We present an outlook on the climate system thermodynamics. First, we construct an equivalent Carnot engine with efficiency $\eta$ and frame the Lorenz energy cycle in a macroscale thermodynamic context. Then, by exploiting the second law, we prove that the lower bound to the entropy production is $\eta$ times the integrated absolute value of the internal entropy fluctuations. An exergetic interpretation is also proposed. Finally, the controversial maximum entropy production principle is reinterpreted as requiring the joint optimization of heat transport and mechanical work production. These results provide tools for climate change analysis and for climate models’ validation.

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule—a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabási-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

The asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations. For systems described by Langevin dynamics the corresponding Euler-Lagrange equation together with the appropriate boundary conditions and an equation for the leading pre-exponential factor are derived. The method is applied to three representative examples and the results are used to improve the accuracy of free-energy estimates based on the application of the Jarzynski equation.

We assess the possibility of probing the diffuse electric double layer at a permeable charge-selective interface, such as a nonblocking electrode or ion-exchange membrane, under a finite steady-state current-voltage bias by small harmonic high-frequency current-voltage disturbances. Our main conclusion is that for a finite underlimiting bias, the electric double layer at such an interface is not amenable to this kind of probe; the high-frequency response of the system is dominated by the quasielectroneutral bulk. This is similar to the previously studied zero-bias case. On the other hand, the extended space charge in such double layers may be probed in this way both by the linear and nonlinear responses, correspondingly by the method of electric impedance spectroscopy and via the previously described anomalous rectification effect. The latter appears preferable over the former as a potential experimental tool for the study of the extended space charge of a nonequilibrium electric double layer.

We develop the general equation for the nonequilibrium reversible-irreversible coupling framework of thermodynamics to handle moving interfaces in the context of a gas that can be dissolved in a surrounding liquid. The key innovation is a “moving interface normal transfer” term required for consistency between the thermodynamic evolution equation and the chain rule of functional calculus. The freedom of atomistic displacements of the interface leads to gauge transformations under which the thermodynamic theory should be invariant. The thermodynamic framework provides a complete set of evolution equations and boundary conditions, as we illustrate for the example of bubble growth and collapse.

Poly (amidoamine) dendrimer nanoparticles are used extensively in diverse biological and medical applications. Examples include gene and drug delivery, where nanoparticles disrupt cell membranes to allow the transport of material into cells. The size and surface chemistry of these particles have a strong effect on their interaction with membranes. This paper proposes a three-dimensional phase-field model to investigate how the interaction drives deformation and morphological evolution of the membrane. Attention is focused on the hole-formation process in the membrane. The simulations have demonstrated that a larger amine-terminated generation 7 dendrimer, which has positive charges, causes the formation of a hole in the membrane. The displaced membrane molecules enclose the particle and form a dendrimer-filled membrane vesicle. The effect is significantly reduced for a smaller dendrimer. An acetamide-terminated dendrimer, which has a neutral charge at the surface, does not cause hole formation. These results agree with experimental observations from atomic force microscopy. The study will provide insight into the design of appropriate nanoparticle surface properties for medical applications.

Some potentially fatal cardiac arrhythmias may be terminated by a series of premature stimuli. Monomorphic ventricular tachycardia, which may be modeled as an excitation wave traveling around in a ring, is one such arrhythmia. We investigated the mechanisms and requirements for termination of such reentry using an ionic cardiac ring model. Termination requires conduction block, which in turn is facilitated by spatial dispersion in repolarization and recovery time. When applying short series of two or three stimuli, we found that for conduction block to robustly occur, the magnitude of the spatial gradient in recovery time must exceed a critical value of 20 ms/cm. Importantly, the required spatial gradient can be induced in this homogeneous system by the dynamics of the stimulus-induced waves—we show analytically the necessary conditions. Finally, we introduce a type of pacing protocol, the “aggressive ramp,” which increases the termination efficacy by exploiting such pacing-induced heterogeneities. This technique, which is straightforward to implement, may therefore have important clinical implications.

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

Recently, it was shown that the amoebalike cell Physarum polycephalum when exposed to a pattern of periodic environmental changes learns and adapts its behavior in anticipation of the next stimulus to come. Here we show that such behavior can be mapped into the response of a simple electronic circuit consisting of a $LC$ contour and a memory-resistor (a memristor) to a train of voltage pulses that mimic environment changes. We also identify a possible biological origin of the memristive behavior in the cell. These biological memory features are likely to occur in other unicellular as well as multicellular organisms, albeit in different forms. Therefore, the above memristive circuit model, which has learning properties, is useful to better understand the origins of primitive intelligence.

By integrating the merits of previous models, a modified through-bond coupling (MTBC) model is proposed in this work and shows obvious improvement compared with previous models. With the MTBC model, the dominant electron coupling pathways in the polypeptide chains were identified, where the N-H bonds were found to be essential to the electron couplings. The local structures of peptides and proteins were finely characterized by the electron couplings and decay factors since they are structure sensitive. The neighboring carbonyl O-O distances are qualitatively correlated with the decay factors, and the deviations from the transconfigurations will weaken the coupling interactions. When the two amino acids being studied are not close in sequence, the couplings through hydrogen bonds are probably the main pathway because the electron transfers in this way save many steps, albeit the decay factor is less than that of per bond, consistent with the classical electron-tunneling model developed by Beratan et al. [Science 252, 1285 (1991)]. It was found that the MTBC model can be effectively extended to study the electron transfers in complex biological systems with the combination of the fragment approach, which takes into account the contributions of key hydrogen bonds.

Most of previous studies concerning the public goods game assume either participation is unconditional or the number of actual participants in a competitive group changes over time. How the fixed group size, prescribed by social institutions, affects the evolution of cooperation is still unclear. We propose a model where individuals with heterogeneous social ties might well engage in differing numbers of public goods games, yet with each public goods game being constant size during the course of evolution. To do this, we assume that each focal individual unidirectionally selects a constant number of interaction partners from his immediate neighbors with probabilities proportional to the degrees or the reputations of these neighbors, corresponding to degree-based partner selection or reputation-based partner selection, respectively. Because of the stochasticity the group formation is dynamical. In both selection regimes, monotonical dependence of the stationary density of cooperators on the group size was found, the latter over the whole range but the former over a restricted range of the renormalized enhancement factor. Moreover, the reputation-based regime can substantially improve cooperation. To interpret these differences, the microscopic characteristics of individuals are probed. We later extend the degree-based partner selection to general cases where focal individuals have preferences toward their neighbors of varying social ties to form groups. As a comparison, we as well investigate the situation where individuals locating on the degree regular graphs choose their coplayers at random. Our results may give some insights into better understanding the widespread teamwork and cooperation in the real world.

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter $\gamma$. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying $\gamma$, this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of $O\left({\text{Ec}}^{-1}\right)$ is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with $1/f^{3/2}$ power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

We have investigated the influence of a time-periodic and spatially homogeneous magnetic field on the linear stability properties and on the nonlinear response of a ferrofluid layer heated from below and from above. A competition between stabilizing thermal and viscous diffusion and destabilizing buoyancy and Kelvin forces occurs. Floquet theory is used to determine the stability boundaries of the motionless conductive state for a harmonic and subharmonic response. Full numerical simulations with a finite difference method were made to obtain nonlinear convective states. The effect of low- and high-frequency modulation on the stability boundaries as well as on the nonlinear oscillations that may occur is investigated.

The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the “fast” variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.

We investigate numerically the negative refraction of a simultaneous normal and parallel incidence planar left-handed metamaterial (LHM) in this paper. This LHM is comprised of fourfold C-shaped rings, which are printed on both sides of the substrates symmetrically, and it can exhibit left-handed properties with electromagnetic wave incident in three different directions. The retrieved result and the simulated result verify the left-handed properties of the fourfold C-shaped metamaterial very well. Then the different electric responses of the normal and parallel incidence cases to the incident electromagnetic wave are discussed, and it is due to the different distribution of the induced currents in the metallic wires.

A fixed time step method is developed for integrating stochastic differential equations (SDE’s) with Poisson white noise (PWN) and Lévy white noise (LWN). The method for integrating SDE’s with PWN has the same structure as that proposed by Kim et al. [Phys. Rev. E 76, 011109 (2007)], but is established by using different arguments. The integration of SDE’s with LWN is based on a representation of Lévy processes by sums of scaled Brownian motions and compound Poisson processes. It is shown that the numerical solutions of SDE’s with PWN and LWN converge weakly to the exact solutions of these equations, so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions. Numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms.

Kinetics of the deposition process of $k$-mers in the presence of desorption or/and diffusional relaxation of particles is studied by Monte Carlo method on a one-dimensional lattice. For reversible deposition of $k$-mers, we find that after the initial “jamming,” a stretched exponential growth of the coverage $\theta \left(t\right)$ toward the steady-state value ${\theta }_{eq}$ occurs, i.e., ${\theta }_{eq}-\theta \left(t\right)\propto \text{exp}\left[-{\left(t/\tau \right)}^{\beta }\right]$. The characteristic time scale $\tau$ is found to decrease with desorption probability $P_{des}$ according to a power law, $\tau \propto P_{des}^{-\gamma }$, with the same exponent $\gamma =1.22\pm 0.04$ for all $k$-mers. For irreversible deposition with diffusional relaxation, the growth of the coverage $\theta \left(t\right)$ above the jamming limit to the closest packing limit (CPL) ${\theta }_{\text{CPL}}$ is described by the pattern ${\theta }_{\text{CPL}}-\theta \left(t\right)\propto E_{\beta }\left[-{\left(t/\tau \right)}^{\beta }\right]$, where $E_{\beta }$ denotes the Mittag-Leffler function of order $\beta ∊\left(0,1\right)$. Similarly to the reversible case, we found that the dependence of the relaxation time $\tau$ on the diffusion probability $P_{dif}$ is consistent again with a simple power-law, i.e., $\tau \propto P_{dif}^{-\delta }$. When adsorption, desorption, and diffusion occur simultaneously, coverage always reaches an equilibrium value ${\theta }_{eq}$, which depends only on the desorption/adsorption probability ratio. The presence of diffusion only hastens the approach to the equilibrium state, so that the stretched exponential function gives a very accurate description of the deposition kinetics of these processes in the whole range above the jamming limit.

We consider 36 planar nets identified by O’Keeffe and Hyde and calculate for each, using the theory of finite Markovian processes, the overall mean walk length $⟨n⟩$ (first passage time) of a reactant diffusing randomly on a finite platelet before being trapped at a reaction center; the results are analyzed in terms of the total number $N$ of lattice sites, the number $N_b$ of boundary sites, the average valence $\overline{\nu }$, and the bond orientation function $\Psi$. We establish that crystalline platelets that are members of the same compatible class are characterized by very comparable catalytic efficiencies. The results obtained are also linked to an analysis of the kinetics of docking in postnucleation stages of protein self-assembly and to a recent conjecture on the symmetries of planar nets and the hard disk freezing transition.

Aqueous foams continuously age due to fluid drainage and bubble coarsening, which makes it difficult to perform steady-state rheological measurements. Consequently we have developed the foam drainage rheology technique, where perfusion counteracts fluid drainage and bubble replenishment counteracts bubble coarsening during measurement of the shear stresses by a rheometer. We evaluate published power-law and Herschel-Bulkley models and find that parameters derived from emulsion experiments cannot describe our results. We propose a hybrid model, which combines our earlier film-shearing model, where the film thickness depends on liquid volume fraction, with a Herschel-Bulkley shear-rate dependence.