The study of the excluded-volume effects on protein stability and reactions or the stability of colloidal suspensions is an active area of research. Using hard-disk collisional dynamics we investigate whether the presence of a crowding agent can induce a shape change from a nonspherical molecule to a spherical one. We show the averaged density profiles and velocity field of hard-disk crowders with an interior noncircular convex shape as a boundary condition. The density profile is not axially symmetric, consistent with other hard-potential experiments with asymmetry. However, more interestingly, the averaged velocity field was found to have a nonzero curl, implying a region of vorticity without a thermal gradient, advective field, or other motivating potential. To explain the occurrence of the vortices, a theoretical model is provided based on angular momentum of hard disks at contact. All these results, as well as difference in pressure along the axes, support the fact that as the packing fraction of the crowder rises, increasing force is exerted on an asymmetric molecule toward a symmetric one.

We present a computational methodology for incorporating thermal effects and calculating relative free energies for elastic fluid membranes subject to spatially dependent intrinsic curvature fields using the method of thermodynamic integration. Based on a simple model for the intrinsic curvature imposed only in a localized region of the membrane, we employ thermodynamic integration to calculate the free-energy change as a function of increasing strength of the intrinsic curvature field and a thermodynamic cycle to compute free-energy changes for different sizes of the localized region. By explicitly computing the free-energy changes and by quantifying the loss of entropy accompanied with increasing membrane deformation, we show that the membrane stiffness increases with increasing intrinsic field, thereby, renormalizing the membrane bending rigidity. The second main conclusion of this work is that the entropy of the membrane decreases with increasing size of the localized region subject to the curvature field. Our results help to quantify the free-energy change when a planar membrane deforms under the influence of curvature-inducing proteins at a finite temperature.

We study the quantum Loschmidt echo (LE) in a Bose-Einstein condensate (BEC) in a double-well potential. The BEC may undergo a dynamical phase transition between two phases: a tunneling phase and a self-trapping phase. For sufficiently weak perturbation, the LE has Gaussian decay in both phases. While, for relatively strong perturbation, the LE has a Gaussian decay in the self-trapping phase and has a stretched exponential decay in the tunneling phase. This qualitative difference in the decaying law of the LE in the two phases provides a characterization of the dynamical phase transition of the BEC. The semiclassical theory is used to explain the numerically observed behaviors of the LE decay.

We monitor the relaxation of internal stresses in a fractal colloidal gel on cessation of flow and find a weak power-law decay, ${\sigma }_i\sim t^{-\alpha }$ over five decades of time where $\alpha \approx 0.07$. The system exhibits physical aging of the elastic modulus, $G^{\prime }\sim t^{\beta }$, with $\beta \approx \alpha$. Imposition of zero stress after waiting time $t_w$ results in strain recovery as the system relaxes without constraint. Remarkably, recoveries at different $t_w$ can be shifted to construct a master curve where data are scaled vertically by $1/{\sigma }_i\left(t_w\right)$ and plotted horizontally as $\left(t-t_w\right)/t_w^{\mu }$, where $\mu \approx 1.25$, indicative of a superaging response.

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by $L=20$ and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a twofold “zero-energy flat band” in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.

Small-angle neutron scattering has been used to study protein unfolding and refolding in protein bovine serum albumin (BSA) due to perturbation in its native structure as induced by three different protein denaturating agents: urea, surfactant, and pressure. The BSA protein unfolds for urea concentrations greater than 4 M and is observed to be independent of the protein concentration. The addition of surfactant unfolds the protein by the formation of micellelike aggregates of surfactants along the unfolded polypeptide chains of the protein and depends on the ratio of surfactant to protein concentration. We make use of the dilution method to show the refolding of unfolded proteins in the presence of urea and surfactant. BSA does not show any protein unfolding up to the pressure of 450 MPa. The presence of urea and surfactant (for concentrations prior to inducing their own unfolding) has been used to examine pressure-induced unfolding of the protein at lower pressures. The protein unfolds at 200 MPa pressure in the presence of urea; however, no unfolding is observed with surfactant. The protein unfolding is shown to be reversible in all the above denaturating methods.

We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension-driven effect leads to such hierarchal pattern with different scales.

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.

A model for the soliton-potential scattering is presented. This model is constructed with a better approximation for adding the potential to the Lagrangian through the metric of background space time. The results of the model are compared with other models, and the differences are discussed.

We consider the motion of particles which are scattered by randomly distributed obstacles. In between scattering events the particles move uniformly. The governing master equation is obtained by mapping the problem onto a master equation which was previously devised for the description of anomalous diffusion of particles with inertia [R. Friedrich et al., Phys. Rev. Lett. 96, 230601 (2006)]. We show that for a scale-free distance distribution of scatterers a time-fractional master equation arises. The corresponding diffusion equation which exhibits a power-law diffusion coefficient is solved in $d$ dimensions via the method of subordination.

Estimating the functional topology of a network from multivariate observations is an important task in nonlinear dynamics. We introduce the nonparametric partial directed coherence that allows disentanglement of direct and indirect connections and their directions. We illustrate the performance of the nonparametric partial directed coherence by means of a simulation with data from synchronized nonlinear oscillators and apply it to real-world data from a patient suffering from essential tremor.

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviors, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here, we explore the full space of dimensionless parameters and present an “asymptotic phase diagram” which delineates the limiting regimes.

Magnetic microparticles suspended on the surface of liquid and energized by vertical alternating magnetic field exhibit complex collective behavior. Various immobile and self-propelled self-assembled structures have been observed. Here, we report on experimental studies of mixing and surface diffusion processes in this system. We show that the pattern-induced surface flows have properties of quasi-two-dimensional turbulence. Correspondingly, the surface advection of tracer particle exhibits properties of Brownian diffusion.

Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (i) one-dimensional inextensibility of filaments, (ii) three-dimensional incompressibility, and (iii) shear strain only longitudinally along filaments. It is shown that twist of filaments about each other is not an independent degree of freedom under ciliary constraints. The constraint on twist appears in the equations of motion for cilia as a term not previously recognized. As another application of the same geometrical idea, a general approach to the polymorphism of bacterial flagella is proposed.

Reciprocal edges represent the lowest-order cycle possible to find in directed graphs without self-loops. Representing also a measure of feedback between vertices, it is interesting to understand how reciprocal edges influence other properties of complex networks. In this paper, we focus on the influence of reciprocal edges on vertex degree distribution and degree correlations. We show that there is a fundamental difference between properties observed on the static network compared to the properties of networks, which are obtained by simple evolution mechanism driven by reciprocity. We also present a way to statistically infer the portion of reciprocal edges, which can be explained as a consequence of feedback process on the static network. In the rest of the paper, the influence of reciprocal edges on a model of growing network is also presented. It is shown that our model of growing network nicely interpolates between Barabási-Albert (BA) model for undirected and the BA model for directed networks.

Copropagation of a laser pulse and a relativistic electron beam in a corrugated plasma channel has been proposed for the direct laser acceleration of electrons [Palastro et al., Phys. Rev. E 77, 036405 (2008)]. The corrugated plasma channel allows for the guiding of laser pulses composed of subluminal spatial harmonics. Phase matching between the electron beam and the spatial harmonics results in acceleration, but for high beam densities, the pulse energy can be rapidly depleted. This depletion may result in interaction times shorter than the waveguide length limited time or pulse length dephasing time. We present an analytic model and self-consistent simulations of the electron beam–laser pulse interaction. A linear dispersion relation is derived. The effect of the electron beam on the pulse after the occurrence of axial bunching is examined. Injection of axially modulated electron beams is also explored. In particular, we find that a properly phased electron beam can transfer energy to the laser pulse as an inverse process to acceleration.

This work studies the damped double sine-Gordon equation driven by a biharmonic force, where a parameter $\lambda$ controls the existence and the frequency of an internal mode. The role of internal oscillations of the kink width in ratchet dynamics of kink is investigated within the framework of collective coordinate theories. It is found that the ratchet velocity of the kink, when an internal mode appears in this system, decreases contrary to what was expected. It is also shown that the kink exhibits a higher mobility in the double sine-Gordon without internal mode, but with a quasilocalized first phonon mode.

Current fluctuations and related steady-state fluctuation relation are investigated in simple coarse-grained lattice-gas analogs of a non-Newtonian fluid driven by a constant and uniform force field in two regimes of small entropy production. Non-Gaussian current fluctuations and deviations from fluctuation relation are observed and related to the existence of growing amorphous correlations and heterogeneous anomalous diffusion regimes.

We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D’Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of nonlocal particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasicontinuous linear chain of infinite length with a spatially self-similar distribution of nonlocal interparticle springs. The self-similarity of the nonlocal harmonic particle-particle interactions results in a dispersion relation of the form of a Weierstrass-Mandelbrot function that exhibits self-similar and fractal features. We also derive a continuum approximation, which relates the self-similar Laplacian to fractional integrals, and yields in the low-frequency regime a power-law frequency-dependence of the oscillator density.

A pure quantum state of large number $N$ of oscillators, interacting via harmonic coupling, evolves such that any small subsystem $n⪡N$ of the global state approaches equilibrium. This provides a different example where stationarity emerges as natural phenomena under quantum dynamics alone, with no necessity to bring in any additional statistical postulates. Mixedness of equilibrated subsystems consisting of $1,2,\dots ,n⪡N$ clearly indicates that small subsystems are entangled with the rest of the state, i.e., the bath. Every single mode oscillator is found to relax in a mixed density matrix of the Boltzmann canonical form. In two oscillator stationary subsystems, intraentanglement within the “system” oscillators is found to exist when the magnitude of the squeezing parameter of the bath is comparable in magnitude with that of the coupling strength.