A continuum model is developed to predict the dielectrophoretic polarizability of coiled DNA molecules under the action of an alternating current electric field. The model approximates the coiled DNA molecule as a charged porous spherical particle. The model explains the discrepancies among scaling laws of polarizability of different-sized DNA molecules with contour length and such discrepancies are attributed to different hydrodynamic behavior. With zero or one fitting parameter, theoretical predictions are in good agreement with various experimental data, even though in experiments there are some uncertainties in regard to certain parameters.

Motivated by therapeutic deep brain stimulation, we carried out a model study on the effects of periodic stimulation on an overly activated neuronal circuit. Our neuronal circuit, modeled as a small-world network of noisy Hodgkin-Huxley neurons, is controlled to undergo the mechanism of coherence resonance to exhibit spontaneous synchronization of neuronal firing. This state of energy burst is then directly modulated by a chain of electric pulses. Our study shows that (i) the stimulation blocks the synchronization by generating traveling waves, (ii) only the pulse with proper frequency can block the synchronization, and (iii) the effects of stimulation are completely reversible. It is also found that the stimulation is effective only when the network maintains fairly good structural regularity.

We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate $p$ on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of $p$ promote biodiversity, they may act detrimentally on spatial pattern formation. For random initial conditions, we observe a phase transition from biodiversity to an absorbing phase, whereby the critical value of mobility grows linearly with increasing values of $p$ on a log-log scale but then saturates as $p$ becomes large. For prepared initial conditions, we observe the formation of single-armed spirals, but only for values of $p$ that are below a critical value. Once above that value, the spirals break up and form disordered spatial structures, mainly because of the percolation of vacant sites. Thus there exists a critical value of the competition rates $p_c$ for stable single-armed spirals in finite populations. Importantly though, $p_c$ increases with increasing system size because noise reinforces the disintegration of ordered patterns. In addition, we also find that $p_c$ increases with the mobility. These phenomena are reproduced by a deterministic model that is based on nonlinear partial differential equations. Our findings indicate that competition is vital for the sustenance of biodiversity and the emergence of pattern formation in ecosystems governed by cyclical interactions.

Glycolysis is one of the most essential intracellular networks, found in a wide range of organisms. Due to its importance and due to its wide industrial applications, many experimental studies on all details of this process have been performed. Until now, however, to the best of our knowledge, there has been no comprehensive investigation of the robustness of this important process with respect to internal and external noise. To close this gap, we applied two complementary and mutually supporting approaches to a full-scale model of glycolysis in yeast: (a) a linear stability analysis based on a generalized modeling that deals only with those effective parameters of the system that are relevant for its stability, and (b) a numerical integration of the rate equations in the presence of noise, which accounts for imperfect mixing. The results suggest that the occurrence of metabolite oscillations in part of the parameter space is a side effect of the optimization of the system for maintaining a constant adenosine triphosphate level in the face of a varying energy demand and of fluctuations in the parameters and metabolite concentrations.

We have developed a method based on the Mie theory for determining the local polymer concentration inside spherical nanoparticles, thereby obtaining vital information about whether the particles are swelling in the solvent or if they are contracted into a more compact structure. In addition, this method can be used to calculate the number density of the particles, the molecular weight of the particles, and (if $M_n$ of the polymer is known) the aggregation number. The calculations are based on the relationship between the size of the nanoparticles and the turbidity of the sample.

The floating potential of an emissive cylindrical probe in a plasma is calculated for an arbitrary ratio of Debye length to probe radius and for an arbitrary ion composition. In their motion to the probe the ions are assumed to be collisionless. For a small Debye length, a two-scale analysis for the quasineutral plasma and for the sheath provides analytical expressions for the emitted and collected currents and for the potential as functions of a generalized mass ratio. For a Debye length that is not small, it is demonstrated that, as the Debye length becomes larger, the probe potential approaches the plasma potential and that the ion density near the probe is not smaller but rather is larger than it is in the plasma bulk.

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007–2008 credit and liquidity crisis.

Thresholds of convection excitation and nonlinear convective flow patterns in a horizontal colloidal-mixture layer heated from below are investigated. We take into consideration the fact that, provided the barometric stratification has been reached prior to imposing the temperature gradient, only oscillatory disturbances develop. The influence of separation ratio, sedimentation length, and Prandtl number on the thresholds of oscillatory convection is studied. To examine the complex nonlinear dynamics of the system, numerical simulations with realistic boundary conditions have been carried out using a finite difference method. Long-wave and cellular instability modes as well as transitions between the conductive state and the traveling-wave regime are discussed. It is shown that the traveling-wave regime is stable within a specified range of heating intensity (the Rayleigh number interval). Complex bifurcation and spatiotemporal properties of dissipative structures caused by the interaction of the gravity-induced concentration gradient, nonlinear advection, and mixing of the fluid with nanoparticles are considered.

We derive analytical expressions for the propagation speed of downward combustion fronts of thin solid fuels with a background flow initially at rest. The classical combustion model for thin solid fuels that consists of five coupled reaction-convection-diffusion equations is here reduced into a single equation with the gas temperature as the single variable. For doing so we apply a two-zone combustion model that divides the system into a preheating region and a pyrolyzing region. The speed of the combustion front is obtained after matching the temperature and its derivative at the location that separates both regions. We also derive a simplified version of this analytical expression expected to be valid for a wide range of cases. Flame front velocities predicted by our analytical expressions agree well with experimental data found in the literature for a large variety of cases and substantially improve the results obtained from a previous well-known analytical expression.

A theoretical investigation is made to understand the onset of thermovibrational convection in a fluid saturated horizontal porous layer subjected to isothermal heating either at the bottom or at the top. Attention is paid to the situation in which the solid and fluid phases of the porous medium may fail to obey thermal equilibrium locally. Vertical harmonic vibrations of arbitrary amplitude and frequency are considered. The threshold for dynamic instability is found via synchronous and subharmonic resonant modes exploiting the Floquet theory. The nonequilibrium effect is felt only for intermediate values of the interphase heat transfer coefficient $H$. It is found that $H$ restrains the onset of convection whereas $\gamma$, the porosity modified conductivity ratio, encourages it. $\gamma$ constricts the convective cells ensuing at the threshold except when the layer heated from below is undergoing small amplitude vibrations. Small values of $\gamma$ expose the competition between synchronous and subharmonic modes for a wider range of vibrational frequencies.

In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron diffusion is small. It consists of two integro-differential equations defined at the boundary of the plasma region: one for the motion and a second equation for the net charge density at the interface. We have computed explicit solutions with cylindrical symmetry and found the dispersion relation for small symmetry-breaking perturbations in the case of finite resistivity. We implement a numerical procedure to solve our model in general situations. As a result we compute the dispersion relation for the cylindrical case and compare it with the analytical predictions. Comparisons with experimental data for a 2D positive streamers discharge are provided and predictions confirmed.

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an $H$-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

We study the diffusive dynamics of phase separation in a symmetric binary (A $+$ B) mixture with a 50:50 composition of A and B particles, following a quench below the demixing critical temperature, both in spatial dimensions $d=2$ and $d=3$. The particular focus of this work is to obtain information about the effects of system size and correction to the growth law via the appropriate application of the finite-size scaling method to the results obtained from the Kawasaki exchange Monte Carlo simulation of the Ising model. Observations of only weak size effects and a very small correction to scaling in the growth law are significant. The methods used in this work and information thus gathered will be useful in the study of the kinetics of phase separation in fluids and other problems of growing length scale. We also provide a detailed discussion of the standard methods of understanding simulation results which may lead to inappropriate conclusions.

We consider surface diffusion of a single particle, which performs site-to-site under-barrier hopping, fulfils intrasite motion between the ground and the first excited states within a quantum well, and interacts with surface phonons. On the basis of quantum kinetic equations for one-particle distribution functions, we study the coherent and incoherent motion of the adparticle. In the latter case, we derive the generalized diffusion coefficients and study various dynamic regimes of the adparticle. The critical values of the coupling constant $G_{\mathrm{cr}}(T,\Omega )$, which separate domains with possible recrossing from those with the monotonic motion of the adparticle, are calculated as functions of temperature $T$ and vibrational frequency $\Omega$. These domains are found to coincide with the regions where the experimentally observed diffusion coefficients change their behavior from weakly dependent on $T$ to quite a sensitive function of the temperature. We also evaluate the off-diagonal distribution functions both in the Markovian limit and when the memory effects become important. The obtained results are discussed in the context of the “long tails” problem of the generalized diffusion coefficients, the recrossing/multiple crossing phenomena, and an eventual interrelation between the adparticle dynamics at short times and the temperature dependence of the diffusion coefficients measured experimentally.

Our theoretical and numerical investigation of the movement of an object that partitions a microtubule filled with small particles indicates that vibrations warranted by thermal equilibrium are reached only after a time that increases exponentially with the number of particles involved. This points to a basic mechanical process capable of breaching, on accessible time scales, the ultimate ergodic constraints that force randomness on bound microscale and nanoscale systems.

Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic lattice by the particle around and on the attractive plane. We compute the fractal dimensions of the set of visited sites both in three dimensions and on the attractive plane, as a function of the strength of attraction $\alpha$. We also investigate the scaling properties of the size distribution of the clusters of nearest-neighbor visited sites on the attractive plane and compute the corresponding scaling exponent $\tau$ as a function of $\alpha$. The fractal dimension of the curves surrounding the clusters is also computed for different values of $\alpha$, which, in the limit $\alpha \to \infty$, tends to that of the outer perimeter of planar Brownian motion, i.e., the self-avoiding random walk (SAW). We find that all measured exponents depend significantly on the strength of attraction.

A theory of aerosol coagulation rates resulting from continuum-regime Brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle Brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of Brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or “coagulation-aged”) mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational “coupled” coagulation rate constant (allowing for simultaneous Brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation “kernels.” Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].

The peculiarities in the dynamic of the director reorientation in a liquid crystal (LC) film under the influence of the electric $\mathbf{\text{E}}$ field directed at an angle $\alpha$ to the magnetic $\mathbf{\text{B}}$ field have been investigated both experimentally and theoretically. Time-resolved deuterium $\mathrm{NMR}$ spectroscopy is employed to investigate the field-induced director dynamics. Analysis of the experimental results, based on the predictions of hydrodynamic theory including both the director motion and fluid flow, provides an evidence for the appearance of the spatially periodic patterns in 4-n-pentyl-4${}^{\prime }$-cyanobiphenyl LC film, at the angles $\alpha >{60}^{\circ }$, in response to the suddenly applied $\mathbf{\text{E}}$. These periodic distortions produce a lower effective rotational viscosity. This gives a faster response of the director rotation than for a uniform mode, as observed in our NMR experiment.

We have studied the interparticle force between two colloidal particles in a nematic liquid crystal experimentally and theoretically. The force $F$ was directly measured using dual-beam optical tweezers and was numerically calculated from the equilibrium tensor field around the particles. The dependence of $F$ on the center-to-center distance $R$ between the particles was studied not only for equal-sized particles but also for different-sized ones in various kinds of configurations and arrangements. The magnitude of $F$ between different-sized particles in the dipole configuration depends on their relative arrangement. Both experimental and theoretical force curves are found to be in good agreement with each other. At large $R$, they also make agreement with those predicted by an electrostatic analogy of nematic field.

The existence of the elusive biaxial phase has been the subject of much discussion since it was predicted by Freiser in 1970. More recently, there have been numerous attempts to find a thermotropic liquid crystal that exhibits a biaxial phase and with this, conflicting reports about whether such a phase has been positively identified in bent-core liquid crystals. One reason for the discrepancy is that there is currently no way to rule out surface effects or anchoring transitions, both of which may give a false positive identification of a uniaxial-biaxial nematic transition. We have developed a technique that uses a magnetic field to align the uniaxial director, thus widening its application to any bent-core nematic material.