An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.

One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.

We study the rise dynamics of a large particle in a granular bed under vertical vibration using molecular dynamics simulations. Systematic variation of the particle properties and external wall friction in the simulations shows that the large particle rising is very sensitive to external wall friction. The dynamical response of the granular bed with wall friction is shown to include an expansion stage and a compression stage within one cycle. With wall friction, large-scale force networks bearing larger-than-average forces are found in the compression stage. However, without wall friction, large strong force networks do not exist. The distribution of normal contact forces in the force networks is found to have an exponential tail similar to those in packing experiments. Numerical estimation of the two-point spatial correlation of normal contact force reveals predominantly short-range force correlation persisting over only 2–3 particle diameters. The structural properties of the force network are analyzed using a graph-theoretic approach, which is a modification of a minimum spanning tree (MST) constructed on the particles in physical space. The modified MST algorithm, which identifies local structures such as nearest neighbors, asymptotically recovers all particle contacts, the force distribution, and spatial force correlation of the force network. This indicates that although wall friction strongly affects the rising dynamics of the Brazil nut over the device scale (tens of particle diameters) through the force network, it does so through local short-range interactions. Thus this study affirms the basis for local constitutive models in continuum descriptions of segregation.

We study a stochastic reaction-diffusion lattice model for describing the calcium dynamics in the endoplasmic reticulum (ER) membrane. Calcium channels and calcium ions are placed in two interpenetrating square lattices which are connected by calcium release and diffusion. Calcium ions are released from the ER through the channels and they can both remain in the membrane or spontaneously leave the membrane into the cytosol. The state of the channel is modulated by calcium ions: a channel can be open, closed, or inactive. The model is studied by numerical simulations and mean field theory and exhibits a phase transition from an active state to an absorbing state which is the result of the catalytic calcium release. The critical behavior of the model is in the directed percolation universality class.

In this work the effects of the wall-fluid interaction on the critical point shift are studied by using a discrete and attractive wall-fluid interaction and density functional theory. In contrast to the previous assumption, it is found that the dependence of critical temperature shift on the wall-fluid interaction does not simply show a monotonic manner, but increases with the strength of the interaction for weak surfaces, then decreases for strong surfaces. The similar trend holds for the systems with different fluid-fluid interactions and different confined spaces. Unlike the capillary critical temperature, the critical density of square-well fluids in a confined space increases monotonically as the wall-fluid interaction becomes more attractive.

We present a method that enables chaotic systems to change its dynamics to stable periodic dynamics by a feedback adjustment. The proposed method uses feedback of a largest value obtained from observations of a fixed interval of time series of the system variable and therefore does not require any a priori detailed information. We apply this method to several chaotic systems and confirm numerically that chaotic states are stabilized to stable periodic ones. Since the stabilized states in the system are formed around a boundary between regular states and chaotic ones, the method provides a kind of adaptation to the edge of chaos.

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schrödinger equation, a wave-kinetic equation is derived. A comparison between coherent and random-phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultrashort optical pulses. In practical terms, this could be achieved by using random-phase plate techniques.

Two-dimensional granular flow in a channel with small exit is studied by both experiments and simulations. We first observe the time variation of the transition from dilute flow state to dense flow state by both experiments and simulations. Then we obtain a relationship between the local flow rate and the local packing fraction in the choke area by use of molecular dynamics simulations. The relationship is a continuous function rather than a discontinuous one. The flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at high value with negative slope. According to the relationship, four flow states—i.e., stable dilute flow state, metastable dilute flow state, unstable dense flow state, and stable dense flow state—are defined for fixed inflow rate. The discontinuities and the complex time variation behavior occurring in the transition between dilute and dense flow states can be attributed to the abrupt variation through unstable flow state.

We study analytically a thermal Brownian motor model and calculate exactly the Onsager coefficients. We show how the reciprocity relation holds and that the determinant of the Onsager matrix vanishes. Such a condition implies that the device is built with tight coupling. This explains why Carnot’s efficiency can be achieved in the limit of infinitely slow velocities. We also prove that the efficiency at maximum power has the maximum possible value, which corresponds to the Curzon-Alhborn bound. Finally, we discuss the model acting as a Brownian refrigerator.

In this paper we model the tomography of scale-free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show analytically that the nodes degree distribution at each layer exhibits a power-law tail with an exponential cutoff. We obtain similar empirical results for the layers surrounding the root of shortest path trees cut from such networks, as well as the Internet.

Using long-term computer simulations and mean-field-like arguments, we investigate the transient time and the properties of the stationary state of the Olami-Feder-Christensen model as function of the coupling parameter $\alpha$ and the system size $N$. The most important findings are that the transient time increases with a nonuniversal exponent of the system size, and that the avalanche size distribution will not approach a power law with increasing system size.

The characteristics of the multiple filaments formed by prefocused and freely propagating femtosecond laser pulses are investigated and compared. It is shown in our experiments that the diameter, length, stability, and interaction for the two cases can be quite different. The filaments formed by prefocused beam indicate dynamic spatial evolution with higher laser intensity and electron density. They have a typical diameter of $100\mu \mathrm{m}$ are of shorter length. In the free propagation case, the filaments exhibit interesting properties such as hundred-meter propagation distance and mm-size diameter. Moreover, only the interaction of the filaments with the energy background affects the evolution of the filaments. Filament-filament interactions such as the filament splitting and merging were not observed in this case.

We study the interaction of counterpropagating pulse solutions for two coupled complex cubic-quintic Ginzburg-Landau equations in an annular geometry. For small approach velocity we find as an outcome of such collisions several results including zigzag bound pulses, stationary bound states of $2\pi$ holes, zigzag $2\pi$ holes, stationary bound states of $\pi$ holes, zigzag bound states of $\pi$ holes, propagating $2\pi$ holes, and propagating $\pi$ holes as the real part of the cubic cross coupling between the counterpropagating waves is increased. We characterize in detail the collisions giving rise to the three states involving $\pi$ holes as an outcome.

Real networks often consist of local units interacting with each other by means of heterogeneous connections. In many cases, furthermore, such networks feature degree mixing properties, i.e., the tendency of nodes with high degree (with low degree) to connect with connectivity peers (with highly connected nodes). Such degree-degree correlations may have an important influence in the spreading of information or infectious agents on a network. We explore the role played by these correlations for the synchronization of networks of coupled dynamical systems. Using a stochastic optimization technique, we find that the value of degree mixing providing optimal conditions for synchronization depends on the weighted coupling scheme. We also show that a minimization of the assortative coefficient may induce a strong destabilization of the synchronous state. We illustrate our findings for weighted networks with scale free and random topologies.

Finite-thickness photonic crystals (PC’s) with periodically corrugated interfaces are suggested to realize some unusual features in the behavior of transmitted Bragg beams (diffraction orders). The scattering of $s$-polarized plane waves by such structures is studied. It follows from the numerical results that rather thin corrugated PC’s borrow their basic properties from both conventional PC’s and gratings, leading to some new effects. In particular, a shift of the actual cutoff frequencies towards larger values than those of the Rayleigh cutoff frequencies can be obtained due to the ordinary opaque range in transmission, within which all propagative orders vanish. This effect can even be enhanced due to the nonordinary behavior arising at the edges of the ordinary opaque range, which manifests itself in that some but not all propagative orders in transmission are suppressed. Hence the opaque ranges for individual orders are wider than the corresponding ordinary range. Besides, frequency ranges exist which are not connected with the edge of the ordinary opaque range, where a similar nonordinary effect does appear. As a result, each propagative order in transmission generally has its own set of opaque ranges. Only a single order can be contributive while several others are formally propagative, too. The corrugations have to be located at the upper interface in order to realize these nonordinary effects. Moving the corrugation from the upper to the lower interface leads to a disappearance of the observed effects, so that their nature cannot be explained exclusively in terms of matching the wave vectors of the diffraction orders and the Floquet-Bloch waves. The conventional sequence of cutoffs for different diffraction orders with respect to each other can be changed for certain structures if the rods of a PC are made of Drude metal. Hence, transmission regimes can be realized which are beyond the classical theory of gratings. Several effects arising when varying the angle of incidence are demonstrated and briefly discussed. The detected effects can be used for controlling the number of actually contributive beams and for obtaining alternating ranges of single-beam and multibeam operation, which should lead to extending the potentials of optical and microwave technologies based on the use of single-beam and multibeam regimes.

K. P. Singh [Phys. Rev. E 69, 056410 (2004)] put forward a scheme of vacuum laser acceleration in a static magnetic field. We point out that one of the assumptions used in their model does not stand on a solid physical ground and that it seriously influences electrons to obtain net energy gains from the laser field.

Relative frequencies of mechanically stable (MS) packings of frictionless bidisperse disks are studied numerically in small systems. The packings are created by successively compressing or decompressing a system of soft purely repulsive disks, followed by energy minimization, until only infinitesimal particle overlaps remain. For systems of up to $14$ particles, most of the MS packings were generated. We find that the packings are not equally probable as has been assumed in recent thermodynamic descriptions of granular systems. Instead, the frequency distribution, averaged over each packing-fraction interval $\mathrm{\Delta }\varphi$, grows exponentially with increasing $\varphi$. Moreover, within each packing-fraction interval, MS packings occur with frequencies $f_k$ that differ by many orders of magnitude. Also, key features of the frequency distribution do not change when we significantly alter the packing-generation algorithm; for example, frequent packings remain frequent and rare ones remain rare. These results indicate that the frequency distribution of MS packings is strongly influenced by geometrical properties of the multidimensional configuration space. By adding thermal fluctuations to a set of the MS packings, we were able to examine a number of local features of configuration space near each packing. We measured the time required for a given packing to break to a distinct one, which enabled us to estimate the energy barriers that separate one packing from another. We found a gross positive correlation between the packing frequencies and the heights of the lowest energy barriers ${ϵ}_0$; however, there is significant scatter in the data. We also examined displacement fluctuations away from the MS packings to assess the size and shape of the local basins near each packing. The displacement modes scale as $d_i\sim {ϵ}_0^{{\gamma }_i}$ with ${\gamma }_i$ ranging from $\sim 0.6$ for the largest eigenvalues to $1.0$ for the smallest ones. These scalings suggest that the packing frequencies are not determined by the local volume of configuration space near each packing, which would require that the dependence of $f_k$ on ${ϵ}_0$ is much stronger than the dependence we observe. The scatter in our data implies that in addition to ${ϵ}_0$ there are also other, as yet undetermined variables that influence the packing probabilities.