We present a theoretical study of solitonlike solutions and their dynamics of ultracold superfluid Fermi gases trapped in a time-dependent three-dimensional (3D) harmonic potential with gain or loss. The 3D analytical solitonlike solutions are obtained without introducing any additional integrability constraints used elsewhere. The propagation of both bright- and dark-soliton-like solutions is investigated. We show that the amplitudes of dark-soliton-like solutions exhibit periodic oscillation, whereas those of the bright-soliton-like ones do not show such behavior. Moreover, we highlight that the oscillation periods of dark-soliton-like solutions predicted by our approach are matched very well with those observed in a recent experiment carried out by Yefsah et al. [T. Yefsah, A. T. Sommer, M. J. H. Ku, L. W. Cheuk, W. Ji, W. S. Bakr, and M. W. Zwierlein, Nature (London) 499, 426 (2013)] in both Bose-Einstein condensation and unitarity regimes.

We have derived a modified one-dimensional lubrication equation to describe the early coalescence behavior of a symmetric sessile drop coalescence for under-liquid substrates, which takes into account the viscosities of both the drop and the surrounding medium. We found a time scale, which governs the process, and there exists a crossover time between the universal scaling of the bridge height growth $h^{*}\sim t^{*}$ (valid for both under-liquid and air) and a much slower bridge growth $h^{*}\sim {t^{*}}^{0.24}$ occurring at a later time. It is also found that the drop coalescence bridge profile has a self-similarity, which breaks up much earlier for under-liquid substrates as opposed to symmetric coalescence in air.

The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways: (i) In the ASIS model a link is removed between two nodes if exactly one of the nodes is infected to suppress the epidemic, while a link is created in the AID model to speed up the information diffusion; (ii) a link is created between two susceptible nodes in the ASIS model to strengthen the healthy part of the network, while a link is broken in the AID model due to the lack of interest in informationless nodes. The ASIS and AID models may be considered as first-order models for cascades in real-world networks. While the ASIS model has been exploited in the literature, we show that the AID model is realistic by obtaining a good fit with Facebook data. Contrary to the common belief and intuition for such similar models, we show that the ASIS and AID models exhibit different but not opposite properties. Most remarkably, a unique metastable state always exists in the ASIS model, while there an hourglass-shaped region of instability in the AID model. Moreover, the epidemic threshold is a linear function in the effective link-breaking rate in the AID model, while it is almost constant but noisy in the AID model.

We have studied the phase diagrams of the one-dimensional spin-1 Blume-Capel model with anisotropy constant $D$, in which equivalent-neighbor ferromagnetic interactions of strength $-J$ are superimposed on nearest-neighbor antiferromagnetic interactions of strength $K$. A rich critical behavior is found due to the competing interactions. At zero temperature two ordered phases exist in the $D/J-K/J$ plane, namely the ferromagnetic $\left(\mathbf{F}\right)$ and the antiferromagnetic one $\left(\mathbf{AF}\right)$. For lower values of $D/J(D/J<0.25)$ these two ordered phases are separated by the point $K_c=0.25J$. For $0.25<D/J\le 0.50$, the paramagnetic phase $\mathbf{P}$ emerges in a region separated between the lines determined by $D/J=0.5-K/J$ and $D/J=K/J$. For $D/J>0.5$, only phases $\mathbf{AF}$ and $\mathbf{F}$ exist and are separated by a line given by $D/J=K/J$. At finite temperatures, we found that the ferromagnetic region of the phase diagram in the $k_{B}T/J-D/J$ plane is enriched by another ferromagnetic phase ${\mathbf{F}}^{{}^{\prime }}$ above a first-order line for $0.195<K/J<0.250$. This first-order line, which separates phases $\mathbf{F}$ and ${\mathbf{F}}^{{}^{\prime }}$, begins at a coexistence point, where phases $\mathbf{F},{\mathbf{F}}^{{}^{\prime }}$, and $\mathbf{P}$ coexist, and ends at an ordered critical point. Similarly, we found that the phase ${\mathbf{F}}^{{}^{\prime }}$ is present in the phase diagram in the $k_{B}T/J-K/J$ plane for $0.228<D/J<0.286$.

The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.

The thermodynamic, dynamic, and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two-dimensional associating lattice gas model that exhibits density and diffusion anomalies, similar to the anomalies present in liquid water. The matrix is a triangular lattice in which fixed obstacles impose restrictions to the occupation of the particles. We show that obstacles shorten all lines, including the phase coexistence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppresses the anomalies but also the liquid-liquid critical point.

In this work, we study connections between dynamic behavior and network parameters, for self-regulatory networks. To that aim, a method to compute the regions in the space of parameters that sustain bimodal or binary protein distributions has been developed. Such regions are indicative of stochastic dynamics manifested either as transitions between absence and presence of protein or between two positive protein levels. The method is based on the continuous approximation of the chemical master equation, unlike other approaches that make use of a deterministic description, which as will be shown can be misleading. We find that bimodal behavior is a ubiquitous phenomenon in cooperative gene expression networks under positive feedback. It appears for any range of transcription and translation rate constants whenever leakage remains below a critical threshold. Above such a threshold, the region in the parameters space which sustains bimodality persists, although restricted to low transcription and high translation rate constants. Remarkably, such a threshold is independent of the transcription or translation rates or the proportion of an active or inactive promoter and depends only on the level of cooperativity. The proposed method can be employed to identify bimodal or binary distributions leading to stochastic dynamics with specific switching properties, by searching inside the parameter regions that sustain such behavior.

Small-angle neutron scattering and dynamic light scattering studies have been carried out to examine the interaction of bovine serum albumin (BSA) protein with different surfactants under varying solution conditions. We show that the interaction of anionic BSA protein $\left(p\mathrm{H}7\right)$ with surfactant and the resultant structure are strongly modified by the charge head group of the surfactant, ionic strength of the solution, and mixed surfactants. The protein-surfactant interaction is maximum when two components are oppositely charged, followed by components being similarly charged through the site-specific binding, and no interaction in the case of a nonionic surfactant. This interaction of protein with ionic surfactants is characterized by the fractal structure representing a bead-necklace structure of micellelike clusters adsorbed along the unfolded protein chain. The interaction is enhanced with ionic strength only in the case of site-specific binding of an anionic surfactant with an anionic protein, whereas it is almost unchanged for other complexes of cationic and nonionic surfactants with anionic proteins. Interestingly, the interaction of BSA protein with ionic surfactants is significantly suppressed in the presence of nonionic surfactant. These results with mixed surfactants thus can be used to fold back the unfolded protein as well as to prevent surfactant-induced protein unfolding. For different solution conditions, the results are interpreted in terms of a change in fractal dimension, the overall size of the protein-surfactant complex, and the number of micelles attached to the protein. The interplay of electrostatic and hydrophobic interactions is found to govern the resultant structure of complexes.

Several devices for single-molecule detection and analysis employ biological and artificial nanopores as core elements. The performance of such devises strongly depends on the amount of time the analytes spend into the pore. This residence time needs to be long enough to allow the recording of a high signal-to-noise ratio analyte-induced blockade. We propose a simple approach, dubbed nanopore tweezing, for enhancing the trapping time of molecules inside the pore via a proper tuning of the applied voltage. This method requires the creation of a strong dipole that can be generated by adding a positive and a negative tail at the two ends of the molecules to be analyzed. Capture rate is shown to increase with the applied voltage while escape rate decreases. In this paper we rationalize the essential ingredients needed to control the residence time and provide a proof of principle based on atomistic simulations.

The survival time $T$ is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time $E\left[T\right]$ of a virus in the complete graph $K_N$ and the star graph $K_{1,N-1}$. By using the survival time, instead of the average fraction of infected nodes, we propose a new method to approximate the SIS epidemic threshold ${\tau }_c$ that, at least for $K_N$ and $K_{1,N-1}$, correctly scales with the number of nodes $N$ and that is superior to the epidemic threshold ${\tau }_c^{\left(1\right)}=\frac{1}{{\lambda }_1}$ of the N-intertwined mean-field approximation, where ${\lambda }_1$ is the spectral radius of the adjacency matrix of the graph $G$. Although this new approximation of the epidemic threshold offers a more intuitive understanding of the SIS process, it remains difficult to compare outbreaks in different graph types. For example, the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate $\frac{\tau }{{\tau }_c^{\left(1\right)}}$. However, when the average fraction of infected nodes is used as a basis for comparison, the virus will survive in the star graph longer than in any other graph, making the star graph the worst-case graph instead of the complete graph. Finally, in non-Markovian SIS, the distribution of the spreading attempts over the infectious period of a node influences the survival time, even if the expected number of spreading attempts during an infectious period (the non-Markovian equivalent of the effective infection rate) is kept constant. Both early and late infection attempts lead to shorter survival times. Interestingly, just as in Markovian SIS, the survival times appear to be exponentially distributed, regardless of the infection and curing time distributions.

Two types of spatiotemporal chaos in the electroconvection of nematic liquid crystals, such as defect turbulence and spatiotemporal intermittency, have been statistically investigated according to the Lagrangian picture. Here fluctuations are traced using the motion of a single particle driven by chaotic convection. In the defect turbulence (fluctuating normal rolls), a particle is mainly trapped in a roll but sometimes jumps to a neighboring roll. Its activation energy is then obtained from the jumping (hopping) rate. This research clarifies that diffusion in the defect turbulence regime in electroconvection can be regarded as a kind of hopping process. The spatiotemporal intermittency appears as a coexistent state of ordered grid domains and turbulent domains. The motion of a single particle shows weak and strong diffusion, respectively, in the ordered and turbulent domains. The diffusion characteristics intermittently change from one to another with certain durations as the domains change. This research has found that the distribution function of the duration that a particle remains in an ordered area has a power-law decay for which the index is different from that obtained by the Eulerian measurement.

Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles underlying biological processes at the molecular level. Recent work has demonstrated that when a thermodynamic system is driven away from equilibrium then the space of controllable parameters has a Riemannian geometry induced by a generalized inverse diffusion tensor. We derive a simple, compact expression for the inverse diffusion tensor that depends solely on equilibrium information for a broad class of potentials. We use this formula to compute the minimal dissipation for two model systems relevant to small-scale information processing and biological molecular motors. In the first model, we optimally erase a single classical bit of information modeled by an overdamped particle in a smooth double-well potential. In the second model, we find the minimal dissipation of a simple molecular motor model coupled to an optical trap. In both models, we find that the minimal dissipation for the optimal protocol of duration $\tau$ is proportional to $1/\tau$, as expected, though the dissipation for the erasure model takes a different form than what we found previously for a similar system.

We introduce a novel type of locally driven systems made of two types of particles (or a polymer with two types of monomers) subject to a chaotic drive with approximately white noise spectrum, but different intensity; in other words, particles of different types are in contact with thermostats at different temperatures. We present complete systematic statistical mechanics treatment starting from first principles. Although we consider only corrections to the dilute limit due to pairwise collisions between particles, meaning we study a nonequilibrium analog of the second virial approximation, we find that the system exhibits a surprisingly rich behavior. In particular, pair correlation function of particles has an unusual quasi-Boltzmann structure governed by an effective temperature distinct from that of any of the two thermostats. We also show that at sufficiently strong drive the uniformly mixed system becomes unstable with respect to steady states consisting of phases enriched with different types of particles. In the second virial approximation, we define nonequilibrium “chemical potentials” whose gradients govern diffusion fluxes and a nonequilibrium “osmotic pressure,” which governs the mechanical stability of the interface.

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths can compete and coexist in a dynamical equilibrium. Our analytical formulation makes a connection to statistical urn models, and we show that temperature is mirrored by the agent's memory. Our simple model of memory may be incorporated into other game models with implications that we briefly discuss.

We study the rheological behavior of concentrated granular suspensions of simple spherical particles. Under controlled stress, the system exhibits an $\mathsf{S}$-shaped flow curve (stress vs shear rate) with a negative slope in between the low-viscosity Newtonian regime and the shear thickened regime. Under controlled shear rate, a discontinuous transition between the two states is observed. Stress visualization experiments with a fluorescent probe suggest that friction is at the origin of shear thickening. Stress visualization shows that the stress in the system remains homogeneous (no shear banding) if a stress is imposed that is intermediate between the high- and low-stress branches. The $\mathsf{S}$-shaped shear thickening is then due to the discontinuous formation of a frictional force network between particles upon increasing the stress.

The glass transition behavior of polystyrene (PS) nanotubes confined in cylindrical alumina nanopores was studied as a function of pore diameter $\left(d\right)$ and polymer tube thickness (δ). Both the calorimetric glass transition temperature and the microstructure measured by a nonradiative energy transfer method indicated that the polymer nanotube, or concave polymer thin film, exhibited significant differences in vitrification behavior compared to the planar one. A closer interchain proximity and an increased $T_{\mathrm{g}}$ were observed for polymer nanotubes with respect to the bulk polymer. $T_{\mathrm{g}}$ for polymer nanotubes was primarily dependent on the curvature radius $d$ of the template, while it was less dependent on the thickness δ of the PS tube wall in the range of 11–23 nm. For small nanotubes $(d=55\mathrm{nm})$, the $T_{\mathrm{g}}$ increased as high as 18 °C above the bulk value. This vitrified property reverted back to the bulk value when the substrate was chemically removed, which indicated the crucial importance of the interfacial effect imposed by the hard wall with a concave geometry.

Transmission of planar layers of cholesteric liquid crystals is studied in pulsed electric fields perpendicular to the helix axis at normal incidence of both linearly polarized and unpolarized light. Spectral and light polarization properties of the primary photonic band and the field-induced bands up to fourth order of Bragg selective reflection are studied in detail. In our experiments we have achieved an electric field strength several times higher than the theoretical values corresponding to the critical field of full helix unwinding. However, the experiments show that despite the high strength of the electric field applied the helix does not unwind, but strongly deforms, keeping its initial spatial period. Strong helix deformation results in distinct spectral band splitting, as well as very high field-induced selective reflectance that can be applied in lasers and other optoelectronic devices. Peculiarities of inducing and splitting the bands are discussed in terms of the scattering coefficient approach. All observed effects are confirmed by numerical simulations. The simulations also show that liquid crystal surface anchoring is not the factor that prevents the helix unwinding. Thus, the currently acknowledged concept of continuous helix unwinding in the electric field should be reconsidered.

A model based on cellular properties is used to analyze the mass growth curves of 20 dinosaurs. This analysis yields the first measurement of the average cellular metabolism of dinosaurs. The organismal metabolism is also determined. The cellular metabolism of dinosaurs is found to decrease with mass at a slower rate than is observed in extant animals. The organismal metabolism increases with the mass of the dinosaur. These results come from both the Saurischia and Ornithischia branches of Dinosauria, suggesting that the observed metabolic features were common to all dinosaurs. The results from dinosaurs are compared to data from extant placental and marsupial mammals, a monotreme, and altricial and precocial birds, reptiles, and fish. Dinosaurs had cellular and organismal metabolisms in the range observed in extant mesotherms.

Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. While typically thought of as being unidirectional, it is not uncommon for axonal propagation of action potentials to happen in both directions. This is the case because action potentials can be initiated at multiple “ectopic” positions along the axon. Two ectopic action potentials generated at distinct sites, and traveling toward each other, will collide. As neuronal information is encoded in the frequency of action potentials, action potential collision and annihilation may affect the way in which neuronal information is received, processed, and transmitted. We investigate action potential propagation and collision using an axonal multicompartment model based on the Hodgkin-Huxley equations. We characterize propagation speed, refractory period, excitability, and action potential collision for slow (type I) and fast (type II) axons. In addition, our studies include experimental measurements of action potential propagation in axons of two biological systems. Both computational and experimental results unequivocally indicate that colliding action potentials do not pass each other; they are reciprocally annihilated.