The adsorption of an off-lattice hydrophobic-polar-model heteropolymer in an attractive hydrophobic nanotube is presented by means of a multicanonical Monte Carlo simulation. In the model, the Lennard-Jones potential is assumed as an interaction potential between the effective monomers and the nanotube wall. The global minimum-energy configurations and the values of radius of gyration and end-to-end distance of these configurations are compared for both pure hydrophobic and polar heteropolymer models and with interaction term included model. The low-energy conformations for heteropolymers are extended when they interact with the nanotube which the conformational extensions are detected with some structural parameters.

We present a theoretical model describing Ogston (pore size comparable to or larger than the characteristic molecular dimension) sieving of rigid isotropic and anisotropic biomolecules in nanofluidic molecular filter arrays comprising of alternating deep and shallow regions. Starting from a quasi-one-dimensional drift-diffusion description, which captures the interplay between the driving electric force, entropic barrier and molecular diffusion, we derive explicit analytical results for the effective mobility and trapping time. Our results elucidate the effects of field strength, device geometry and entropic barrier height, providing a robust tool for the design and optimization of nanofilter/nanopore systems. Specifically, we show that Ogston sieving becomes negligible when the length of shallow region becomes sufficiently small, mainly due to efficient diffusional transport through the short shallow region. Our theoretical results are in line with experimental observations and provide important design insight for nanofluidic systems.

A Hopf bifurcation with translational invariance has been widely considered as an appropriate model for the appearance of spiral vortices in counter-rotating Taylor-Couette flow. Our experimental work demonstrates that flow conditions close to the axial boundaries are responsible for the type of bifurcation scenario, i.e., either asymmetric pure traveling waves or more complex behavior, such as defect states or symmetric mixed states appearing from a Hopf bifurcation. The measurements were performed in the first Taylor-Couette experiment with independently rotating endwalls confining the system in axial direction. The rotation rate of the (synchronous) endwalls is found to be an essential control parameter for the spatial amplitude distribution of the traveling waves and also reflects symmetry of the corresponding flow pattern appearing from the Hopf bifurcation.

Thermal runaway instability induced by material softening due to shear heating represents a potential mechanism for mechanical failure of viscoelastic solids. In this work we present a model based on a continuum formulation of a viscoelastic material with Arrhenius dependence of viscosity on temperature and investigate the behavior of the thermal runaway phenomenon by analytical and numerical methods. Approximate analytical descriptions of the problem reveal that onset of thermal runaway instability is controlled by only two dimensionless combinations of physical parameters. Numerical simulations of the model independently verify these analytical results and allow a quantitative examination of the complete time evolutions of the shear stress and the spatial distributions of temperature and displacement during runaway instability. Thus we find that thermal runaway processes may well develop under nonadiabatic conditions. Moreover, nonadiabaticity of the unstable runaway mode leads to continuous and extreme localization of the strain and temperature profiles in space, demonstrating that the thermal runaway process can cause shear banding. Examples of time evolutions of the spatial distribution of the shear displacement between the interior of the shear band and the essentially nondeforming material outside are presented. Finally, a simple relation between evolution of shear stress, displacement, shear-band width, and temperature rise during runaway instability is given.

Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network, or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks, and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of $2\times 2$ games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g., the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.

Laboratory experiments are reported in an immiscible two-fluid system, where thermal convection is initiated by heating at the bottom and cooling at the top. The lava-lamp regime is characterized by a robust periodic exchange process where warm blobs rise from the bottom, attach to the top surface for a while, then cold blobs sink down again. Immiscibility allows to reach real steady (dynamical equilibrium) states which can be sustained for several days. Two modes of lava-lamp convection could be identified by recording and evaluating temperature time series at the bottom and at the top of the container: a “slow” mode is determined by an effective heat transport speed at a given temperature gradient, while a second mode of constant periodicity is viscosity limited. Contrasting of laboratory and geophysical observations yields the conclusion that the frequently suggested lava-lamp analogy fails for the accepted models of mantle convection.

In many situations, the statistical properties of wave systems with chaotic classical limits are well described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system-specific information into the statistical model, such as the introduction of the average scattering matrix in the Poisson kernel. Here, it is shown that the average impedance matrix, which also characterizes the system-specific properties, can be expressed in terms of classical trajectories that travel between ports and thus can be calculated semiclassically. Theoretical results are compared with numerical solutions for a model wave chaotic system.

We present a study of the escape time from a metastable state of an overdamped Brownian particle in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise-enhanced stability effect for all the initial unstable states used and for all values of the correlation time ${\tau }_c$ investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noises, depending on the value of ${\tau }_c$ with respect to the relaxation time of the system.

We study properties of a single-well fourth-order potential perturbed by a periodically modulated stable noise. Periodic modulation of the stable noise asymmetry results in an occurrence of the dynamical hysteresis which is the manifestation of the stochastic resonance in the system at hand. We show that the single-well potential with time modulated stable driving is a minimalistic setup, allowing the occurrence of the stochastic resonance (as measured by the hysteresis loop area). Finally, we demonstrate that the observed stochastic resonance is of the double type, i.e., the system efficiency measured by the hysteresis loop area depends in a nonmonotonous way both on the scale parameter (noise intensity) and on the stability exponent characterizing tails asymptotic of noise pulses.

The time dependence of the Fourier transform phase of coherently scattered radiation from a system undergoing ordering is studied. Specifically, we derive a simple model that takes into account the known scaling laws for ordering dynamics to predict the statistical behavior of the Fourier transform phase. We consider a two-dimensional system of domains undergoing ordering for both the nonconserved and conserved order-parameter cases (models A and B, respectively). Predictions from our model are compared with numerical experiments, where a time-dependant Ginzburg-Landau equation is integrated to compute the dynamics of the real-space system; then a simple numerical (discrete) Fourier transform is applied to compute the Fourier phase as well as the amplitude (directly related to scattering intensity). An average phase-decorrelation time (the average time it takes for the phase to change by a specific amount) is obtained using both our theoretical model and the numerical results. This quantity is then used to implement a phase-retrieval strategy that consists of measuring scattering intensities of the same nonequilibrium system at different times and then applying an iterative phase-retrieval algorithm (like Fienup’s hybrid input-output) recursively with improved initial estimates for faster convergence and higher convergence rates.

A nematic cell subjected to a large electric field undergoes a molecular reorientation that affects the electrical current flowing through it. To analytically establish the dependence of the current on the applied voltage, the cell is considered as parallel of resistance, $R\left(t\right)$, and capacitance, $C\left(t\right)$, that are connected with the nematic director profile. This profile is determined in the quasistatic regime in which the nematic orientation follows the time variation in the external field normal to the cell plates without delay. The analysis performed for a weakly anchored cell shows that the current presents a peak when the applied voltage overcomes the threshold voltage for the transition of Fréedericksz at a critical time $t^{\ast }$ as in the case of strong anchoring. For large voltages, $R\left(t\right)\to R_{\parallel }$ and $C\left(t\right)\to C_{\parallel }$, where $\parallel$ refers to the nematic director. We show that, for large enough time $t⪢t^{\ast }$, it is possible to connect the measured current with the extrapolation length characterizing the sample by means of simple analytical expressions. This connection can be used to experimentally estimate the anchoring energy by means of current measurements.

The dye sunset yellow (SY) forms columnar aggregates via $\pi \text{−}\pi$ stacking in aqueous solutions. These aggregates develop orientational and translational order at elevated concentrations to exhibit the nematic (N) and columnar (C) mesophases. Positional-order correlation lengths of the aggregates in the directions parallel and perpendicular to the stacking direction were measured as functions of temperature, concentration, and ionic content of solutions with synchrotron x-ray scattering in magnetically aligned samples. Average length of aggregates (i.e., the number of SY molecules in an aggregate) grows monotonically with concentration while their effective transverse separation decreases. The scission energy, $E$, determined from the Arrhenius thermal evolution of the longitudinal correlation length, is found to be $4.3\pm 0.3k_{B}T$ and $3.5\pm 0.2k_{B}T$, in the N and C phases, respectively. Temperature and concentration dependence of $E$ suggests that chromonic aggregation is not an isodesmic process. The aggregate length decreases with decreasing $p\text{H}$ when HCl is added to the solution.

The massive field theory approach in fixed space dimensions $d<4$ is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls, and for the mixed case of one inert and one repulsive wall. The well-known correspondence between the field theoretical ${\varphi }^4$ $O\left(n\right)$-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. In order to make the theory UV finite in renormalization-group sense in $3\le d<4$ dimensions we performed the standard mass renormalization and additional surface-enhancement constants renormalization. Besides, our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results, and with the results of Monte Carlo simulations.

Single-molecule force-extension data are typically compared to ideal models of polymer behavior that ignore the effects of self-avoidance. Here, we demonstrate a link between single-molecule data and the scaling pictures of a real polymer. We measure a low-force elasticity regime where the extension $L$ of chemically denatured single-stranded DNA grows as a power law with force $f$: $L\sim f^{\gamma }$, with $\gamma \approx 0.60–0.69$. This compares favorably with the “tensile-blob” model of a self-avoiding polymer, which predicts $\gamma =2/3$. We show that the transition out of the low-force regime is highly salt dependent, and use the tensile-blob model to relate this effect to the salt dependence of the polymer’s Kuhn length and excluded-volume parameter. We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. Finally, we show that the low-force elasticity becomes linear $\left(\gamma =1\right)$ at $\approx 3\text{M}$ salt, and interpret this as a $\Theta$ point of the polymer. At this point, the force-extension data is best described by the wormlike chain model, from which we estimate the bare (nonelectrostatic) persistence length of the polymer to be $\approx 0.6\text{nm}$.

We develop a theoretical framework, based on a bond-polarizability model, for simulating the impulsive force experienced on a protein or an assembly of proteins from a pulsed light source by coupling the laser electric field to an atomic distortion. The mechanism is impulsive stimulated Raman scattering (ISRS) where mechanical distortions produce variation in the electronic polarization through atomic displacements similar to vibrational Raman scattering. The magnitude of the impulsive force is determined from the empirical two-body bond-polarizability model and the intensity of the incident light. We apply the method to the M13 bacteriophage protein capsid system by performing several classical molecular-dynamics simulations that include the additional impulsive laser scattering force at various light intensities and pulse widths. The results of the molecular-dynamics simulations are then qualitatively interpreted with a simple harmonic oscillator model driven by ISRS. The intensity of light required to produce damage to the capsid in the simulations was found to be far higher than what was found in recent pulsed laser scattering experiments of M13 phage, suggesting that the observed inactivation of viruses with ultrashort laser pulses involves processes and/or mechanisms not taken into account in the present simulations.

The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape $P\left(k\right)=\left(1/3\right){\left(2/3\right)}^{k-2}$, independent of the probability distribution from which the series was generated. Accordingly, visibility graphs with other $P\left(k\right)$ are related to nonrandom series. Numerical simulations confirm the accuracy of the theorems for finite series. In a second part, we show that the method is able to distinguish chaotic series from independent and identically distributed (i.i.d.) theory, studying the following situations: (i) noise-free low-dimensional chaotic series, (ii) low-dimensional noisy chaotic series, even in the presence of large amounts of noise, and (iii) high-dimensional chaotic series (coupled map lattice), without needs for additional techniques such as surrogate data or noise reduction methods. Finally, heuristic arguments are given to explain the topological properties of chaotic series, and several sequences that are conjectured to be random are analyzed.

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as social networks. Lately, it was found that many of these networks display some common topological features, such as high clustering, small average path length (small-world networks), and a power-law degree distribution (scale-free networks). The topological features of a network are commonly related to the network’s functionality. However, the topology alone does not account for the nature of the interactions in the network and their strength. Here, we present a method for evaluating the correlations between pairs of nodes in the network. These correlations depend both on the topology and on the functionality of the network. A network with high connectivity displays strong correlations between its interacting nodes and thus features small-world functionality. We quantify the correlations between all pairs of nodes in the network, and express them as matrix elements in the correlation matrix. From this information, one can plot the correlation function for the network and to extract the correlation length. The connectivity of a network is then defined as the ratio between this correlation length and the average path length of the network. Using this method, we distinguish between a topological small world and a functional small world, where the latter is characterized by long-range correlations and high connectivity. Clearly, networks that share the same topology may have different connectivities, based on the nature and strength of their interactions. The method is demonstrated on metabolic networks, but can be readily generalized to other types of networks.

The quantum dynamics of the dissipative two-level system with nonzero bias and sub-Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. It has been shown that for the sub-Ohmic bath it is necessary to use the non-Markovian approach, especially for the short time behavior of the coupled system and environment. The nonequilibrium correlation $P\left(t\right)$ has been calculated to show that a finite bias may favor the short time coherence. The spectrum of the susceptibility ${\chi }^{″}\left(\omega \right)$ of the sub-Ohmic case may have a double peak structure in the range of $\omega >0$ when the coupling $\alpha$ is relatively strong. Besides, the coherence-decoherence transition point ${\alpha }_c$ is determined for different $0<s\le 1$ by the condition of ${\chi }^{″}\left(\omega =0\right)=\infty$ when $\alpha ={\alpha }_c$. Finally, we show that Shiba’s relation is exactly satisfied in our results.

Gravity-dominated systems have a negative specific heat. We investigate the negative specific heat of self-gravitating systems enclosed in a spherical container with reflecting walls by means of $N$-body simulations. To simulate nonequilibrium processes, a particle reflected at a nonadiabatic wall is cooled to mimic energy loss by reflecting walls, while an adiabatic wall is employed for microcanonical ensembles. We show that a negative specific heat occurs not only in the microcanonical ensemble but also in certain nonequilibrium processes with the nonadiabatic wall. With increasing cooling rates, the dependence of temperature $\widehat{T}$ on energy $\epsilon$, i.e., the $\epsilon -\widehat{T}$ curve, gradually deviates from the microcanonical ensemble and approaches a certain common curve at a low-energy region. The common curve agrees with an $\epsilon -\widehat{T}$ curve for stellar polytropes, especially for the polytrope index of $n\sim 5$. We show that the stellar polytrope should be related to the present nonequilibrium process appearing in the self-gravitating system with the nonadiabatic wall. In the nonequilibrium process, a rapid change in velocity at the nonadiabatic wall significantly affects the velocity and density profiles. In particular, the greater the cooling rate, the greater the local velocity gradient at a low-energy region.

The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by “Jeans swindle” for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological $N$-body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from “shuffled lattice” initial conditions. These show qualitative properties of the evolution (notably its “self-similarity”) like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.