We studied the evolution of elliptic heavy ${\text{SF}}_6$ gas cylinder surrounded by air when accelerated by a planar Mach 1.25 shock. A multiple dynamics imaging technology has been used to obtain one image of the experimental initial conditions and five images of the time evolution of elliptic cylinder. We compared the width and height of the circular and two kinds of elliptic gas cylinders and analyzed the vortex strength of the elliptic ones. Simulations are in very good agreement with the experiments, but due to the different initial gas cylinder shapes, a certain difference of the initial density peak and distribution exists between the circular and elliptic gas cylinders, and the latter initial state is more sensitive and more inenarrable.

Finger tip splitting and finger tip narrowing phenomena are not commonly observed during early flow stages in parallel-plate rectangular Hele-Shaw cells. However, an interesting experimental study performed by Zhao et al. [Phys. Rev. A 45, 2455 (1992)] showed that finger tip behavior can be significantly affected by the addition of a small gradient to the gap of the cell, so that the plates are no longer exactly parallel. It was found that pattern forming events at the finger tip are dictated by the sign of the gap gradient, where positive (negative) sign produces wider (narrower) fingers. We approach the nonparallel-plate situation analytically through a perturbative mode coupling theory and show that these important finger tip features can be predicted at early nonlinear stages of the dynamics.

Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as Gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an $N$ wave not commonly discussed in the context of thin films. Simulations employing a controlled approximation of a compressive-undercompressive wave pair demonstrate possibilities for applications of localized forcing as microfluidic valve. In the simulations, localized forcing provides a control parameter that can be used to determine mass flux and film profiles.

We provide a rigorous proof of the fact that the level density of all known $\text{su}\left(m\right)$ spin chains of Haldane-Shastry type associated with the $A_{N-1}$ root system approaches a Gaussian distribution as the number of spins $N$ tends to infinity. Our approach is based on the study of the large-$N$ limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the transfer matrix.

In this work, it is shown that the detailed fluctuation theorem for the total entropy production of a charged particle in a two-dimensional harmonic trap under the action of an electromagnetic field is valid in two physical situations. The proof of the theorem is achieved if the particle is initially distributed with a canonical distribution at equilibrium with the thermal bath. The two examined cases are the following: in the first case, the charged particle in the harmonic trap is subjected to an arbitrary time-dependent electric field; in the second one, the minimum of the harmonic trap is arbitrarily dragged by such an electric field. The theoretical framework is developed within the context of stochastic thermodynamics and the Langevin dynamics for the charged particle.

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.

We perform a comparative study of the free energies and the density distributions in hard-sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique [T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 (2009)] we obtain crystal free energies to a high precision. The free energies from fundamental measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that fundamental measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional [H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 (2006)] exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.

Bubble-nucleation processes of a Lennard-Jones liquid are studied by molecular dynamics simulations. Waiting time, which is the lifetime of a superheated liquid, is determined for several system sizes, and the apparent finite-size effect of the nucleation rate is observed. From the cumulative distribution function of the nucleation events, the bubble-nucleation process is found to be not a simple Poisson process but a Poisson process with an additional relaxation time. The parameters of the exponential distribution associated with the process are determined by taking the relaxation time into account, and the apparent finite-size effect is removed. These results imply that the use of the arithmetic mean of the waiting time until a bubble grows to the critical size leads to an incorrect estimation of the nucleation rate.

We construct a coarse-grained model of parallel actin bundles crosslinked by compact globular bundling proteins, such as fascin and espin, necessary components of filopodial and mechanosensory bundles. Consistent with structural observations of bundles, we find that the optimal geometry for crosslinking is overtwisted, requiring a coherent structural change of the helical geometry of the filaments. We study the linker-dependent thermodynamic transition of bundled actin filaments from their native state to the overtwisted state and map out the “twist-state” phase diagram in terms of the availability as well as the flexibility of crosslinker proteins. We predict that the transition from the uncrosslinked to fully crosslinked state is highly sensitive to linker flexibility: flexible crosslinking smoothly distorts the twist state of bundled filaments, while rigidly crosslinked bundles undergo a phase transition, rapidly overtwisting filaments over a narrow range of free crosslinker concentrations. Additionally, we predict a rich spectrum of intermediate structures, composed of alternating domains of sparsely bound (untwisted) and strongly bound (overtwisted) filaments. This model reveals that subtle differences in crosslinking agents themselves modify not only the detailed structure of parallel actin bundles, but also the thermodynamic pathway by which they form.

The Hopfield network is reconstructed as an inverse Ising problem by passing messages. The applied susceptibility propagation algorithm is shown to improve significantly on other mean-field-type methods and extends well into the low-temperature region. However, this iterative algorithm is limited by the nature of the supplied data. Its performance deteriorates as the data become highly magnetized, and this method finally fails in the presence of the frozen type data where at least two of its magnetizations are equal to 1 in absolute value. On the other hand, a threshold behavior is observed for the susceptibility propagation algorithm and the transition from good reconstruction to poor one becomes sharper as the network size increases.

An approach based on combining nonparametric Gaussian process (GP) modeling with certain local topological considerations is presented for prediction (one-step look ahead) of complex physical systems that exhibit nonlinear and nonstationary dynamics. The key idea here is to partition system trajectories into multiple near-stationary segments by aligning the boundaries of the partitions with those of the piecewise affine projections of the underlying dynamic system, and deriving nonparametric prediction models within each segment. Such an alignment is achieved through the consideration of recurrence and other local topological properties of the underlying system. This approach was applied for state and performance forecasting in Lorenz system under different levels of induced noise and nonstationarity, synthetic heart-rate signals, and a real-world time-series from an industrial operation known to exhibit highly nonlinear and nonstationary dynamics. The results show that local Gaussian process can significantly outperform not just classical system identification, neural network and nonparametric models, but also the sequential Bayesian Monte Carlo methods in terms of prediction accuracy and computational speed.

This study investigates shear-induced liquid structure changes in nanoscale Couette flows and their corresponding flow boundary conditions. Molecular dynamics simulations are used to model a liquid argon slab confined between two smooth rigid copper walls with an applied velocity at the upper wall to generate a planar Couette flow. Depending on the applied wall velocity, different liquid structures or the orderings of the liquid at liquid-solid interfaces are identified when reaching steady states. We define three regimes based on the ordering of the liquid structure: Newtonian, layer, and oversheared. Each regime is characterized by the spatial probability distribution and structure factor. These liquid structures are strongly correlated with the liquid velocity and density profiles in the flow. Ultimately, the liquid structures also determine the boundary conditions from pure slip to multilayer locking at liquid-solid interfaces. Our results show that temperature and liquid-solid interaction parameter are also important factors in influencing the liquid structures formed near interfaces.

Consider a film of viscous liquid covering a solid surface, which it does not wet. If there is an initial hole in the film, the film will retract further, forming a rim of fluid at the receding front. We calculate the shape of the rim as well as the speed of the front using lubrication theory. We employ asymptotic matching between the contact line region, the rim, and the film. Our results are consistent with simple ideas involving dynamic contact angles and permit us to calculate all free parameters of this description, previously unknown.

Three-dimensional images of sandstones containing residual nonwetting phase were obtained using synchrotron x-ray tomography with a resolution of approximately $9\mu \text{m}$. We determined the size distribution of disconnected nonwetting phase clusters (ganglia); the number of ganglia of size $s$ is $N\left(s\right)\sim s^{-\tau }$ with $\tau =2.05$. The vast majority of the residual phase was contained in large clusters, spanning many pores. This result implies that we have clusters of all sizes providing a huge surface area for geochemical reactions and dissolution while allowing mobilization of the residual phase during improved oil recovery in hydrocarbon reservoirs and carbon dioxide storage in aquifers.

The mechanism of sustained oscillation in the flow past a circular cylinder is investigated numerically, in which impulsive force is given at a certain point in the flow and subsequent spatiotemporal development of induced disturbance is observed. The impulsive force generates an intense localized disturbance at the point of forcing, which is transmitted immediately up to a region just behind the cylinder, and there it yields an transient and eigen modes of disturbance having a packet form. Extending the conventional notions of convective and absolute modes of instability established on the parallel flow approximation to nonparallel flows, we define “passive” and “active” modes of instability, respectively, and evaluate the growth rate of each mode. It was found that the entire flow field is stable to active mode below the critical Reynolds number for the global instability though some extent of the flow behind the cylinder is unstable to passive mode, while the flow becomes unstable to active mode everywhere simultaneously when the Reynolds number exceeds the critical value. The numerical analysis brought us a conclusion that the oscillation is sustained by superiority of the growth of disturbance due to instability over the decrease due to advection of the packet.

The accuracy of the lattice Boltzmann method (LBM) for describing the behavior of a gas in the continuum limit is systematically investigated. The asymptotic analysis for small Knudsen numbers is carried out to derive the corresponding fluid-dynamics-type equations, and the errors of the LBM are estimated by comparing them with the correct fluid-dynamics-type equations. We discuss the following three important cases: (I) the Mach number of the flow is much smaller than the Knudsen number, (II) the Mach number is of the same order as the Knudsen number, and (III) the Mach number is finite. From the von Karman relation, the above three cases correspond to the flows of (I) small Reynolds number, (II) finite Reynolds number, and (III) large Reynolds number, respectively. The analysis is made with the information only of the fundamental properties of the lattice Boltzmann models without stepping into their detailed form. The results are therefore applicable to various lattice Boltzmann models that satisfy the fundamental properties used in the analysis.

We extend a model of community isolation in the $d$-dimensional lattice to a case with an imposed imbalance between the birth rates of competing communities. We provide analytical and numerical evidences that in the asymmetric two-species model there exists a well-defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e., the characteristic time $t_c$ is minimal. The critical value of the parameter depends only on the lattice dimensionality and is independent of the system size. A similar phenomenon is observed in the multispecies case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multispecies case are absent or very rare when either there is a strictly dominant species that outnumbers the others or there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multispecies system.

An efficient method for enhancement of a random bit generation rate from a physical source of randomness is proposed. It is based on the repeated application of the operation of symmetrization of random data. This procedure allows one to transform asymptotically any nonsymmetrical distribution into a perfectly symmetrical one. As a result, one can extract up to 46 uncorrelated and unbiased bits from each variate, increasing an effective rate up to 46 times with respect to the mean frequency of random events. The method was tested with spontaneous switchings in a bistable vertical cavity laser. A statistical analysis of the generated random bit sequences which passed the standard randomness tests (ENT, NIST Statistical Test Suites, and Diehard) is presented.

Magnetic resonance imaging has been used to measure particle velocities, exceeding $1\text{m}{\text{s}}^{-1}$ in a two-phase granular system, namely, a spouted bed. The measurements are complicated due to the high voidage, i.e., low particle density, in the region of the highest particle velocity. However, applying gradient shapes which allow fast switching and, thus, short encoding and observation times in combination with a short echo time enable these measurements. It was found that the profile of the particle velocity is nonparabolic. Based on these measurements it was possible to confirm observations made in numerical simulations that there must be a continuous momentum exchange between the annulus region and the spout along the entire length of the spout.

Simple expressions are presented for the equations of state of a correlated electrolyte solution, calculated straightforwardly within a full nonlinear Debye-Hückel approach in terms of the mean potential at contact, that predict quantitatively different phase behavior from the popular Debye-Hückel limiting law. The theory includes pair correlations accurately and may provide a basis for a quantitative theoretical study of organic or multivalent ionic solutions. As an example, cohesive effects are addressed of strong couplings between ions on the effective interactions between nanoparticles.