Molecular-dynamics calculations of the translational dynamic structure factor in liquid ${\text{CO}}_2$ and ${\text{CD}}_4$ are analyzed by means of the generalized Langevin equation for the intermediate scattering function in the second-order memory function approximation. We give a rigorous general relation among the decay times of the memory and the lifetimes of the modes of the density-density correlation function. The comparison of the various characteristic times among them and with the collision time, carried out as a function of the wave vector, reveals strong relationships between the memory relaxation and the density-density correlation modes, some of which have purely “collisional” and other “collective” character. We show that essential information about the life time of structural properties in a molecular liquid at nanometer dimensions can be obtained if the time behavior of the correlation function is considered in addition to that of the memory function.

Amyloidlike proteins form highly organized aggregates, such as fibrils and plaques, preceded by the assembly of a wide range of unstructured oligomers and protofibrils. Despite their importance in a number of human neurodegenerative diseases, a comprehensive understanding of their kinetics and thermodynamics is still missing. We investigate, by computer simulations, a realistic model of amyloid molecules interacting via the experimentally determined Derjaguin-Landau-Verwey-Overbeek potential and derive its phase diagram. We show that fibrils and plaques, along with their precursors, correspond to different equilibrium and metastable thermodynamics phases and discuss the dynamical mechanisms leading to the nucleation and self-assembly of large scale structures.

This paper presents molecular-dynamics (MD) simulations of DNA oligonucleotide and water molecules translocating through carbon nanotube (CNT) channels. An induced pressure difference is applied to the system by pushing a layer of water molecules toward the flow direction to drive the oligonucleotide and other molecules. This MD simulation investigates the changes that occur in the conformation of the oligonucleotide due to water molecules in nanochannels while controlling the temperature and volume of the system in a canonical ensemble. The results show that the oligonucleotide in the (8,8)–(12,12) CNT channel forms a folded state at a lower pressure, whereas the oligonucleotide in the (10,10)–(14,14) CNT channel forms a folded state at a higher pressure instead. The van der Waals forces between the water molecules and the oligonucleotide suggest that the attraction between these two types of molecules results in the linear arrangements of the bases of the oligonucleotide. For a larger nanotube channel, the folding of the oligonucleotide is mainly dependent on the solvent (water molecules), whereas pressure, the size of the nanotube junction, and water molecules are the considering factors of the folding of the oligonucleotide at a smaller nanotube channel. For a folded oligonucleotide, the water distribution around the oligonucleotide is concentrated at a smaller range than that for the distribution around an unfolded oligonucleotide.

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations—both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

We present a theoretical and numerical analysis of liquid surface waves (LSWs) localized at the boundary of a phononic crystal consisting of split-ring resonators (SRRs). We first derive the homogenized parameters of the fluid-filled structure using a three-scale asymptotic expansion in the linearized Navier-Stokes equations. In the limit when the wavelength of the LSW is much larger than the typical heterogeneity size of the phononic crystal, we show that it behaves as an artificial fluid with an anisotropic effective shear modulus and a dispersive effective-mass density. We then analyze dispersion diagrams associated with LSW propagating within an infinite array of SRR, for which eigensolutions are sought in the form of Floquet-Bloch waves. The main emphasis is given to the study of localized modes within such a periodic fluid-filled structure and to the control of low-frequency stop bands associated with resonances of SRRs. Considering a macrocell, we are able to compute the dispersion of LSW supported by a semi-infinite phononic crystal of SRRs. We find that the dispersion of this evanescent mode nearly sits within the first stop band of the doubly periodic structure. We further discover that it is linked to the frequency at which the effective-mass density of the homogenized phononic crystal becomes negative. We demonstrate that this surface mode displays the hallmarks of all-angle negative refraction and it leads to a superlensing effect. Last, we note that our homogenization results for the velocity potential can be applied mutatis mutandis to designs of electromagnetic and acoustic superlenses for transverse electric waves propagating in arrays of infinite conducting SRRs and antiplane shear waves in arrays of cracks shaped as SRRs.

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson’s analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

An analytic model is developed for energetic electrons interacting with plasmas. This model rigorously treats the effects of energy loss upon Coulomb interactions and reveals several important features, including the coupling of scattering and energy loss—which previous calculations had erroneously treated as independent in cases where an electron lost a significant amount (or all) of its energy. The unique transparency and generality of these calculations allows for straightforward applications when quantitatively evaluating the energy deposition of energetic electrons in various plasmas, including those in inertial confinement fusion.

Under the assumption of Callaway’s model of the Boltzmann-Peierls equation, the Chapman-Enskog method for a phonon gas forms the basis to derive various hydrodynamic equations for the energy density and the drift velocity of interest when normal processes dominate over resistive ones. The first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) are satisfactory in that they are entropy consistent and ensure linear stability of the rest state. However, the entropy density contains a weakly nonlocal term, the entropy production is a degenerate function of variables, and the next order in the Chapman-Enskog expansion gives the equations with linearly unstable rest solutions. In the context of Burnett and super-Burnett equations, a similar type of problem was recognized by several authors who proposed different ways to deal with it. Here we report on yet another possible device for obtaining more satisfactory equations. Namely, inspired by the fact that there exists no unique way to truncate the Chapman-Enskog expansion, we combine the Chapman-Enskog procedure with the method of variable transformation and subsequently find a class of $\epsilon$-dependent transformations through which it is possible to derive the second-order equations possessing a local entropy density and nondegenerate expression for the entropy production. Regardless of this result, we also show that although the method cannot be used to construct linearly stable third-order equations, it can be used to make the originally stable first-order equations asymptotically stable.

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, $a$, giving rise to a corresponding continuous temperature profile, $T\left(a\right)$, which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves toward a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff’s law. The analytical results are supported by event driven simulations for a large, but discrete number of species.

A globally coupled network of ON and OFF cells is studied using neural field theory. ON cells increase their activity when the amplitude of an external stimulus increases, while OFF cells do the opposite given the same stimulus. Theory predicts that, without input, multiple transitions to oscillations can occur depending on feedback delay and the difference between ON and OFF resting states. Static spatial stimuli can induce or suppress global oscillations via a Andronov-Hopf bifurcation. This is the case for either polarity of such stimuli. In contrast, only excitatory inputs can induce or suppress oscillations in an equivalent network built of ON cells only even though oscillations are more prevalent in such systems. Nonmonotonic responses to local stimuli occur where responses lateral to the stimulus switch from excitatory to inhibitory as the input amplitude increases. With local time-periodic forcing, the unforced cells oscillate at twice the driving frequency via full-wave rectification mediated by the feedback. Our results agree with simulations of the neural field model, and further, qualitative agreement is found with the behavior of a network of spiking stochastic integrate-and-fire model neurons.

We report an experimental study of the kinetics of actin assembly mediated by branching and capping proteins. Our findings confirm the recent prediction of a “branching explosion” occurring during polymerization. Fluorescence imaging shows a number of actin filaments with branches within a few minutes of polymerization, induced by the activated branching protein complex Arp2/3, but the number of visible branches decreases over time. The light-scattering intensity displays an overshoot as a function of time, which we attribute to the formation of highly branched clusters early in polymerization. Furthermore, the overshoot occurs over a limited range of the ratio of concentrations of branching and capping proteins, also consistent with the theoretical model. These results establish a natural link between the kinetic theory of actin assembly in vitro and the cytoskeletal structure and actin dynamics in motile cells.

In this Brief Report, we perform molecular-dynamics simulations of an interface containing charged functional groups of different valences in contact with 2:1 ionic solution. We take into account both the finite sizes of the ions in solution and the functional groups but we neglect the structural details of the solvent (primitive model). We show that the interaction between a charged interface (of given surface charge density) and electrolyte depends strongly on the individual charges of the interfacial groups originating the surface charge. In particular, we show that charge inversion (i.e., interfacial charges attracting counterions in excess of their own nominal charge) is enhanced by the presence of multivalent interfacial groups (such as certain phospholipids). Overall, our results reveal that in primitive models of the ion-interface interaction not only the ionic size and valence are important but also the size and valence of the interfacial charged groups have a significant impact.

When an experimentalist or a biological mechanism applies an external force onto a cell chemically sticking to its substrate, a reacting “suction” force, due to the slow penetration of the surrounding fluid between the cell and the substrate, opposes to the dissociation. This force can overcome other known adhesive forces when the process is sufficiently violent (typically ${10}^5\text{pN}$). Its maximal contribution to the total adhesive energy of the cell can then be estimated to $2\times {10}^{-3}\text{J}/{\text{m}}^2$. The physical origin of this effect is quite simple and it may be compared to that leaning a “suction cup” against a bathroom wall. We address the consequences of this effect on (i) the separation energy, (ii) the motion of the fluid surrounding the cell, and more especially on the pumping of the fluid by moving cells, and (iii) the inhibition of cell motion.

We investigate how the addition of a large-scale steady motion, either shear or uniform flow, modifies the magnetic transport properties of a family of chaotic velocity fields with different correlation times. We compute numerically the kinematic $\alpha$ effect that those flows give rise to and show that it is reduced by the presence of a large-scale motion parallel to the large-scale magnetic field, except under certain conditions when it can be slightly enhanced via resonances. The $\alpha$ effect is shown to depend on the nature of the large-scale motion and on the temporal characteristics of the chaotic flow. These results highlight the strong influence that a shear or a uniform flow can have on the turbulent transport of magnetic fields.

We numerically solve the Bloch-Torrey equation by discretizing the differential operators in real space using finite differences. The differential equation is either solved directly in time domain as initial-value problem or in frequency domain as boundary-value problem. Especially the solution in time domain is highly efficient and suitable for arbitrary domains and dimensions. As examples, we calculate the average magnetization and the frequency distribution for capillaries and cells which are idealized as cylinders and spheres, respectively. The solution is compared with the commonly used Gaussian approximation and the strong-collision approximation. While these approximations become exact in limiting cases (small or large diffusion coefficient), they strongly deviate from the numerical solution for intermediate values of the diffusion coefficient.

Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [A. Y. Potekhin, G. Chabrier, and F. J. Rogers, Phys. Rev. E 79, 016411 (2009)], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted-chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong-coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.

When a two-dimensional Ising ferromagnet is quenched from above the critical temperature to zero temperature, the system eventually converges to either a ground state or an infinitely long-lived metastable stripe state. By applying results from percolation theory, we analytically determine the probability to reach the stripe state as a function of the aspect ratio and the form of the boundary conditions. These predictions agree with simulation results. Our approach generally applies to coarsening dynamics of nonconserved scalar fields in two dimensions.

We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as $\xi \sim {\left(\text{ln}t\right)}^{1/\tilde{\chi }}$. This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as $E_B\left(\ell \right)\sim {\ell }^{\tilde{\chi }}$ with a length scale $\ell$. Numerical data strongly suggest that the energy barrier exponent $\tilde{\chi }$ is identical to the energy fluctuation exponent $\chi =1/3$. We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as $\xi \sim t^{1/z}$ with a nonuniversal dynamic exponent $z$. The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.

We explore an analogy between the thermodynamics of a free dissipative quantum particle in one dimension and that of an electromagnetic field between two mirrors of finite conductivity. While a free particle isolated from its environment will effectively be in the high-temperature limit for any nonvanishing temperature, a finite coupling to the environment leads to quantum effects ensuring the correct low-temperature behavior. Even then, it is found that under appropriate circumstances the entropy can be a nonmonotonic function of the temperature. Such a scenario with its specific dependence on the ratio of temperature and damping constant also appears for the transverse electric mode in the Casimir effect. The limits of vanishing dissipation for the quantum particle and of infinite conductivity of the mirrors in the Casimir effect both turn out to be noncontinuous.