), these parameters are given. The analytical expression of the packing fraction is thoroughly compared with experiments reported in the literature, and good agreement is found.

An understanding of the polarization characteristics is a prevailing issue in electrostatics and scattering theory and is also vital to the rational design of future dielectric nanostructures. In this work, a finite-element methodology has been applied to simulate two-phase heterostructures containing a polarizable dielectric inclusion. The inclusions investigated can be considered as arbitrarily shaped cross sections of infinite three-dimensional objects, where the properties and characteristics are invariant along the perpendicular cross-sectional plane. Given the paucity of experimental and numerical data, we set out to systematically investigate the trends that shape and permittivity contrast between the inclusion and the host matrix have on the depolarization factor (DF). The effect of the first–versus second-order concentration virial coefficient on the value of the DF is considered for a variety of inclusion shapes and a large set of material properties. Our findings suggest that the DF for such inclusions is highly tunable depending on the choice of these parameters. These results can provide a useful insight for the design of artificial two-phase heterostructures with specific polarization properties.

We present a multiscale model based on the classical lattice time-dependent density-functional theory to study microstructure evolution in multiphase systems. As a first test of the method, we study the static and dynamic properties of isolated inclusions. Three cases are explored: elastically homogeneous systems, elastically inhomogeneous systems with soft inclusions, and elastically inhomogeneous systems with hard inclusions. The equilibrium properties of inclusions are shown to be consistent with previous results: both homogeneous and hard inclusions adopt a circular shape independent of their size, whereas soft inclusions are circular below a critical radius and elliptic above. In all cases, the Gibbs-Thomson relation is obeyed, except for a change in the prefactor at the critical radius in soft inclusions. Under growth conditions, homogeneous inclusions exhibit a Mullins-Sekerka shape instability [W. Mullins and R. Sekerka, J. Appl. Phys. 34, 323 (1963)], whereas in inhomogeneous systems, the growth of perturbations follows the Leo-Sekerka model [P. Leo and R. Sekerka, Acta Metall. 37, 3139 (1989)]. For soft inclusions, the mode instability regime is gradually replaced by a tip-growing mechanism, which leads to stable, strongly out-of-equilibrium shapes even at very low supersaturation. This mechanism is shown to significantly affect the growth dynamics of soft inclusions, whereas dynamical corrections to the growth rates are negligible in homogeneous and hard inclusions. Finally, due to its microscopic formulation, the model is shown to automatically take into account phenomena caused by the presence of the underlying discrete lattice: anisotropy of the interfacial energy, anisotropy of the kinetics, and preferential excitation of shape perturbations commensurate with the rotational symmetry of the lattice.

We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel, we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes an orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments. We derive the specific form of the interaction kernel from the detailed analysis of microscopic interaction of two filaments mediated by a moving molecular motor and extend our results to include variable motor density and motor attachment to the substrate.

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependavxx on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.

We generalize the degree-organizational view of real-world networks with broad degree distributions in a landscape analog with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes correspond to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or in molecular networks to functional localization.

The recurrence time distribution of mushroom billiards with a parabolic-shaped hat is investigated. Classical dynamics exhibits sharply divided phase space, and the recurrence time distribution obeys the algebraic law like well-known classes of billiards. However, due to the existence of a specific type of marginally unstable periodic orbits that forms a crossing in phase space, the sticky motion occurs not as a simple drift along the straight line. Numerical experiments reveal and also theoretical analyses predict that an exponent for the cumulative recurrence time distribution approaches 2 in the asymptotic regime, but in a relatively small recurrence time scale it significantly deviates from the predicted universality, which is explained by the slowdown behavior around a crossing point of the periodic orbit family.

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.

Angular distribution of protons is measured from ethanol droplet spray irradiated by linearly polarized $150\mathrm{fs}$ laser pulses at an intensity of $1.1\times {10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$. Fast protons (with energies $>16\mathrm{keV}$) with an anisotropic distribution can be observed only in or near the polarization plane of the laser fields, while the slow protons (with energies $\leqq 16\mathrm{keV}$) emit with nearly an isotropic distribution. Two-dimensional particle-in-cell simulations suggest that three groups of protons originate from different acceleration regimes in the laser-droplet interaction. The first group with the highest energies is accelerated backwards by the anisotropic charge-separation field near the front surface (laser-droplet interaction side) due to the resonance absorption; the second group (forward emission) is generated by the target-normal sheath acceleration mechanism; and the third group, with the lowest energies, is accelerated by the hydrodynamic expansion of the droplet plasmas.

In this paper, we develop a temporal correlation transfer equation (CTE) for ultrasound-modulated multiply scattered light. The equation can be used to obtain the time-varying specific intensity of light produced by a nonuniform ultrasound field in optically scattering media that have a heterogeneous distribution of optical parameters. We also develop a Monte Carlo algorithm that can provide the spatial distribution of the optical power spectrum in optically scattering media with focused ultrasound fields, and heterogeneous distributions of optically scattering and absorbing objects. Derivation of the CTE is based on the ladder diagram approximation of the Bethe-Salpeter equation that assumes moderate ultrasound pressures. We expect the CTE to be applicable to a wide spectrum of conditions in the ultrasound-modulated optical tomography of soft biological tissues.

A theory of active sonar (or radar) pulse wave form design, for optimal target detection in cluttered environments, is presented. The received target signal is maximized via a cost function $\mathcal{L}$ that incorporates both the signal-to-noise ratio and a generalization of the Heisenberg uncertainty principle, which is used to balance bandwidth (or range resolution) against signal gain. The optimal pulse wave form is the ground state solution to a one-dimensional Schrödinger-type equation in frequency space, with an effective potential energy that tends to concentrate pulse energy in frequency bands where the target reflectivity dominates the clutter reflectivity.

A particular basis set method developed by one of the authors, involving maximally localized orthogonal Weyl-Heisenberg wavelets (or “weylets”) and a phase space truncation scheme, has been successfully applied to exact quantum calculations for many degrees of freedom (DOF’s) [B. Poirier and A. Salam, J. Chem. Phys. 121, 1740 (2004)]. However, limitations in accuracy arise in the many-DOF case, owing to memory limits on conventional computers. This paper addresses this accuracy limitation by introducing phase space region operators (PSRO’s) that customize individual weylet basis functions for the problem of interest. The construction of the PSRO’s is straightforward, and does not require a priori knowledge of the desired eigenstates. The PSRO, when applied to weylets, as well as to simple phase space Gaussian basis functions, exhibits remarkable improvements in accuracy, reducing computed eigenvalue errors by orders of magnitude. The method is applied to various model systems at varying DOF’s.