In present study, the transition of thermocapillary convection from the axisymmetric stationary flow to oscillatory flow in liquid bridges of 5cst silicon oil (aspect ratio 1.0 and 1.6) is investigated in microgravity conditions by the linear instability analysis. The corresponding marginal instability boundary is closely related to the gas/liquid configuration of the liquid bridge noted as volume ratio. With the increasing volume ratio, the marginal instability boundary consists of the increasing branch and the decreasing branch. A gap region exists between the branches where the critical Marangoni number of the corresponding axisymmetric stationary flow increases drastically. Particularly, a unique axisymmetric oscillatory flow (the critical azimuthal wave number is $m=0$) in the gap region is reported for the liquid bridge of aspect ratio 1.6. Moreover, the energy transfer between the basic state and the disturbance fields of the thermocapillary convection is analyzed at the corresponding critical Marangoni number, which reveals different major sources of the energy transfer for the development of the disturbances in regimes of the increasing branch, the gap region and the decreasing branch, respectively.

The steady-state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The models include the magnetohydrodynamic (MHD) equations, linear pressure model, and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.

The rank-ordered multifractal analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one-parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through rank-ordered scaling or nonscaling parametric variables. The idea of the ROMA technique is applied to analyze the multifractal characteristics of the auroral zone electric-field fluctuations observed by the SIERRA sounding rocket. The observed fluctuations span across contiguous multiple regimes of scales with different multifractal characteristics. We extend the ROMA technique such that it can take into account the crossover behavior—with the possibility of collapsing probability distribution functions—over these contiguous regimes.

We study the formation and stability of monochromatic waves induced by large-scale modulations in the framework of the complex Ginzburg-Landau equation with parametric nonresonant forcing dependent on the spatial coordinate. In the limiting case of forcing with very large characteristic length scale, analytical solutions for the equation are found and conditions of their existence are outlined. Stability analysis indicates that the interval of existence of a monochromatic wave can contain a subinterval where the wave is stable. We discuss potential applications of the model in rheology, fluid dynamics, and optics.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random-walk approach, but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

While the classical nucleation theory (CNT) is widely used to predict the rate of first-order phase transitions, its validity has been questioned due to discrepancies with experiments. We systematically test the individual components of CNT by computer simulations of the Ising models and confirm its fundamental assumptions under a wide range of conditions ($h=0.01\text{–}0.13J$, $T=0.44\text{–}0.84T_c$ in two-dimensions and $h=0.30\text{–}0.60J$, $T=0.48\text{–}0.62T_c$ in three dimensions). First, CNT accurately predicts the nucleation rate if the correct droplet free energy is provided. Furthermore, theoretical prediction of droplet free energy matches numerical results very well in the two-dimensional (2D) Ising model, if appropriate correction terms are added. This establishes the 2D Ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters.

Heat conduction through the Frenkel-Kontorova chain under the influence of an ac driving force applied locally at one boundary is studied by nonequilibrium molecular dynamics simulations. We observe the occurrence of thermal resonance, namely, there exists a value of the driving frequency at which the heat flux takes its maximum value. The resonance frequency is determined by the dynamical parameters of the model, which has been numerically explored. Remarkably, the heat can be pumped from the low-temperature heat bath to the high temperature one by suitably adjusting the frequency of the ac driving force. By examining effects of the driving amplitude on heat conduction, we show that the amplitude threshold for nonlinear supratransmission is absent when the system is in contact with heat baths, namely, the heat flux smoothly increases with the increasing of amplitude.

We combine the hypernetted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature—volume fraction phase diagram. The zero-temperature (hard-sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that “mean-field” mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.

We study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed.

The effect of solvation-related interaction on the low-temperature dynamics of proteins is studied by taking into account the desolvation barriers in the interactions of native contacts. It is found out that about the folding transition temperature, the protein folds in a cooperative manner, and the water molecules are expelled from the hydrophobic core at the final stage in the folding process. At low temperature, however, the protein would generally be trapped in many metastable conformations with some water molecules frozen inside the protein. The desolvation takes an important role in these processes. The number of frozen water molecules and that of frozen states of proteins are further analyzed with the methods based on principal component analysis (PCA) and the clustering of conformations. It is found out that both the numbers of frozen water molecules and the frozen states of the protein increase quickly below a certain temperature. Especially, the number of frozen states of the protein increases exponentially following the decrease in the temperature, which resembles the basic features of glassy dynamics. Interestingly, it is observed that the freezing of water molecules and that of protein conformations happen at almost the same temperature. This suggests that the solvation-related interaction performs an important role for the low-temperature dynamics of the model protein.

The dynamic behavior of end-labeled DNA during free-solution electrophoresis is investigated using a simple dumbbell model for the labeled DNA. We study the effect of the applied field, label size, and chain stiffness on DNA conformation and electrophoretic mobility. High applied fields are predicted to magnify the size-dependence of mobility and to yield a nonmonotonic dependence of electrophoretic mobility on applied field. The effectiveness of leveraging label size and DNA chain stiffness for improving resolution is also discussed in the context of DNA deformation. To evaluate the most salient model predictions, we use capillary electrophoresis experiments to characterize the size- and field-dependent mobility of dsDNA fragments (300 bp–2 kbp) end-functionalized with streptavidin. Our experimental results are found to be in generally good accord with expectations based on the dumb-bell model. We discuss implications of these findings for fast, size-based separation of DNA in free solution.

The mean field model proposed by Makeev and Nieuwenhuys [J. Chem. Phys. 108, 3740 (1998)] simulates the oscillatory behavior experimentally observed in the $\text{NO}+{\text{H}}_2$ reaction on the surface Pt(100). This model reproduces quite well the kinetic oscillations and the transition to chaos via the Feigenbaum route, that is to say, through bifurcations involving period doubling. From this model, we analyze the response of the natural oscillations of period-1 (P1, one maximum) to periodic perturbations superposed to the partial pressure of one of the reactants. The perturbed model reproduces the periodic states found in the autonomous model, the route to chaos through bifurcations with period doubling, and the appearance of chaos via the route of intermittency, which shows alternation of periodic oscillations with intervals of disordered oscillations in the same time evolution. Experimentally it has been observed that the reaction shows a great sensitivity to reactant partial pressures and temperature. In experimental conditions slightly different to those considered in Makeev and Nieuwenhuys (MN) model, oscillations with period-3 (P3, three maxima) have been observed. At $T=457\text{K}$ and certain pressures, these P3 oscillations do not appear in MN model, although they appear at $T=456\text{K}$. The same effect (P3 oscillations) is obtained at $T=457\text{K}$ in our perturbed model, due to the modulation of $p_{{\text{H}}_2}$. In a second step we show how the modulation of the perturbing frequency influences on the oscillations P1 of the perturbed system. The results show that the periodic behavior loses its regularity at low values of the normalized amplitude and of the modulated frequency of the perturbation. Other aspect observed in the perturbed model is that the amount of products varies in relation to nonperturbed model. When the oscillations are periodic or they follow the Feigenbaum route to chaos, the production average decreases or slightly increases, whereas it always increases if there are intermittencies, the most significant percentage increase being for ${\text{NH}}_3$ (nearly 10%).

We study the decay of a prepared state $E_0$ into a continuum $\left\{E_k\right\}$ in the case of non-Ohmic models. This means that the coupling is $\left|V_{k,0}\right|\propto {\left|E_k-E_0\right|}^{s-1}$ with $s\ne 1$. We find that irrespective of model details there is a universal generalized Wigner time $t_0$ that characterizes the decay of the survival probability $P_0\left(t\right)$. The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the band profile. But depending on nonuniversal features of the model a power-law decay might take over: it is only for an Ohmic coupling to the continuum that we get a robust exponential decay that is insensitive to the nature of the intracontinuum couplings. The analysis highlights the coexistence of perturbative and nonperturbative features in the dynamics. It turns out that there are special circumstances in which $t_0$ is reflected in the spreading process and not only in the survival probability, contrary to the naive linear-response theory expectation.

The emission from an electron in the field of a relativistically strong laser pulse is analyzed. At pulse intensities of $J\ge 2\times {10}^{22}\text{W}/{\text{cm}}^2$ the emission from counterpropagating electrons is modified by the effects of quantum electrodynamics (QED), as long as the electron energy is sufficiently high: $\mathcal{E}\ge 1\text{GeV}$. The radiation force experienced by an electron is for the first time derived from the QED principles and its applicability range is extended toward the QED-strong fields.

Bremsstrahlung is correlated with high-energy electrons in laser-heated plasma [K. Brueckner, Phys. Rev. Lett. 36, 677 (1976)]. Since the result is important to the National Ignition Campaign (NIC) we reconsider the derivation, and the energy dependence of the Gaunt factor(s). We find an expression for bremsstrahlung we can Abel invert, and we demonstrate the accuracy of the transform with a simple numeric exercise.

The evolution of the Erdős-Rényi (ER) network by adding edges is a basis model for irreversible kinetic aggregation phenomena. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel $K_{ij}\sim ij$, where $ij$ is the product of the sizes of two merging clusters. Here we study that when the giant cluster is discouraged to develop by a sublinear kernel $K_{ij}\sim {\left(ij\right)}^{\omega }$ with $0\le \omega <1/2$, the percolation transition (PT) is discontinuous. Such discontinuous PT can occur even when the ER dynamics evolves from proper initial conditions. The obtained evolutionary properties of the simple model sheds light on the origin of the discontinuous PT in other nonequilibrium kinetic systems.

We demonstrate that a topology-induced Bose-Einstein condensation (BEC) takes place in a complex network. As a model topology, we consider the deterministic Apollonian network which exhibits scale-free, small-world, and hierarchical properties. Within a tight-binding approach for noninteracting bosons, we report that the BEC transition temperature and the gap between the ground and first excited states follow the same finite-size scaling law. An anomalous density dependence of the transition temperature is reported and linked to the structure of gaps and degeneracies of the energy spectrum. The specific heat is shown to be discontinuous at the transition, with low-temperature modulations as a consequence of the fragmented density of states.

We study analytically and numerically the anomalous diffusion across periodically modulated parabolic potential within Langevin and Fokker-Planck descriptions. We find that the probability of particles passing over the saddle is affected strikingly by the periodical modulation with average zero bias. Particularly, the initial phase plays an important role in the modulation effect. The effect of the correlation time of external Ornstein-Uhlenbeck noise on dynamical process is also discussed. A reduction in overpassing probability is observed due to finite correlation time.

Second-harmonic dielectric response under dc fields in an antiferroelectric liquid-crystal 4-(1-methyl-heptyloxycarbonyl)phenyl 4-octylcarbonyloxybiphenyl- 4-carboxylate (MHPOCBC) has been investigated. The second-harmonic response from the amplitude mode in the smectic-$C_{\alpha }^{\ast }$ phase was observed due to the symmetry breaking by the application of dc electric fields. A Landau theory was developed in order to analyze experimentally obtained frequency dispersions. From the analysis we found a softening of the amplitude mode with increasing the dc field at a temperature close to the smectic-$C_{\alpha }^{\ast }$-smectic-$A$ phase transition point. It was turned out that the relaxation frequency of the amplitude mode decreases linearly with the applied electric field.

Dielectric spectroscopy measurements have been performed on a bent-core nematic liquid crystal and on its binary mixtures with a calamitic nematic. We have detected more dispersions in the bent-core compound than in the calamitic one, including one at an unusually low frequency of a few kilohertz. The dispersions detected in the mixtures have been identified and the spectra have been split into contributions of the constituents. In order to connect the dielectric increment with the molecular dipole moment we have applied a sophisticated conformational calculation not performed before for a large, flexible mesogen molecule with numerous polar groups.