Optical beams with null central intensity have potential applications in the field of atom optics. The spatial and temporal evolution of a central shadow dark hollow Gaussian (DHG) relativistic laser pulse propagating in a plasma is studied in this article for first principles. A nonlinear Schrodinger-type equation is obtained for the beam spot profile and then solved numerically to investigate the pulse propagation characteristics. As series of numerical simulations are employed to trace the profile of the focused and compressed DHG laser pulse as it propagates through the plasma. The theoretical and simulation results predict that higher-order DHG pulses show smaller divergence as they propagate and, thus, lead to enhanced energy transport.

We analyze recent experiments that show that a cylinder can be suspended in a stable position by placing it on a vertically moving belt that is covered by a thin layer of very viscous oil. The weight of the cylinder is supported by viscous forces in the fluid layer, and the cylinder rotates with respect to its axis in the direction of the belt motion. We propose a simple model for stable suspension of the cylinder, based on lubrication ideas.

In order to determine a proper value for the density of dry DNA films we have used a method based upon the measurement of interference effects in transmission spectra of thin DNA layers. Our results show that the methodology is effective and the density of DNA in this state, 1.407 g/cm${}^3$, is much lower than the commonly used 1.7 g/cm${}^3$. Obtaining accurate values for the DNA film density will allow the optical constants for DNA to be recalculated, which were previously obtained assuming a higher DNA density. Furthermore, since our recent investigations have shown a strong dependence of the sample composition on DNA film formation and thus on its density, such a method will be important in characterizing particle interactions with DNA film and their dose dependence.

We derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive Gaussian noise. Our study focuses on two cases: (i) a harmonic oscillator subjected to Gaussian colored noise with an arbitrary correlation function and (ii) nonlinear oscillators with a general potential driven by Gaussian white noise. We also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy. To illustrate our general results, we consider specifically the case of exponentially correlated noise for (i) and power-law and bistable potentials for (ii). Our theoretical results are substantiated by Langevin simulations.

We show that in a quantum mechanical many-body system of Boltzmann particles having space inversion symmetry the spectrum of the autocorrelation function of a local observable can always be given, similarly to the classical case [Phys. Rev. E 85, 022102 (2012)], in terms of a series of Lorentzian functions multiplied by the proper quantum detailed balance factor. This is done by transforming the continued fraction representation, which is derived via recurrent relations and without the use of the generalized Langevin equation hierarchy, into a series expansion. In this way characteristic frequencies can be defined, also in quantum mechanics, which refer to the particular autocorrelation. These are the frequencies of the eigenmodes of the relaxation function connected to the observable. We also show that in practical cases of interest in experimental spectroscopy, and particularly in inelastic neutron and x-ray scattering, the use of a finite number of Lorentzian shapes for an approximate description of the data is related to a reduction of the number of the relevant dynamical variables taken into account, equivalent to the lowering of the dimensionality of the orthogonalized space onto which the dynamic of the system is projected. Examples of application are given for the spectrum of the velocity autocorrelation function of liquid parahydrogen, calculated with a quantum simulation algorithm (path-integral centroid molecular dynamics), and for the molecular center-of mass dynamic structure factor in liquid carbon dioxide as computed by means of classical molecular dynamics simulation.

We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean-square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean-square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

Open lattices are characterized by low-volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due to their open structures. We theoretically investigate the stabilizing effects of entropy in the self-assembly of open lattices from patchy particles. A preliminary account of these findings and their comparison to experiment was presented recently [Mao, Chen, and Granick, Nat. Mater. 12, 217 (2013)]. We found that rotational entropy of patchy particles can provide mechanical stability to open lattices, whereas vibrational entropy of patchy particles can lower the free energy of open lattices and, thus, enables the selection of open lattices verses close-packed lattices which have the same potential energy. These effects open the door to significant simplifications of possible future designs of patchy particles for open-lattice self-assembly.

We provide broadband dielectric loss spectra of glass-forming glycerol with varying additions of LiCl. The measurements covering frequencies up to 10 THz extend well into the region of the fast β process, commonly ascribed to caged molecular dynamics. Aside from the known variation of the structural α relaxation time and a modification of the excess wing with ion content, we also find a clear influence on the shallow loss minimum arising from the fast β relaxation. Within the framework of mode-coupling theory, the detected significant broadening of this minimum is in reasonable accord with the found variation of the α-relaxation dynamics. A correlation between α-relaxation rate and minimum position holds for all ion concentrations and temperatures, even below the critical temperature defined by mode-coupling theory.

We give a detailed theory of nematic fluctuations in liquid-crystal elastomers (LCEs) and calculate relaxation rates as obtained by dynamic light scattering (DLS). In ideal LCEs, a nematic state is formed by a spontaneous orientational symmetry breaking of an isotropic state, manifesting itself in an existence of a coupled director-shear soft mode (Goldstone mode). The relaxation rate of the soft mode (a pure bend and a pure splay mode) goes to zero in a long-wavelength limit. In a real, nonideal sample with a locked-in anisotropy, on the other hand, the relaxation rates of these modes become finite. Nonideal elastomers are characterized by a plateau in the stress-strain curve, and the soft mode can be detected only upon stretching to the point of elastic instability at which the director starts to rotate. We use the semisoft model of Gaussian elasticity to derive relaxation rates as a function of deformation for different scattering geometries. We show that the bend-mode relaxation rate goes to zero at the threshold strain, so it is the soft mode. The splay mode, on the other hand, is not soft because the relaxation rate is finite at the threshold strain. We provide experimental evidence and compare DLS measurements of splay and bend modes of two side-chain LCE samples differing in crosslinking densities. Results of both samples are in complete agreement with the predictions of the semisoft model, which indicates that director relaxation properties are not influenced much by the crosslinking conditions.

We consider elongated cylindrical particles, modeling, e.g., DNA fragments or nanorods, while they translocate under the action of an externally applied voltage through a solid state nanopore. Particular emphasis is put on the concomitant potential energy landscape encountered by the particle on its passage through the pore due to the complex interplay of various electrohydrodynamic effects beyond the realm of small Debye lengths. We find that the net potential energy difference across the membrane may be of opposite sign for short and long particles of equal diameters and charge densities (e.g., oligomers). Thermal noise thus leads to biased diffusion through the pore in opposite directions. By means of an additional membrane gate electrode it is even possible to control the specific particle length at which this transport inversion occurs.

To elucidate the physical properties of the force generation mechanism in molecular motors, we have obtained an analytical solution of the bidimensional Fokker-Plank equation which describes a common setup used in single molecule experiments. As a first application of this general result, we have shown that the size of the trapping system affects the dwell time of a multistable particle linearly. A quantitative application to skeletal actomyosin complex, using direct observation of force generation dynamics in the literature, shows that the size of the trapping system used was important for increasing the dwell time of the myosin head stable states to an observable time scale.

We suggest a method of studying coherence in finite-level systems coupled to the environment and use it for the Hamiltonian that has been used to describe the light-harvesting pigment-protein complex. The method works with the adiabatic states and transforms the Hamiltonian to a form in which the terms responsible for decoherence and population relaxation are separated out. Decoherence is then accounted for nonperturbatively and population relaxation using a Markovian master equation. Almost analytical results can be obtained for the seven-level system, and the calculations are very simple for systems with more levels. We apply the treatment to the seven-level system, and the results are in excellent agreement with the exact numerical results of Nalbach et al. [Nalbach, Braun, and Thorwart, Phys. Rev. E 84, 041926 (2011)]. Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence causes only damping of oscillations and does not lead to transfer to the reaction center. Population relaxation is necessary for efficient transfer to the reaction center, in agreement with earlier findings. Our results show that the transformation to the adiabatic basis followed by a Redfield type of approach leads to results in good agreement with exact simulation.

We introduce a model for translational molecular motors to demonstrate that a multivalent catalytic walker with flexible, uncoordinated legs can transform the free energy of surface-bound substrate sites into mechanical work and undergo biased, superdiffusive motion, even in opposition to an external load force. The walker in the model lacks any inherent orientation of body or track, and its legs have no chemomechanical coupling other than the passive constraint imposed by their connection to a common body. Yet, under appropriate kinetic conditions, the walker's motion is biased in the direction of unvisited sites, which allows the walker to move nearly ballistically away from the origin as long as a local supply of unmodified substrate sites is available. The multivalent random walker model is mathematically formulated as a continuous-time Markov process and is studied numerically. We use Monte Carlo simulations to generate ensemble estimates of the mean squared displacement and mean work done for this nonergodic system. Our results show that a residence time bias between visited and unvisited sites leads to superdiffusive motion over significant times and distances. This mechanism can be used to adapt any enzyme-substrate system with appropriate kinetics for use as a functional chemical implementation of a molecular motor, without the need for structural anisotropy or conformationally mediated chemomechanical coordination.

Protein sequence evolution has resulted in a vast repertoire of molecular functionality crucial to life. Despite the central importance of sequence evolution to biology, our fundamental understanding of how sequence composition affects evolution is incomplete. This report describes the utilization of lattice model simulations of directed evolution, which indicate that, on average, peptide and protein evolvability is strongly dependent on initial sequence composition. The report also discusses two distinct regimes of sequence evolution by point mutation: (a) the “classical” mode where sequences “crawl” over free energy barriers towards acquiring a target fold, and (b) the “quantum” mode where sequences appear to “tunnel” through large energy barriers generally insurmountable by means of a crawl. Finally, the simulations indicate that oily and charged peptides are the most efficient substrates for evolution at the “classical” and “quantum” regimes, respectively, and that their respective response to temperature is commensurate with analogies made to barrier crossing in classical and quantum systems. On the whole, these results show that sequence composition can tune both the evolvability and the optimal mode of evolution of peptides and proteins.

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous $N$-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

The significance of thermally driven flows for the propulsion of Leidenfrost solids on a ratchet surface is studied based on a numerical solution of the Boltzmann equation. The resulting flow patterns are dominated by vortices developing at the edges of the ratchet teeth. In a previous analysis it had been claimed that thermally driven flows could cause the propulsion of Leidenfrost objects. In contrast to that analysis, it is found that such flows make an insignificant contribution to the thrust of Leidenfrost solids on ratchet surfaces, which is dominated by the pressure-driven flow due to the sublimating solid.

Gross-Pitaevskii or nonlinear-Schrödinger equations with a sinusoidal potential is commonly used to describe nonlinear periodic media, such as photonic lattices in optics and Bose-Einstein condensates (BECs) loaded into optical lattices (OLs). Previous studies have shown that the 2D version of this equation, with the self-focusing (SF) nonlinearity, supports stable solitons in the semi-infinite gap. It is known, too, that under both the self-defocusing (SDF) and SF nonlinearities, several families of gap solitons (GSs) exist in finite bandgaps. Here, we investigate the stability of 2D dipole-mode GS families, via the computation of their linear-stability eigenvalues and direct simulations of the perturbed evolution. We demonstrate that, under the SF nonlinearity, one species of dipole GSs is stable in a part of the first finite bandgap, provided that the OL depth exceeds a threshold value, while other dipole and multipole modes are unstable in that case. Bidipole bound states (vertical, horizontal, and diagonal), as well as square- and rhombic-shaped vortices and quadrupoles, built of stable fundamental dipoles, are stable too. Under the SDF nonlinearity, the family of dipole solitons is shown to be stable in a part of the second finite bandgap. Transformations of unstable dipole GSs are studied by means of direct simulations. Direct simulations are also performed to investigate the stability of other GS families, in the first and second bandgaps, under both types of the nonlinearity. In particular, “tripole” solitons, sustained in the second bandgap under the action of the SF nonlinearity, demonstrate stable behavior in the course of long propagation, in a certain region within the bandgap.

We present an efficient Monte Carlo method for the lattice sphere packing problem in $d$ dimensions. We use this method to numerically discover de novo the densest lattice sphere packing in dimensions 9 through 20. Our method goes beyond previous methods, not only in exploring higher dimensions but also in shedding light on the statistical mechanics underlying the problem in question. We observe evidence of a phase transition in the thermodynamic limit $d\to \infty$. In the dimensions explored in the present work, the results are consistent with a first-order crystallization transition but leave open the possibility that a glass transition is manifested in higher dimensions.

A bifurcation diagram for anisotropic magnetic particles in a precessing magnetic field is analyzed. It is found that a synchronous regime in the case of a prolate particle exists for all precession angles of the magnetic field if the frequency of field rotation is below some critical value. An oblate particle has a synchronous regime in a limited range of precession angle. To understand the flow of suspensions of these particles in precessing fields, it is essential to take into account the differing dynamics of prolate and oblate particles.

We use atomic force microscopy to measure the distance-dependent solvation forces and the dissipation across liquid films of octamethylcyclotetrasiloxane (OMCTS) confined between a silicon tip and a highly oriented pyrolytic graphite substrate without active excitation of the cantilever. By analyzing the thermal bending fluctuations, we minimize possible nonlinearities of the tip-substrate interaction due to finite excitation amplitudes because these fluctuations are smaller than the typical 1 Å, which is much smaller than the characteristic interaction length. Moreover, we avoid the need to determine the phase lag between cantilever excitation and response, which suffers from complications due to hydrodynamic coupling between cantilever and fluid. Consistent results, and especially high-quality dissipation data, are obtained by analyzing the power spectrum and the time autocorrelation of the force fluctuations. We validate our approach by determining the bulk viscosity of OMCTS using tips with a radius of approximately 1 $\mu$m at tip-substrate separations $>$5 nm. For sharp tips we consistently find an exponentially decaying oscillatory tip-substrate interaction stiffness as well as a clearly nonmonotonic variation of the dissipation for tip-substrate distances up to 8 and 6 nm, respectively. Both observations are in line with the results of recent simulations which relate them to distance-dependent transitions of the molecular structure in the liquid.