We studied the velocity dependence of mechanical unfolding of single protein molecules with the atomic force microscope. We showed that with enough realizations, the free energy surfaces reconstructed from Jarzynski’s equality converge with respect to pulling velocity, in good agreement with theory. Using the I27 domain of titin as an example, we estimated the required number of realizations for a given pulling velocity, and suggested the optimal range of velocities for single-molecule experiments. The results demonstrate that Jarzynski’s equality is a powerful and practical tool for reconstructing free energy landscapes.

The basic physics properties and simplified model descriptions of the paradigmatic “percolation” transport in low-frequency electrostatic (anisotropic magnetic) turbulence are theoretically analyzed. The key problem being addressed is the scaling of the turbulent diffusion coefficient with the fluctuation strength in the limit of slow fluctuation frequencies (large Kubo numbers). In this limit, the transport is found to exhibit pseudochaotic, rather than simply chaotic, properties associated with the vanishing Kolmogorov-Sinai entropy and anomalously slow mixing of phase-space trajectories. Based on a simple random-walk model, we find the low-frequency percolation scaling of the turbulent diffusion coefficient to be given by $D/\omega \propto Q^{2/3}$ (here $Q⪢1$ is the Kubo number and $\omega$ is the characteristic fluctuation frequency). When the pseudochaotic property is relaxed, the percolation scaling is shown to cross over to Bohm scaling. The features of turbulent transport in the pseudochaotic regime are described statistically in terms of a time fractional diffusion equation with the fractional derivative in the Caputo sense. Additional physics effects associated with finite particle inertia are considered.

We show that the thermodynamic entropy density is proportional to the largest Lyapunov exponent (LLE) of a discrete hydrodynamical system, a deterministic two-dimensional lattice gas automaton. The definition of the LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems. This relation is justified using a Markovian model. In an irreversible process with an initial density difference between both halves of the system, we find that Boltzmann’s $H$ function is linearly related to the expansion factor of the LLE although the latter is more sensitive to the presence of traveling waves.

Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated $H$ theorem, whereas the $q$ average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cutoff factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the $q$ average, is carefully re-examined and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.

We investigate effects of physical characteristics of the vibrating base in a vibrated granular bed system on the bulk granular behavior of the bed using molecular dynamics simulations. With a vibrating base that exhibits low coefficient of restitution for particle-base collisions, a monolayer of granular materials was observed to form dynamically on the surface of the base. Such a system was shown to be both qualitatively and quantitatively equivalent to one with a bumpy base composed of discrete solid particles undergoing the same type of imposed oscillatory motion. The “bumpiness” of such a base, as defined by the size of particles constituting the vibrating base, was also found to have insignificant effects on the behavior of the bulk granular materials. The observations made in this study may point toward a possible methodology to model vibrating granular bed systems with inelastic bases using continuum theories.

The dynamics and rheology of semidilute unentangled micellar solutions are investigated by Langevin dynamics mesoscopic simulations coupled to a microreversible kinetic model for scissions and recombinations. Two equilibrium state points, differing by the scission energy and therefore by the corresponding average micelle length, have been examined. The kinetic rates are tuned by an independent parameter of the model, whose range is chosen in such a way that the kinetics always strongly couple to the chain dynamics. Our results confirm, as predicted by Faivre and Gardissat, that the stress relaxation, as well as the monomer diffusion, is characterized by a time ${\tau }_{\Lambda }$, defined by the lifetime of a segment $\Lambda$, whose Rouse relaxation time is equal to its lifetime. Moreover, the power-law dependence of the zero-shear viscosity versus ${\tau }_{\Lambda }$ was evidenced. Under stationary shear, the chains are deformed and their average bond length is increased, which enhances the overall scission frequency. In turn, this induces an overall shortening of the chains in order to increase the overall corresponding chain-end recombination frequency, as required by the stationary conditions. Nonequilibrium simulations show that the chain deformation and orientation, as well as the rheology of the system, can be expressed as universal functions of a single reduced shear rate ${\beta }_{\Lambda }=\dot{\gamma }{\tau }_{\Lambda }$ (with $\dot{\gamma }$ the bare shear rate). Furthermore, local analysis of the kinetics under stationary shear gives insights on the variation of the average length with shear rate.

Polymer films nanoimprinted with checkerboard patterns of square wells align calamitic (rodlike) liquid crystals vertically, horizontally, or tilted depending on the depth/width ratio of the wells. The liquid crystal prefers planar orientation on polymer films that are smooth but when the films are topographically patterned, the increasing elastic energy density as the wells become narrower eventually overcomes the surface anchoring of the polymer and the liquid crystal director field makes a transition from planar to homeotropic. Similar effects have been demonstrated in both nematics and smectics, and the behavior is confirmed by theory and computer simulation.

We investigated the dynamics of single DNA molecules driven by the electrophoretic force in several tapered contraction-expansion microchannels. Under high localized electric-field gradients, fast transition between the stretching and compression of DNA molecules was achieved. Numerically, a combination of the finite element method and the coarse-grained Brownian dynamics simulation was used to capture the dynamics of single DNA molecules simplified as freely-draining bead-spring wormlike chains. A generalized predictor-corrector time marching scheme was proposed in this work. It was found that the initial conformation, the initial center-of-mass location, and the electric-field strength are three major factors affecting the DNA dynamics. The forced relaxation due to the reverse compression in the expansion zone can speed the relaxation of DNA molecules compared with the free relaxation in the bulk. We have also simulated DNA dynamics in different contraction-expansion microchannels by changing the length or the small-end width of the contraction zone (with other geometrical lengths fixed). Decreasing the small-end width can provide higher DNA stretching due to both increased Deborah number and increased accumulated strain. Increasing the length of the contraction zone, on the other hand, only slightly increases the accumulated strain, while greatly decreases the Deborah number, causing a decrease in DNA stretching. Experimentally, DNA molecules were gradually stretched in the contraction zone and then were quickly compressed back within a short distance outside the contraction zone. DNA chains in different initial configurations demonstrate different behaviors in contraction-expansion microchannels. The Brownian dynamics simulation results are in qualitative agreement with the experimental observations.

The onset of Fourier’s law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the ballistic (invalid Fourier’s law) to diffusive (valid Fourier’s law) regimes is characterized by a thermal length scale, which is directly related to the profile of the local temperature. In the same vein, dephasing is shown to give rise to classical Fourier’s law, similarly to the onset of Ohm’s law in mesoscopic conductors.

We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high order in an expansion in the inverse Heisenberg time. We present results for systems with and without time-reversal symmetry, as well as for the symplectic case, and extend recent results to nonlocalized initial states. We further analyze related photodissociation and photoionization phenomena and semiclassically compute cross-section correlations, including their Ehrenfest-time dependence.

Experimental measurements of the center of the ${\mathrm{H}}_{\beta }$ Stark profile on three different installations have been done to study its asymmetry in wide ranges of electron density, temperature, and plasma conditions. Theoretical calculations for the analysis of experimental results have been performed using the standard theory and computer simulations and included separately quadrupolar and quadratic Stark effects. Earlier experimental results and theoretical calculations of other authors have been reviewed as well. The experimental results are well reproduced by the calculations at high and moderate densities.

The effect of cubic-quintic nonlinearity and associated intercomponent couplings on the modulational instability (MI) of plane-wave solutions of the two-component discrete nonlinear Schrödinger (DNLS) equation is considered. Conditions for the onset of MI are revealed and the growth rate of small perturbations is analytically derived. For the same set of initial parameters as equal amplitudes of plane waves and intercomponent coupling coefficients, the effect of quintic nonlinearity on MI is found to be essentially stronger than the effect of cubic nonlinearity. Analytical predictions are supported by numerical simulations of the underlying coupled cubic-quintic DNLS equation. Relevance of obtained results to dense Bose-Einstein condensates (BECs) in deep optical lattices, when three-body processes are essential, is discussed. In particular, the phase separation under the effect of MI in a two-component repulsive BEC loaded in a deep optical lattice is predicted and found in numerical simulations. Bimodal light propagation in waveguide arrays fabricated from optical materials with non-Kerr nonlinearity is discussed as another possible physical realization for the considered model.

A new formula for the phase velocity of electromagnetic waves presented by Chen et al. [Appl. Phys. Lett. 88, 121125 (2006)] is investigated and discussed here. The difference between the result obtained with the new formula and that obtained directly using the phase term is small for a fundament-mode Gaussian laser beam. However, this difference is qualitative in some high-order Gaussian-mode laser beams. Using the new formula for such beams, discontinuities arise in the distribution of the phase velocity. This distribution is not rotationally symmetric with respect to the optical axis, and an imaginary phase velocity may appear near these discontinuities.

We study the dynamic properties of a model for wetting with two competing adsorbates on a planar substrate. The two species of particles have identical properties and repel each other. Starting with a flat interface one observes the formation of homogeneous droplets of the respective type separated by nonwet regions where the interface remains pinned. The wet phase is characterized by slow coarsening of competing droplets. Moreover, in $2+1$ dimensions an additional line of continuous phase transition emerges in the bound phase, which separates an unordered phase from an ordered one. The symmetry under interchange of the particle types is spontaneously broken in this region and finite systems exhibit two metastable states, each dominated by one of the species. The critical properties of this transition are analyzed by numeric simulations.

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a different universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states and we support our theory by extensive Monte Carlo simulations.

The simple system of two two-level identical atoms couple to single-mode optical cavity in the resonance case is studied for investigating the thermal entanglement. It is interesting to see that the critical temperature is only dependent on the coefficient of atom-atom dipole-dipole interaction. Based on the mode, we construct and investigate a entangled quantum Otto engine (QOE). Expressions for several important performance parameters such as the heat transferred, the work done in a cycle, and the efficiency of the entangled QOE in zero $G$ are derived in terms of thermal concurrence. Some intriguing features and their qualitative explanations are given. Furthermore, the validity of the second law of thermodynamics is confirmed in the entangled QOE. The results obtained here have general significance and will be helpful to understand deeply the performance of an entangled QOE.

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

By dynamic light scattering we have studied suspensions of ferrimagnetic maghemite $\left(\gamma {\text{-Fe}}_2{\text{O}}_3\right)$ nanoparticles in $n$-decane with attractive interparticle interaction. The measurements in the suspensions of different concentrations ranging from 0.21 to $25.8\text{wt}\%$ have been compared in zero external field and in the magnetic field of 270 mT. In all samples well-defined relaxation process was observed. In the absence of an external field the suspensions were homogeneous, while in the magnetic field most of the suspensions undergo phase separation in a needlelike islands of a very dense suspension surrounded by a dilute suspension. The underfield dynamical behavior is found to be anisotropic and diffusive in both directions at low concentration. For the more concentrated sample, in the direction parallel to the external field, it remains diffusive with a larger diffusion coefficient while it is not so in the perpendicular direction, in which the mean-squared displacement grows faster than linearly with time and the dependence of the relaxation rate on the scattering vector $q$ is not quadratic. In this direction the dynamics of the system present similar features as glasses or gels close to the dynamical arrest.

We study the surface growth generated by the random deposition of particles of different sizes. A model is proposed where the particles are aggregated on an initially flat surface, giving rise to a rough interface and a porous bulk. By using Monte Carlo simulations, a surface has grown by adding particles of different sizes, as well as identical particles on the substrate in $\left(1+1\right)$ dimensions. In the case of deposition of particles of different sizes, they are selected from a Poisson distribution, where the particle sizes may vary by 1 order of magnitude. For the deposition of identical particles, only particles which are larger than one lattice parameter of the substrate are considered. We calculate the usual scaling exponents: the roughness, growth, and dynamic exponents $\alpha$, $\beta$, and $z$, respectively, as well as, the porosity in the bulk, determining the porosity as a function of the particle size. The results of our simulations show that the roughness evolves in time following three different behaviors. The roughness in the initial times behaves as in the random deposition model. At intermediate times, the surface roughness grows slowly and finally, at long times, it enters into the saturation regime. The bulk formed by depositing large particles reveals a porosity that increases very fast at the initial times and also reaches a saturation value. Excepting the case where particles have the size of one lattice spacing, we always find that the surface roughness and porosity reach limiting values at long times. Surprisingly, we find that the scaling exponents are the same as those predicted by the Villain-Lai-Das Sarma equation.

We present a coarse-grained lattice model to study the influence of water on the recognition process of two rigid proteins. The basic model is formulated in terms of the hydrophobic effect. We then investigate several modifications of our basic model showing that the selectivity of the recognition process can be enhanced by considering the explicit influence of single solvent particles. When the number of cavities at the interface of a protein-protein complex is fixed as an intrinsic geometric constraint, there typically exists a characteristic fraction that should be filled with water molecules such that the selectivity exhibits a maximum. In addition, the optimum fraction depends on the hydrophobicity of the interface so that one has to distinguish between dry and wet interfaces.