Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter. Here we show that the algorithm is even more efficient if the system is not chaotic and demonstrate by numerical experiments that an accurate reconstruction of the complete traffic state can be obtained at a very low computational cost by monitoring only a small percentage of vehicles.

Complex plasmas are low-temperature plasmas that contain micrometer-size particles in addition to the neutral gas particles and the ions and electrons that make up the plasma. The microparticles interact strongly and display a wealth of collective effects. Here we report on linked numerical simulations that reproduce many of the experimental results of complex plasmas. We model a capacitively coupled plasma with a fluid code written for the commercial package comsol. The output of this model is used to calculate forces on microparticles. The microparticles are modeled using the molecular dynamics package lammps, which we extended to include the forces from the plasma. Using this method, we are able to reproduce void formation, the separation of particles of different sizes into layers, lane formation, vortex formation, and other effects.

We consider the $p$-spin model with spin $1/2$ on all pure Husimi lattices. Using an effective representation of the recursion relations, the phase transitions of the model on all pure Husimi lattices are investigated. First, the nonexistence of the second order phase transitions in the model on all pure Husimi lattices is proven exactly. Then the existence and properties of the first order phase transitions in a zero external magnetic field are studied in detail. An implicit polynomial equation for determining temperatures below which the paramagnetic and ferromagnetic phases coexist in the model on all pure Husimi lattices is found. In addition, an implicit equation for exactly determining the transition temperatures of the first order phase transitions in a zero external magnetic field on all pure Husimi lattices is derived and discussed.

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassylike ordering dynamics may completely inhibit the appearance of the ground-state structures.

The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in time asymptotic expansions in the target radius of the solution to the corresponding diffusion equation. Our approach is based on combining expansions of a long-time approximation of the solution, involving the first eigenvalue and eigenfunction of the Laplacian, with expansions of a short-time correction calculated by a pseudopotential approximation. These expansions allow the calculation of corresponding expansions of the first passage time density for the diffusing molecule to find the target. We demonstrate the accuracy of our method in approximating the first passage time density and related statistics for the spherically symmetric problem where the domain is a large concentric sphere about a small target centered at the origin.

We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.

The structure of magnetic fields was investigated in stagnated wire-array $Z$ pinches using a Faraday rotation diagnostic at the wavelength of 266 nm. The distribution of current in the pinch and trailing material was reconstructed. A significant part of current can switch from the main pinch to the trailing plasma preheated by x-ray radiation of the pinch. Secondary implosions of trailing plasma generate kinetic energy and provide enhanced heating and radiation of plasma at stagnation. Hot spots in wire-array $Z$ pinches also provide enhanced radiation of the $Z$ pinch. A collapse of a single hot spot radiates 1$\%$–3$\%$ of x-ray energy of the $Z$ pinch with a total contribution of hot spots of 10$\%$–30$\%$.

Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem: the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation.

We show that for the lattice Boltzmann model, the existing paradigm in computer science for the choice of the data structure is suboptimal. In this paper we use the requirements of physical symmetry necessary for recovering hydrodynamics in the lattice Boltzmann description to propose a hybrid data layout for the method. This hybrid data structure, which we call a structure of an array of structures, is shown to be optimal for the lattice Boltzmann model. Finally, the possible advantages of establishing a connection between group theoretic symmetry requirements and the construction of the data structure is discussed in the broader context of grid-based methods.

The dynamic equilibrium model suggests that surface nanobubbles can be stable due to an influx of gas in the vicinity of the bubble contact line, driven by substrate hydrophobicity, that balances the outflux of gas from the bubble apex. Here, we develop an alternate formulation of this mechanism that predicts rich behavior in agreement with recent experimental measurements. Namely, we find that stable nanobubbles exist in narrow temperature and dissolved gas concentration ranges, that there is a maximum and minimum possible bubble size, and that nanobubble radii decrease with temperature.

The field theoretic renormalization group and operator product expansion are used for an investigation of the anomalous scaling behavior of correlation functions of the weak magnetic field in the framework of the compressible Kazantsev-Kraichnan model. Two-loop expressions for the anomalous exponents of the correlation functions of arbitrary order in the presence of large-scale anisotropy are found as functions of compressibility. The influence of compressibility on the hierarchy of the anisotropic contributions is discussed, and it is shown that already relatively small compressibility can destroy the standard hierarchy of anisotropic anomalous exponents in the framework of which the leading contribution to the anomalous scaling is given by the isotropic shell.

Radiation reaction effects will play an important role in near-future laser facilities, yet their theoretical description remains obscure. We explore the Ford-O’Connell equation for radiation reaction, and discuss its relation to other commonly used treatments. By analyzing the interaction of a high energy electron in an intense laser pulse, we find that radiation reaction effects prevent the particle from accessing a regime in which the Landau-Lifshitz approximation breaks down.

A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.

Nematic shells of liquid crystals have been provided in microscales. Defect structures in the shells are very essential in the electro-optical applications of such colloidal objects. We have numerically minimized the free energy of symmetric and asymmetric spherical shells of the nematic liquid crystal. Considering degenerate planar anchoring on the surfaces and isotropic nematic elasticity, a variety of defect structures are observed by controlling or varying the thicknesses of the shell and its degree of asymmetry. In symmetric shells, our calculations show that boojums (bipolar) defects appear in thick shells and tetrahedral (baseball) defects in thin shells. In asymmetric shells, while we are in the bipolar regime, the boojums defects transform to trigonal configurations. Free energy landscape shows that in this regime the inner droplet is not stable in the center and it is trapped in an off-center minimum energy position. For the case of thin shells, there are two degenerate director textures with similar tetrahedral configuration of the disclination lines. The levels are split in asymmetric shells. The stability of the inner droplet in the center position depends on director texture. It is stable for one texture and unstable for the other one. For an unstable pattern there is no minimum energy position for the inner droplet and it moves until it touches the outer boundary.

Bistable liquid crystal displays (LCDs) offer the potential for considerable power savings compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically distinct means that contrast can be maintained in a display without an externally applied electric field. An applied field is required only to switch the device from one state to the other, as needed. In this paper we examine the basic physical principles involved in generating multiple stable states and the switching between these states. We consider a two-dimensional geometry in which variable surface anchoring conditions are used to control the steady-state solutions and explore how different anchoring conditions can influence the number and type of solutions and whether or not switching is possible between the states. We find a wide range of possible behaviors, including bistability, tristability, and tetrastability, and investigate how the solution landscape changes as the boundary conditions are tuned.

We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this nonequilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the nonequilibrium fluctuations and the modified fluctuation-dissipation relation in connection with nonconservative forces due to shear flow.

We obtain a general expression for the orientational energy of an individual anisometric particle suspended in uniform nematic liquid crystals when the main axis of the particle rotates with respect to the nematic director. We show that there is a qualitative and quantitative analogy between the internal and external problems for cylindrical volumes of nematic liquid crystals, and on this basis we obtain an estimate of the orientational energy of a particle of cylindrical (rodlike, needlelike, or ellipsoidal) shape. For an ensemble of such particles we propose a modified form of their orientational energy in the nematic matrix. This orientational energy has the usual second-order term, and additional fourth-order term in the scalar product of the nematic director and the vector which characterizes an average direction of the main axes of the particles. As an example we obtain the expression for the free energy density of ferronematics, i.e., colloidal suspensions of needlelike magnetic particles in nematic liquid crystals. Unlike previous models, the free energy density includes the proposed modified form of the particle orientational energy, and also a contribution describing the surface saddle-splay deformations of the liquid crystal matrix.

We present a numerical study of stretching monodomain smectic-$A$ elastomer sheets, computed using the finite element method. When stretched parallel to their smectic layer normal the smectic layers are unstable to a transition to a buckled state. We model macroscopic deformations by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine-scale layer buckling. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson ratios postbuckling. We examine the spatial distribution of the microstructure phases for various stretching angles relative to the layer normal and for different length-to-width aspect ratios. When stretching parallel to the layer normal the majority of the sample forms a bidirectionally buckled microstructure, except at the clamps where a unidirectionally buckled microstructure is predicted. When stretching at small inclinations to the layer normal the phase of the sample is sensitive to the aspect ratio of the sample, with the bidirectionally buckled phase persistent to large angles only for small aspect ratios. We relate these theoretical results to experiments on smectic-$A$ elastomers.

We investigated the signal-to-noise ratio ($S/N$) of real-time single-molecule fluorescence imaging (SMFI) using zero-mode waveguides (ZMWs). The excitation light and the fluorescence propagating from a molecule in the ZMW were analyzed by computational optics simulation. The dependence of the $S/N$ on the ZMW structure was investigated with the diameter and etching depth as the simulation parameters. We found that the SMFI using a conventional ZMW was near the critical level for detecting binding and dissociation events. We show that etching the glass surface of the ZMW by 60 nm enhances the $S/N$ six times the conventional nonetched ZMWs. The enhanced $S/N$ improves the temporal resolution of the SMFI at physiological concentrations.

Recent experiments have demonstrated that the ATP-utilizing chromatin assembly and remodeling factor (ACF) is a dimeric, processive motor complex which can move a nucleosome more efficiently towards longer flanking DNA than towards shorter flanking DNA strands, thereby centering an initially ill-positioned nucleosome on DNA substrates. We give a Fokker-Planck description for the repositioning process driven by transitions between internal chemical states of the remodelers. In the chemical states of ATP hydrolysis during which the repositioning takes place a power stroke is considered. The slope of the effective driving potential is directly related to ATP hydrolysis and leads to the unidirectional motion of the nucleosome-remodeler complex along the DNA strand. The Einstein force relation allows us to deduce the ATP-concentration dependence of the diffusion constant of the nucleosome-remodeler complex. We have employed our model to study the efficiency of positioning of nucleosomes as a function of the ATP sampling rate between the two motors which shows that the synchronization between the motors is crucial for the remodeling mechanism to work.