A simple model of the transfer of charge and ion evaporation in the meniscus of an ionic-liquid ion source working in the purely ionic regime is proposed on the basis of order-of-magnitude estimates which show that, in this regime, (i) the flow in the meniscus is dominated by the viscosity of the liquid and is affected very little by the mass flux accompanying ion evaporation, and (ii) the effect of the space charge around the evaporating surface is negligible and the evaporation current is controlled by the finite electrical conductivity of the liquid. The model predicts that a stationary meniscus of a very polar liquid undergoing ion evaporation is nearly hydrostatic and can exist only below a certain value of the applied electric field, at which the meniscus attains its maximum elongation but stays smooth. The electric current vs applied electric field characteristic displays a frozen regime of negligible ion evaporation at low fields and a conduction-controlled regime at higher fields, with a sharp transition between the two regimes owing to the high sensitivity of the ion evaporation rate to the electric field. A simplified treatment of the flow in the capillary or liquid layer through which liquid is delivered to the meniscus shows that the size of the meniscus decreases and the maximum attainable current increases when the feeding pressure is decreased, and that appropriate combinations of feeding pressure and pressure drop may lead to high maximum currents.

We measured the thermodynamical and transport properties of boron in the warm dense matter regime ($15000\text{K}<T<25000\text{K}$ and $\rho =0.094\text{g}/{\text{cm}}^3$). Experimental data are compared with quantum molecular dynamics (QMD) simulations. We find a very good agreement between data and calculations, which permits us to transform experimental energies into temperatures, and allows us to compare conductivities with an average atom model coupled with a Kubo-Greenwood calculations. Contact is made between computationally intensive QMD simulation codes and fast average atom models.

This work surveys techniques based on classical density functionals for modeling the quantum dispersion of physisorbed hydrogen at $77\mathrm{K}$. Two such techniques are examined in detail. The first is based on the “open ring approximation” (ORA) of Broukhno et al., and it is compared with a technique based on the semiclassical approximation of Feynman and Hibbs (FH). For both techniques, a standard classical density functional is used to model hydrogen molecule–hydrogen molecule (i.e., excess) interactions. The three-dimensional (3D) quantum harmonic oscillator (QHO) system and a model of molecular hydrogen adsorption into a graphitic slit pore at $77\mathrm{K}$ are used as benchmarks. Density functional results are compared with path-integral Monte Carlo simulations and with exact solutions for the 3D QHO system. It is found that neither of the density functional treatments are entirely satisfactory. However, for hydrogen physisorption studies at $77\mathrm{K}$ the ORA based technique is generally superior to the FH based technique due to a fortunate cancellation of errors in the density functionals used. But, if more accurate excess functionals are used, the FH technique would be superior.

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.

In this paper we propose a generalization of the one-dimensional outflow dynamics (KD). The rule is introduced as a simplification of Galam dynamics (GD) proposed in an earlier paper. We simulate three types of outflow dynamics, GD, Stauffer et al. dynamics, and KD, both on the square and triangular lattices and show whether the outflow dynamics is sensitive to the lattice structure. Moreover, we took into account several types of initial configuration—random, “stripes,” and “circle.” We investigate the dependence between the mean relaxation time and the initial density $p$ of up-spins for each type of initial conditions, as well as dependence between the mean relaxation time and the size of the system. As a result, we show differences and similarities between three types of the outflow dynamics.

We calculate analytically the work distribution of a quantum harmonic oscillator with arbitrary time-dependent angular frequency. We provide detailed expressions for the work probability density for adiabatic and nonadiabatic processes, in the limits of low and high temperature. We further verify the validity of the quantum Jarzynski equality.

The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated nonmonotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength, and damping constant on the dimer transport properties are also examined in detail.

It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power-law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Lévy noise at the macroscopic level.

It has been recently shown [I. Fouxon et al., Phys. Rev. E 75, 050301(R) (2007); I. Fouxon et al., Phys. Fluids 19, 093303 (2007)] that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. We report molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the “attempted” density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.

We investigate crystalline order on a two-dimensional paraboloid of revolution by assembling a single layer of millimeter-sized soap bubbles on the surface of a rotating liquid, thus extending the classic work of Bragg and Nye on planar soap bubble rafts. Topological constraints require crystalline configurations to contain a certain minimum number of topological defects such as disclinations or grain boundary scars whose structure is analyzed as a function of the aspect ratio of the paraboloid. We find the defect structure to agree with theoretical predictions and propose a mechanism for scar nucleation in the presence of large Gaussian curvature.

Leukemias arise due to mutations in the genome of hematopoietic (blood) cells. Hematopoiesis has a multicompartment architecture, with cells exhibiting different rates of replication and differentiation. At the root of this process, one finds a small number of stem cells, and hence the description of the mutation-selection dynamics of blood cells calls for a stochastic approach. We use stochastic dynamics to investigate to which extent acquired hematopoietic disorders are associated with mutations of single or multiple genes within developing blood cells. Our analysis considers the appearance of mutations both in the stem cell compartment as well as in more committed compartments. We conclude that in the absence of genomic instability, acquired hematopoietic disorders due to mutations in multiple genes are most likely very rare events, as multiple mutations typically require much longer development times compared to those associated with a single mutation.

We numerically study the influence of neuronal threshold modulation on the properties of cortical traveling waves. For that reason we simplify a Wilson-Cowan-type integrodifferential equation model of propagating neocortical activity to a spatially discrete version. Further we introduce a noisy threshold. Depending on the noise level we find different states of the network activity, ranging from asynchronous oscillations, traveling waves, to synchronous oscillations. Finally, we induce the transition between these different states by an external modulation.

This paper proposes an approach to changing the types of neuronal excitability via bifurcation control. A washout filter-aided dynamic feedback controller is introduced to bifurcation dynamics of a two-dimensional Hindmarsh-Rose type model neuron, which shows a saddle-node on invariant circle (SNIC) bifurcation from quiescence to periodic spiking and then exhibits type-I excitability. At first, a Hopf bifurcation is created at a desired parameter value before the SNIC bifurcation occurs, and then the criticality of the created Hopf bifurcation is regulated by choosing appropriate values of the controller parameters. In this manner, the model neuron starts to show type-II excitability. Therefore the type of neuronal excitability is transformed from type-I excitability to type-II excitability for the model neuron via the washout filter-aided dynamic feedback controller. In such a controller, the linear control gain is determined by the two basic critical conditions for the Hopf bifurcation, i.e., the eigenvalue assignment and the transversality condition. We apply the center manifold and normal form theory to deduce a closed-form analytic expression for the bifurcation stability coefficient, which is a function with respect to the nonlinear control gain. A suitable nonlinear control gain is chosen to make the bifurcation stability coefficient negative, and thus the criticality of the created Hopf bifurcation can be changed from subcritical to supercritical. In addition, the amplitude of the corresponding periodic solution can be also regulated by the nonlinear control gain.

The impact of high-order moments on the statistical modeling of transition arrays in complex spectra is studied. It is shown that a departure from the Gaussian, which is usually employed in such an approach, may be observed even in the shape of unresolved spectra due to the large value of the kurtosis coefficient. The use of a Gaussian shape may also overestimate the width of the spectra in some cases. Therefore, it is proposed to simulate the statistical shape of the transition arrays by the more flexible generalized Gaussian distribution which introduces an additional parameter—the power of the argument in the exponential—that can be constrained by the kurtosis value. The relevance of the statistical line distribution is checked by comparisons with smoothed spectra obtained from detailed line-by-line calculations. The departure from the Gaussian is also confirmed through the analysis of $2p$-$3d$ transitions of recent absorption measurements. A numerical fit is proposed for an easy implementation of the statistical profile in atomic-structure codes.

We present an accurate method to include arbitrary singular distributions of forces in the lattice Boltzmann formulation of hydrodynamics. We validate our method with several examples involving Stokeslet, stresslet, and rotlet singularities, finding excellent agreement with analytical results. A minimal model for sedimenting particles is presented using the method. In the dilute limit, this model has accuracy comparable to, but computational efficiency much greater than, algorithms that explicitly resolve the size of the particles.

A parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales.

The extraction of information from measured data about the interactions taking place in a network of systems is a key topic in modern applied sciences. This topic has been traditionally addressed by considering bivariate time series, providing methods which are sometimes difficult to extend to multivariate data, the limiting factor being the computational complexity. Here, we present a computationally viable method based on black-box modeling which, while theoretically applicable only when a deterministic hypothesis about the processes behind the recordings is plausible, proves to work also when this assumption is severely affected. Conceptually, the method is very simple and is composed of three independent steps: in the first step a state-space reconstruction is performed separately on each measured signal; in the second step, a local model, i.e., a nonlinear dynamical system, is fitted separately on each (reconstructed) measured signal; afterward, a linear model of the dynamical interactions is obtained by cross-relating the (reconstructed) measured variables to the dynamics unexplained by the local models. The method is successfully validated on numerically generated data. An assessment of its sensitivity to data length and modeling and measurement noise intensity, and of its applicability to large-scale systems, is also provided.

We show that steady-state work fluctuations in periodically modulated systems display universal features, which are not described by the standard fluctuation theorems. Modulated systems often have coexisting stable periodic states. We find that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. We also show that the work variance displays scaling with the distance to a bifurcation point where a stable state disappears and find the critical exponent for a saddle-node bifurcation.

An algorithm based on backward induction is devised in order to compute the optimal sequence of games to be played in Parrondo games. The algorithm can be used to find the optimal sequence for any finite number of turns or in the steady state, showing that ABABB… is the sequence with the highest steady state average gain. The algorithm can also be generalized to find the optimal adaptive strategy in a multiplayer version of the games, where a finite number of players may choose, at every turn, the game the whole ensemble should play.

We study the ground state energy $E_G\left(n\right)$ of $N$ classical $O\left(n\right)$ vector spins with the Hamiltonian $\mathcal{H}=-{\sum }_{i>j}{J}_{ij}{\vec{S}}_i\bullet {\vec{S}}_j$ where the coupling constants $\left\{J_{ij}\right\}$ are arbitrary. We prove that $E_G\left(n\right)$ is independent of $n$ for all $n>n_{\max }\left(N\right)=\lfloor (\sqrt{8N+1}-1)∕2\rfloor$. We show that this bound is the best possible. We also derive an upper bound for $E_G\left(m\right)$ in terms of $E_G\left(n\right)$, for $m<n$. We obtain an upper bound on the frustration in the system, as measured by $F\left(n\right)\equiv [{\sum }_{i>j}\mid J_{ij}\mid +E_G(n\left)\right]∕{\sum }_{i>j}\mid J_{ij}\mid$. We describe a procedure for constructing a set of $J_{ij}$’s such that an arbitrary given state, $\left\{{\vec{S}}_i\right\}$, is the ground state. We show that the problem of finding the ground state for the special case $n=N$ is equivalent to finding the ground state of a corresponding soft-spin problem.