Discharge streamers in experiments branch frequently. Arrayás et al. [Phys. Rev. Lett. 88, 174502 (2002)] presented simulations of branching streamers and interpreted them as physical branching events. The numerical results were criticized by Kulikovsky [Phys. Rev. Lett. 89, 229401 (2002)]. Using an adaptive grid algorithm, we here present numerical experiments on the effect of grid resolution on streamer branching. The convergence of branching time with stepwise finer grid sizes provides a quantitative correction on the earlier, low-resolution results in overvolted gaps. Furthermore, streamers can branch even in undervolted, but sufficiently long gaps, but fewer branching modes are accessible than in higher fields.

In this paper we study the impact of degree correlations in the subgraph statistics of scale-free networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the average number of Hamiltonian paths in a three-core of real world networks. We prove our results in the two-vertex correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.

We show that inhomogeneous boundary conditions (BCs) in a distributed reaction-diffusion excitable system are a natural source of permanent perturbations that can induce wave trains, which can be characterized as mixed-mode temporal oscillations and, when a parameter is varied, admit a period-adding bifurcation. To that end we analyze: a pair of coupled excitable and oscillatory cells, a distributed FitzHugh-Nagumo model, and a distributed five-variable model that describes $\mathrm{CO}$ catalytic oxidation. The obtained results account for the recently reported experimental observations of mixed-mode oscillations showing a period-adding bifurcation during $\mathrm{CO}$ oxidation on a disk-shaped catalytic cloth with imposed cold temperature BC.

We study spatiotemporal patterns resulting from instabilities induced by nonlocal spatial coupling in the Oregonator model of the light-sensitive Belousov-Zhabotinsky reaction. In this system, nonlocal coupling can be externally imposed by means of an optical feedback loop which links the intensity of locally applied illumination with the activity in a certain vicinity of a particular point weighted by a given coupling function. This effect is included in the three-variable Oregonator model by an additional integral term in the photochemically induced bromide flow. A linear stability analysis of this modified Oregonator model predicts that wave and Turing instabilities of the homogeneous steady state can be induced for experimentally realistic parameter values. In particular, we find that a long-range inhibition in the optical feedback leads to a Turing instability, while a long-range activation induces wave patterns. Using a weakly nonlinear analysis, we derive amplitude equations for the wave instability which are valid close to the instability threshold. Therein, we find that the wave instability occurs supercritically or subcritically and that traveling waves are preferred over standing waves. The results of the theoretical analysis are in good agreement with numerical simulations of the model near the wave instability threshold. For larger distances from threshold, a secondary breathing instability is found for traveling waves.

We consider the escape of ballistic trajectories from an open, vase-shaped cavity. Such a system serves as a model for microwaves escaping from a cavity or electrons escaping from a microjunction. Fixing the initial position of a particle and recording its escape time as a function of the initial launch direction, the resulting escape-time plot shows “epistrophic fractal” structure—repeated structure within structure at all levels of resolution with new features appearing in the fractal at longer time scales. By launching trajectories simultaneously in all directions (modeling an outgoing wave), a detector placed outside the cavity would measure a train of escaping pulses. We connect the structure of this chaotic pulse train with the fractal structure of the escape-time plot.

High-energy electron cooling, presently considered as an essential tool for several applications in high-energy and nuclear physics, requires an accurate description of the friction force which ions experience by passing through an electron beam. Present low-energy electron coolers can be used for a detailed study of the friction force. In addition, parameters of a low-energy cooler can be chosen in a manner to reproduce regimes expected in future high-energy operation. Here, we report a set of dedicated experiments in CELSIUS aimed at a detailed study of the magnetized friction force. Some results of the accurate comparison of experimental data with the friction force formulas are presented.

We introduce and discuss a three-dimensional mesoscopic lattice Boltzmann model for the numerical simulation of strongly-interacting fluids with dynamic inhomogeneities. The model is based on an extension of the standard lattice Boltzmann dynamics in which streaming between neighboring lattice sites is constrained by the value of the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamically heterogeneous fluids, such as long-time relaxation, non-Gaussian density distributions and dynamic heterogeneities. Due to its intrinsically parallel dynamics and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo, and lattice glass models.

Stochastic nature due to distance and energy fluctuations of single protein molecules involved in electron-transfer (ET) reactions is studied. Distance fluctuations have been assumed previously for causing the slow fluctuations in the ET rates between a donor-acceptor pair constrained to a native protein. Although the observed $t^{-1∕2}$ power law can be derived using Langevin dynamics with a simple chain model, some discrepancies exist. The friction coefficient and the Rouse segment time constant deduced from experimental data are several orders of magnitude too large, even though the extracted force constant is reasonable. Therefore, questions are raised about the distance-fluctuation mechanism and the activationless ET hypothesis. As an alternative mechanism, we considered fluctuations in activation energy and analyzed the data from two different single protein experiments to determine spectral distribution of energy fluctuations.

An analytical model is presented for predicting the transport and capture of therapeutic magnetic nanoparticles in the human microvasculature. The nanoparticles, with surface bound drug molecules, are injected into the vascular system upstream from malignant tissue, and are captured at the tumor site using a local applied magnetic field. The applied field is produced by a rare-earth cylindrical magnet positioned outside the body. An analytical expression is derived for predicting the trajectory of a particle as it flows through the microvasculature in proximity to the magnet. In addition, a scaling relation is developed that enables the prediction of the minimum particle radius required for particle capture. The theory takes into account the dominant magnetic and fluidic forces, which depend on the position and properties of the magnet, the size and magnetic properties of the nanoparticles, the dimensions of the microvessel, the hematocrit level of the blood, and the flow velocity. The model is used to study noninvasive drug targeting, and the analysis indicates that submicron particles can be directed to tumors that are several centimeters from the field source.

Ultrasound-modulated optical tomography is an imaging technique that detects ultrasonically tagged light in optically turbid media to obtain images with optical contrast and ultrasonic spatial resolution. A CCD-camera-based speckle contrast detection scheme has been introduced previously to detect modulated light emerging from the ultrasonic sample volume. Differences in speckle contrast were experimentally observed when ultrasound was applied compared to when it was not. In this paper we provide an analytic explanation for this phenomenon and connect speckle statistics with ultrasonic field parameters. The theory predicts that speckle contrast changes linearly with applied acoustic intensity. This prediction is experimentally validated for both 1 and $3.5\mathrm{MHz}$ ultrasound. Signal dependence on ultrasound frequency is discussed.

We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks—a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability $p$ of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution $P\left(k\right)$ and clustering coefficient $C$ for all $p$, as well as the average path length $\ell$ for $p=0$ and $1$. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to $562500$ renormalized probability bins to represent the distribution. For $p<0.494$, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with $p$, and exponential decay of correlations away from $T_c$. For $p\ge 0.494$, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching $T_c$ from below, the magnetization and the susceptibility, respectively, exhibit the singularities of $\exp (-C∕\sqrt{T_c-T})$ and $\exp (D∕\sqrt{T_c-T})$, with $C$ and $D$ positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all $p$, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

The influence of dissipation on the simplified Fermi-Ulam accelerator model (SFUM) is investigated. The model is described in terms of a two-dimensional nonlinear mapping obtained from differential equations. It is shown that a dissipative SFUM possesses regions of phase space characterized by the property of area preservation.

We show that, by inserting suitable finite networks at a site of a chain, it is possible to realize filters and high-pass/low-pass devices for solitons propagating along the chain. The results are presented in the framework of coupled optical waveguides; possible applications to different contexts, such as photonic lattices and Bose-Einstein condensates in optical networks are also discussed. Our results provide a first step in the control of the soliton dynamics through the network topology.

Energy landscape mappings are performed for two different molecular systems under mechanical loads. Barrier heights are observed to scale as $\Delta U\sim {\delta }^{3∕2}$, where $\delta$ is a residual load. Catastrophe theory predicts that this scaling should arise for vanishing $\delta$; however, this region is irrelevant in physical processes at finite temperature because thermal fluctuations cause the system to cross over the barrier before reaching the small-$\delta$ regime. Surprisingly, we find that the $\Delta U\sim {\delta }^{3∕2}$ scaling is valid far beyond the vanishing $\delta$ regime described by catastrophe theory. We discuss how this scaling will therefore be relevant at finite temperatures and gives corrections to Eyring’s theory for transition rates.

We consider a Brownian particle acted on by a linear conservative force, a nonlinear frictional force, and multiplicative colored and additive white noises; the frictional force can be negative when the external energy supply is large enough. We numerically calculate the mean first passage time (MFPT) for the particle to escape from an unstable limit cycle and find resonant activation, i.e., the MFPT first decreases, followed by a rise after passing through a minimum with increasing noise correlation time $\tau$ for a fixed noise variance. For fixed noise strength of the multiplicative noise the MFPT increases linearly with $\tau$. This is in sharp contrast to the case of fluctuations of nonlinear potentials, in which the MFPT first increases nonlinearly before reaching a limiting value. Our model could be useful for understanding some biological processes.

In the $Q$ range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor $S(Q,\omega )$ generalize in different ways the results obtained from linearized-hydrodynamics theory in the $Q\to 0$ limit. Here we show that the models most commonly fitted to experimental $S(Q,\omega )$ spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation $Q$ range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the $Q$ dependence of the mode frequencies. The emerging picture describes the acoustic modes as $Q$-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.

Inclusion of protein lysozyme molecules in the lipidic mono-olein cubic phase induces a transition from a $Pn\overline{3}m$ structure to an $Im\overline{3}m$ one. The small-angle x-ray scattering method with high-intensity synchrotron radiation enabled us to follow closely the transition depending on the conditions of lysozyme solutions. We show that concentrated lysozyme solutions induced the appearance of the $Im\overline{3}m$ structure coexisting with the $Pn\overline{3}m$ structure. From the relation between the lattice parameters of these two structures it is shown that they are related by the Bonnet transformation of the underlying triply periodic minimal surfaces. We found that the transition also occurred at lower lysozyme concentration when $\mathrm{NaCl}$ induced an attraction between lysozyme molecules. The origin of the transition was considered as a frustration in the cubic phase where lysozyme molecules were highly confined. A simple estimation of the frustration was given, which took into account the translational entropy of lysozyme molecules. At the highest concentration of lysozyme and $\mathrm{NaCl}$ the $Im\overline{3}m$ structure was found to disappear and left only the $Pn\overline{3}m$ structure. This was probably either due to the crystallization or phase separation of lysozyme solutions ongoing microscopically, which absorbed lysozyme molecules from channels of the cubic phase and thus removed the frustration.

A boundary dynamics of sweeping interface is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is formulated as the small diffusion limit of the Mullins-Sekerka problem of crystal growth. It is demonstrated that a steadily extending finger solution exists for a finite range of propagation speed, but numerical simulations suggest they are unstable and the interface shows a complex time development.

Recent experiments have revealed several surprising features of the phase equilibria in protein solutions: liquid-liquid phase separation which is, in some cases, metastable with respect to the liquid-solid equilibrium, and in others—unobservable; widely varying crystallization enthalpies, including completely athermal crystallization; the co-existence of several crystalline polymorphs; and others. Other studies have shown that the solvent molecules at the hydrophobic and polar patches on the protein molecular surfaces are structured, introducing repulsive forces at surface separations equal to several water molecule sizes. In search of a causal link between the latter and former findings, we apply Monte Carlo simulation techniques in the investigation of phase diagrams associated with globular biological molecules in solution. We account for the solvent structuring via short-range isotropic two-body intermolecular potentials exhibiting multiple extrema. We show that the introduction of a repulsive maximum or a secondary attractive minimum at separations longer than the primary attractive minimum has dramatic effects on the phase diagram: liquid-liquid separation curves are driven to lower or higher temperatures, the sensitivity of the solubility curve (liquidus) to temperature, i.e., the enthalpy of crystallization, is significantly reduced or enhanced, metastable liquid-liquid separation may become stable and vice versa, and both low- and high-density crystalline phases are observed. The similarity of these features of the simulated phase behavior to those observed experimentally suggests that at least some of the mysteries of the protein phase equilibria may be due to the structuring of the solvent around the protein molecular surfaces. Another conclusion is that at least some of the dense liquids seen in protein solutions may be stable and not metastable with respect to a solid phase.