We study the dynamics of a single paramagnetic colloidal particle dispersed in water and circulating around a cylindrical magnetic domain (“magnetic bubble”) when driven by an external rotating magnetic field. We record the particle trajectories and measure its angular displacement by changing the strength, frequency, and ellipticity of the applied magnetic field and show that this simple system exhibits several interesting phenomena, from synchronous-asynchronous rotations, to localized oscillations. We complement the experimental results with numerical simulations which explore the dynamical regimes of the rotating particle.

We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low-degree nodes and among high-degree nodes. This paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes. The alternate method indicates that some networks show a false disassortative mixing induced by superrich nodes and have no tendency to be genuinely disassortative. Our results also show that the previously observed fragility of scale-free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes.

We consider synchronization of coupled chaotic systems and propose an adaptive strategy that aims at evolving the strength of the coupling to achieve stability of the synchronized evolution. We test this idea in a simple configuration in which two chaotic systems (a sender and a receiver) are unidirectionally coupled and we study the conditions for the receiver to adaptively synchronize with the sender. Numerical simulations show that, under certain conditions, our strategy is successful in dynamically evolving the coupling strength until it converges to a value that is compatible with synchronization.

We study the existence of stationary shock waves in uniform and periodic heterogeneous highly nonlinear granular chains governed by a power-law contact interaction, comparing discrete and continuum approaches, as well as experiments. We report the presence of quasisteady shock fronts without the need for dissipative effects. When viscous effects are neglected, the structure of the leading front appears to be solely the result of dispersive effects related to the lattice wave dispersion and, for heterogeneous bead chains, to the impedance mismatch between material domains. We report analytically and numerically the shock-width scaling with the variation in the particles periodicity (cell size) and compare the obtained results with experiments. We check the state $(-)$ behind the shock front via quasistatic compression analysis and report a very good agreement between theory and numerical data.

In this paper the homotopy perturbation method is used for calculation of the frequencies of the coupled secular oscillations and axial secular frequencies of a nonlinear ion trap. The motion of the ion in a rapidly oscillating field is transformed to the motion in an effective potential. The equations of ion motion in the effective potential are in the form of a Duffing-like equation. The homotopy perturbation method is used for solving the resulted system of coupled nonlinear differential equations and the resulted axial equation for obtaining the expressions for ion secular frequencies as a function of nonlinear field parameters and amplitudes of oscillations. The calculated axial secular frequencies are compared with the results of Lindstedt-Poincare method and the exact results.

This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi et al., Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behaviors of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in $2+1$ dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides a clear experimental realization of this outstanding truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.

Using an approximation scheme within the convective diffusion (two-body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure formation in sheared colloidal systems. The theory, verified against numerics and experiments, explains the induction time followed by explosive (irreversible) rise of viscosity observed in charge-stabilized colloidal and protein systems under steady shear. The Arrhenius-type equation with shear derived here, extending Kramers’ theory in the presence of shear, clearly demonstrates the important role of shear drive in activated-rate processes as they are encountered in soft condensed matter.

This research focuses on the electrokinetic motion of fullerenes suspended in liquid crystal host medium, which are investigated in the homogeneously aligned nematic liquid crystal cells driven by in-plane field. We investigated the effect of electrophoretic and dielectrophoretic forces and related parameters of the colloidal fullerenes in liquid crystals. The electrophoretic mobility, zeta potential, and critical voltage have been evaluated. Fullerenes suspended in liquid crystal medium migrated toward the positive electrode, but were pulled back in the opposite direction when the polarity was reversed especially at low frequency range $\left(<5\text{Hz}\right)$. At higher electric field and higher frequency ranges, the net displacement of fullerenes has been observed. We demonstrate that the dielectrophoretic force dominated the motion in the colloidal fullerenes by a proper analysis of different electrophoretic parameters. In addition, the electrodynamics of fullerenes was explained by applying the theory of the dielectrophoresis and Schwarz’s formula. We propose a model to estimate the density of fullerenes suspended in liquid crystal medium.

We subject the primary sequence of proteins gathered from the Structural Classification of Proteins (SCOP) database to a discrete wavelet transform (DWT) analysis to search for predictors of secondary structures. We use proteins with both alpha helices and beta sheets (the $A/B$, $A+B$ databases from SCOP). The amino acids composing the protein are converted to their hydrophobicity values using three hydrophobicity scales. Results prove to be independent of the scale used. Using a DWT multiresolution decomposition, each protein is coarse grained, in effect, creating snapshots of each protein at multiple scales. For each protein, a control data set is formed by generating random realizations that remove the positional informational in the sequence but still contain the same amino acid frequencies. Regions of salient hydrophobicity in the protein sequence are identified by comparing the transforms of the original sequence with those of the control set, at each resolution. We find significant matching between regions of salient hydrophobicity and the locations of secondary structure along the amino acid chains. We calculate the sensitivity, specificity, and Matthews correlation to quantify the agreement between the wavelet detected structures and the real protein. In addition we are able to distinguish between the morphologically different subsets, $A/B$ and $A+B$. We also construct a correlation function based on the DWT that correlates quasilocalized structures at lengths in wavelet space. Through a similar comparison to the control data sets, features in this space-scale correlation are identified that show correspondence to the typical lengths of the secondary structures.

An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Building such a tool requires the development and successful integration of a number of biophysical and mathematical models. In this paper, we work toward this long-term goal by formulating a cellular automaton model of tumor growth that accounts for several different inter-tumor processes and host-tumor interactions. In particular, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass and considers the impact that organ-imposed physical confinement and environmental heterogeneity have on tumor size and shape. Furthermore, the algorithm is able to account for cell-level heterogeneity, allowing us to explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. This computational tool we have built has a number of applications in its current form in both predicting tumor growth and predicting response to treatment. Moreover, the latent power of our algorithm is that it also suggests other tumor-related processes that need to be accounted for and calls for the conduction of new experiments to validate the model’s predictions.

Viscous fingering dynamics driven by centrifugal forcing is studied for arbitrary viscosity contrast. Theoretical methods, including exact solutions, and numerics based on a phase-field approach are used. Both confirm that pinch-off singularities in patterns originated from the centrifugally driven instability may occur spontaneously and be inherent to the two-dimensional Hele-Shaw dynamics. They are systematically more frequent for lower viscosity contrasts consistently with experimental evidence. The analytical insights provide an interpretation of this fact in terms of the asymptotic matching of the different regions of the fingering patterns. The phase-field numerical scheme is shown to be particularly adequate to elucidate the existence of finite-time singularities through the dependence of the singularity time on the interface thickness, in particular for varying viscosity contrast.

We study the evolution of a family of dumbbell-shaped liquid patches surrounded by air inside a rotating Hele-Shaw cell with lubrication methods and numerical simulations. Depending on initial conditions, the dumbbell either stretches to infinity, pinches off at the neck to form a droplet, or collects into a circular drop at the center of rotation. Whether or not pinch-off occurs results from a subtle interplay between centrifugal and capillary forces. In particular, rotation may delay or even prevent pinch-off from occurring owing to stretching and smoothing of the fluid neck. However, frequently rotation may have the opposite effect leading to pinch-off where the relaxation toward a circular drop would be observed in an ordinary Hele-Shaw cell.

Lagrangian transport induced by peristaltic waves traveling on the boundaries of a two-dimensional rectangular closed channel is studied analytically. Based on the Lagrangian description, an asymptotic analysis is performed to generate explicit expressions for the leading-order oscillatory as well as the higher-order time-mean mass transport (or steady streaming) velocities as functions of the wave properties. Two cases are considered. The first case, which is for slow wave frequency or very small wave amplitude such that the steady-streaming Reynolds number $\left({\text{Re}}_s\right)$ is very small, recovers the one studied previously in the literature, but with all the results fully presented in the Lagrangian sense. The second case, corresponding to high-frequency pumping such as ${\text{Re}}_s$ is order unity, is where it has been handled analytically. It is found that the overall mixing resulting from the mass transport can depend on the phase shift of the two waves, the wave number, the frequency, as well as the amplitude of the waves.

Two mechanisms by which Marangoni convection can be produced at the interface of water with its vapor are: (1) by imposing a temperature gradient parallel to the water-vapor interface, and (2) by imposing a temperature gradient perpendicular to the interface that results in the liquid becoming unstable. A series of evaporation experiments conducted with ${\text{H}}_2\text{O}$ and with ${\text{D}}_2\text{O}$ maintained at the mouth of a stainless-steel funnel indicated the presence of Marangoni convection, but the mechanism producing the convection was unclear. We have investigated the mechanism using a funnel constructed with a polymethyl methacrylate that has a small thermal conductivity relative to that of water and repeating the evaporation experiments. Marangoni convection was eliminated with this funnel even though the Marangoni number, Ma, was in the range $8277\le \text{Ma}\le 27847$. A comparison of the assumptions made in the theories available to predict the onset of Marangoni convection with the observations made in this study indicates some of the assumptions are invalid: although generally neglected, energy transport through the vapor to the interface of evaporating water is significant; there is an interfacial temperature discontinuity, but it is in the opposite direction of that assumed in the existing theories: the interfacial-vapor temperature is greater than that of the liquid during evaporation; and the prediction of the critical Marangoni number is based on an arbitrarily chosen value of the heat-transfer coefficient. When the temperature gradient is perpendicular to the water-vapor interface, these invalid assumptions indicate present theories do not apply to volatile liquids.

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.

Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We demonstrate that this so-called gain-loss asymmetry vanishes if the temporal dependence structure is destroyed by scrambling the time series. We also show that an artificial index constructed by a simple average of a number of individual stocks display gain-loss asymmetry—this allows us to explicitly analyze the dependence between the index constituents. We consider mutual information and correlation-based measures and show that the stock returns indeed have a higher degree of dependence in times of market downturns than upturns.

Numerical and experimental investigations of intermittency in chaotic systems often lead to claims of universal classes based on the scaling of the average length of the laminar phase with parameter variation. We demonstrate that the scaling in general depends on the choice of the threshold used to define a proper laminar region in the phase space. For sufficiently large values of the threshold, the scaling exponent tends to converge but significant fluctuations can occur particularly for continuous-time systems. Insights into the dependence can be obtained using the idea of Poincaré recurrence.

We present a theory for the coagulation reaction $A+A\to A$ for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (“anomalous kinetics”) and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.

Velocity and cluster distributions for particles with unidirectional motion in one dimension are studied. The particles never pass each other, like cars on a narrow road that does not allow overtaking. As a result, particles cluster behind slow particles (queues are formed behind slow cars). Thus, the actual velocity of each particle is to a large extent determined by slow particles further ahead. Considering all possible permutations of $N$ particles with initial velocities $\left\{v_i\right\}$, the average number of particles with actual velocity $v_i$ is $\left(N+1\right)/\left[i\left(i+1\right)\right]$ (in the sequence $\left\{v_i\right\}$, the initial velocities are listed with monotonically increasing values). For $i$ large and $v_i\propto i$ the average number of actual velocities is thus a power law in $v_i$, even though the average cluster density is found to be independent of cluster size, $L$. On the other hand, the cluster density varies significantly with cluster velocity; we obtain $\left[\left(N-i\right)!\left(N-L\right)!\right]/\left[N\cdot N!\left(N-L-i+1\right)!\right]$. The average velocity at a given position in the sequence of $N$ particles, and the average global velocity are determined. Explicit results for several distributions of the initial velocities show that the global velocity depends sensitively on the form of this distribution.

A model has been developed to investigate the growth of droplets in a supersaturated cold vapor taking into account their possible solid-liquid phase transition. It is shown that the solid-liquid phase transition is nontrivially coupled, through the energy released in attachment, to the nucleation process. The model is based on the one developed by J. Feder, K. C. Russell, J. Lothe, and G. M. Pound [Adv. Phys. 15, 111 (1966)], where the nucleation process is described as a thermal diffusion motion in a two-dimensional field of force given by the derivatives of a free-energy surface. The additional dimension accounts for droplets internal energy. The solid-liquid phase transition is introduced through a bimodal internal energy distribution in a Gaussian approximation derived from small clusters physics. The coupling between nucleation and melting results in specific nonequilibrium thermodynamical properties, exemplified in the case of water droplets. Analyzing the free-energy landscapes gives an insight into the nucleation dynamics. This landscape can be complex but generally exhibits two paths: the first one can generally be ascribed to the solid state, while the other to the liquid state. Especially at high supersaturation, the growth in the liquid state is often favored, which is not unexpected since in a supersaturated vapor the droplets can stand higher internal energy than at equilibrium. From a given critical temperature that is noticeably lower than the bulk melting temperature, nucleation may end in very large liquid droplets. These features can be qualitatively generalized to systems other than water.