Molecular and cell biological processes often use proteins and structures that are significantly longer in one dimension than they are in the other two, for example, DNA, actin, and bacterial flagella. The dynamics of these structures are the consequence of the balance between the elastic forces from the structure itself and viscous forces from the surrounding fluid. Typically, the motion of these filamentary objects is described using variations of the Kirchhoff rod equations with resistive forces from the fluid treated as body forces acting on the centerline. In reality, though, these forces are applied to the surface of the filament; however, the standard derivation of the Kirchhoff equations ignores surface traction stresses. Here, we rederive the Kirchhoff rod equations in the presence of resistive traction stresses and determine the conditions under which treating the drag forces as body forces is reasonable. We show that in most biologically relevant cases the standard implementation of resistive forces into the Kirchhoff rod equations is applicable; however, we note one particular biological system where the Kirchhoff rod formalism may not apply.

Consider a generally closed system of continuous three-space coordinates $\mathbf{x}$ with a differentiable amplitude function $\psi \left(\mathbf{x}\right).$ What is its level of order $\mathbb{R}$? Define $\mathbb{R}$ by the property that it decreases (or stays constant) after the system is coarse grained. Then $\mathbb{R}$ turns out to obey $\mathbb{R}=8^{-1}{L}^{2}I,$where quantity $I=4\int d\mathbf{x}\nabla {\psi }^{*}·\nabla \psi$ is the classical Fisher information in the system and $L$ is the longest chord that can connect two points on the system surface. In general, order $\mathbb{R}$ is (i) unitless, and (ii) invariant to uniform stretch or compression of the system. On this basis, the order $\mathbb{R}$ in the Universe was previously found to be invariant in time despite its Hubble expansion, and with value $\mathbb{R}=26.0\times {10}^{60}$ for flat space. By comparison, here we model the Universe as a string-based “holostar,” with amplitude function $\psi \left(\mathbf{x}\right)\propto 1/r$ over radial interval $r=(r_0,r_H).$ Here $r_0$ is of order the Planck length and $r_H$ is the radial extension of the holostar, estimated as the known value of the Hubble radius. Curvature of space and relative motion of the observer must now be taken into account. It results that a stationary observer observes a level of order $\mathbb{R}=(8/9){(r_H/r_0)}^{3/2}=0.42\times {10}^{90};$ while for a free-falling observer $\mathbb{R}=2^{-1}{(r_H/r_0)}^2=0.85\times {10}^{120}.$ Both order values greatly exceed the above flat-space value. Interestingly, they are purely geometric measures, depending solely upon ratio $r_H/r_0.$ Remarkably, the free-fall value $\sim {10}^{120}$ of $\mathbb{R}$ approximates the negentropy of a universe modeled as discrete. This might mean that the Universe contains about equal amounts of continuous and discrete structure.

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the present work it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found.

We study cavitation dynamics when focusing ring-shaped femtosecond laser beams in water. This focusing geometry reduces detrimental nonlinear beam distortions and enhances energy deposition within the medium, localized at the focal spot. We observe remarkable postcollapse dynamics of elongated cavitation bubbles with high-speed ejection of microbubbles out of the laser focal region. Bubbles are ejected along the laser axis in both directions (away and towards the laser). The initial shape of the cavitation bubble is also seen to either enhance or completely suppress jet formation during collapse. In the absence of jetting, microbubble ejection occurs orthogonal to the laser propagation axis.

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

The condensation of the spinless ideal charged Bose gas in the presence of a magnetic field is revisited. The conventional approach is extended to include the macroscopic occupation of excited kinetic states lying in the lowest Landau level, which plays an essential role in the case of large magnetic fields. In that limit, signatures of two diffuse phase transitions (crossovers) appear in the specific heat. In particular, at temperatures lower than the cyclotron frequency, the system behaves as an effectively one-dimensional free boson system, with the specific heat equal to $\frac{1}{2}N{k}_B$ and a gradual condensation at lower temperatures.

Weibull's distribution is the principal phenomenological law of relaxation in the physical sciences and spans three different relaxation regimes: subexponential (“stretched exponential”), exponential, and superexponential. The probabilistic theory of extreme-value statistics asserts that the linear scaling limits of minima of ensembles of positive-valued random variables, which are independent and identically distributed, are universally governed by Weibull's distribution. However, this probabilistic theory does not take into account spatial geometry, which often plays a key role in the physical sciences. In this paper we present a general and versatile model of random reactions in random environments and establish a geometry-based theory for the universal emergence of Weibull's distribution.

The crucial problem for better understanding the nature of glass transition and related relaxation phenomena is to find proper interrelations between the molecular dynamics and thermodynamics of viscous systems. To make progress towards this goal the recently observed density scaling of viscous liquid dynamics has been very intensively and successfully studied in the past few years. However, previous attempts at related scaling of volumetric data yielded results inconsistent with those found from the density scaling of molecular dynamics. In this paper, we show that volumetric data obtained from simulations in simple molecular models based on the Lennard-Jones (LJ) potential, such as the Kob-Andersen binary LJ liquid, its repulsive inverse power-law version, and the Lewis-Wahnström $o$-terphenyl model, can be scaled by using the same value of the exponent, which scales dynamic quantities and is directly related to the exponent of the repulsive inverse power law that underlies short-range approximations of the LJ potential.

We develop an analytic theory of the polymer mediated interactions between nanocolloids reversibly adsorbing the excluded volume polymers. This theory describes the limit of the weak adsorption where the correlation length $\xi$ of the polymer system is much smaller than the characteristic adsorption length (colloid absorbance) $\alpha$. By making use of the developed theory, we calculate the colloid immersion energy and the potential of the polymer mediated interactions as functions of the colloid radius $R$, the absorbance $\alpha$, and the polymer volume fraction ${\phi }_P$.

Free-energy calculations for high-dimensional systems, such as peptides or proteins, always suffer from a serious sampling problem in a huge conformational space. For such systems, path-based free-energy methods, such as thermodynamic integration or free-energy perturbation, are good choices. However, both of them need sufficient sampling along a predefined transition path, which can only be controlled using restrained or constrained dynamics. Constrained simulations produce more reasonable free-energy profiles than restrained simulations. But calculations of standard constrained dynamics require an explicit expression of reaction coordinates as a function of Cartesian coordinates of all related atoms, which may be difficult to find for the complex transition of biomolecules. In this paper, we propose a practical solution: (1) We use restrained dynamics to define an optimized transition path, divide it into small fragments, and define a virtual reaction coordinate to denote a position along the path. (2) We use constrained dynamics to perform a formal free-energy calculation for each fragment and collect the values together to provide the entire free-energy profile. This method avoids the requirement to explicitly define reaction coordinates in Cartesian coordinates and provides a novel strategy to perform free-energy calculations for biomolecules along any complex transition path.

We derive the grand partition function of protein chain by restricting dihedral angles to exist only in five distinct states and assume that the dominant noncovalent potential is the hydrogen bond interaction. We investigate the phase transition of protein secondary structures and the order of the transition through analyzing its heat capacity. Our theory demonstrates the presence of $\alpha$-$\beta$-coil structural phase transition in the protein polyalanine.

A possible mechanism of superdiffusion of ultracold atoms in a one-dimensional polarization optical lattice, observed experimentally in Phys. Rev. Lett. 108, 093002 (2012), is suggested. The analysis is based on a consideration of anomalous diffusion in a fractal comb [Phys. Rev. E 83, 052106 (2011)]. It is shown that the transport exponent is determined by the fractal geometry of the comb due to recoil distributions resulting in Lévy flights of atoms.

Nonequilibrium localized states under the influence of translational coupling are studied experimentally and theoretically. We show that localized structures are deformed and advected in the direction of the coupling, thus undergoing different instabilities. Experimentally, localized structures are obtained in a light valve with optical feedback. By introducing a tilt of one mirror in the feedback loop, localized structures acquire a translational coupling. To understand the phenomenon in a universal framework we consider a prototypical model of localized states with translational coupling in one and two spatial dimensions. The model allows us to analytically characterize the propagation speed and the deformation exhibited by the localized state profiles as well as to figure out different mechanisms of destabilization of these dissipative structures. The results are in good qualitative agreement with the experimental and numerical observations.

The effect of electrical conductivity on the wavelength of an electrohydrodynamic instability of a leaky dielectric-perfect dielectric (LD-PD) fluid interface is investigated. For instabilities induced by dc fields, two models, namely the PD-PD model, which is independent of the conductivity, and the LD-PD model, which shows very weak dependence on the conductivity of the LD fluid, have been previously suggested. In the past, experiments have been compared with either of these two models. In the present work, experiments, analytical theory, and simulations are used to elucidate the dependence of the wavelength obtained under dc fields on the ratio of the instability time (${\tau }_s=1/s_{\max }$) and the charge relaxation time (${\tau }_c=\epsilon {\epsilon }_0/\sigma$, where ${\epsilon }_0$ is the permittivity of vacuum, $\epsilon$ is the dielectric constant, and $\sigma$ is the electrical conductivity). Sensitive dependence of the wavelength on the nondimensional conductivity $S_2={\sigma }_2{\mu }_2{h}_0^2/\left({\epsilon }_0^2{\phi }_0^2{\delta }^2\right)$ (where ${\sigma }_2$ is the electrical conductivity, ${\mu }_2$ is the viscosity, $h_0$ is the thickness of the thin liquid film, ${\phi }_0$ is the rms value of the applied field, and $\delta$ is a small parameter) is observed and the PD-PD and the LD-PD cases are observed only as limiting behaviors at very low and very high values of $S_2$, respectively. Under an alternating field, the frequency of the applied voltage can be altered to realize several regimes of relative magnitudes of the three time scales inherent to the system, namely ${\tau }_c$, ${\tau }_s$, and the time period of the applied field, ${\tau }_f$. The wavelength in the various regimes that result from a systematic variation of these three time scales is studied. It is observed that the linear Floquet theory is invalid in most of these regimes and nonlinear analysis is used to complement it. Systematic dependence of the wavelength of the instability on the frequency of the applied field is presented and it is demonstrated that nonlinear simulations are necessary to explain the experimental results.

The anomalous scaling of the single-time structure functions of a passive scalar field advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and the operator-product expansion with inclusion of additional ultraviolet divergences related to the spatial dimension $d=2$. Some modification of the standard minimal subtraction scheme is used to calculate the turbulent Prandtl number and the anomalous exponents within the one-loop approximation of a perturbation theory. It is shown that the taking into account of these additional divergences is in full agreement with results obtained in the framework of the usual analytical expansion technique, which are valid for $d>2$.

We experimentally investigate the impact of a liquid jet on a soap film. We observe that the jet never breaks the film and that two qualitatively different steady regimes may occur. The first one is a refractionlike behavior obtained at small incidence angles when the jet crosses the film and is deflected by the film-jet interaction. For larger incidence angles, the jet is absorbed by the film, giving rise to a new class of flows in which the jet undulates along the film with a characteristic wavelength. Besides its fundamental interest, this paper presents a different way to guide a micrometric flow of liquid in the inertial regime and to probe foam stability submitted to violent perturbations at the soap film scale.

Radiation losses of electrons in ultraintense laser fields constitute a process that can be important for electron and ion acceleration and creation of secondary emissions. The importance of this effect for ion acceleration to high energies is studied as a function of the laser intensity and the target thickness and density. For instance, in the piston regime, radiation losses lead to a reduction of the piston velocity and to less-efficient ion acceleration. Radiation losses have been implemented in the relativistic particle-in-cell code by using a renormalized Lorentz-Abraham-Dirac model.

In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can be dealt with only by use of an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom, if ever, discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity.

We describe a model for the study of the interaction of short x-ray free-electron laser (XFEL) pulses with matter. Hydrodynamics is solved in one-dimensional planar geometry together with XFEL energy deposition, transport by thermal conduction and electron-ion energy exchange. Along with XFEL energy deposition, a proper detailed configuration accounting atomic physics model has been implemented in line with the calculations. Simulations typical of current XFEL conditions of irradiation are presented and discussed. Finally, the corresponding spectral emission of this XFEL-heated matter is calculated with the unresolved transition array formalism.

We compute analytically the mean number of common sites, $W_N\left(t\right)$, visited by $N$ independent random walkers each of length $t$ and all starting at the origin at $t=0$ in $d$ dimensions. We show that in the $(N-d)$ plane, there are three distinct regimes for the asymptotic large-$t$ growth of $W_N\left(t\right)$. These three regimes are separated by two critical lines $d=2$ and $d=d_c\left(N\right)=2N/(N-1)$ in the $(N-d)$ plane. For $d<2$, $W_N\left(t\right)\sim t^{d/2}$ for large $t$ (the $N$ dependence is only in the prefactor). For $2<d<d_c\left(N\right)$, $W_N\left(t\right)\sim t^{\nu }$ where the exponent $\nu =N-d(N-1)/2$ varies with $N$ and $d$. For $d>d_c\left(N\right)$, $W_N\left(t\right)\to \mathrm{const}$ as $t\to \infty$. Exactly at the critical dimensions there are logarithmic corrections: for $d=2$, we get $W_N\left(t\right)\sim t/{\left[\ln t\right]}^N$, while for $d=d_c\left(N\right)$, $W_N\left(t\right)\sim \ln t$ for large $t$. Our analytical predictions are verified in numerical simulations.