This paper is devoted to an experimental and theoretical investigation of the crater formed by the impact of a single drop onto a semi-infinite target of the same liquid. The shape of the crater at various time instances after impact has been observed using a high-speed video system and then accurately characterized. A theoretical model for the crater expansion has been developed, which is able to predict the temporal variation of the crater depth for sufficiently high Weber, Froude, and Reynolds numbers. The flow around the crater is approximated by an irrotational velocity field past a moving and expanding sphere. The equations describing the propagation of the surface of the crater have been obtained from the balance of stresses at the crater interface, accounting for inertia, gravity, and surface tension. The temporal evolution of the crater depth has been calculated by numerical solution of the equations of motion. The agreement between the theoretical predictions and experimental data are rather good.

Nonlinear interfacial motion in incompressible Richtmyer-Meshkov instability is theoretically investigated using the renormalization group approach. The amplitude equation describing the asymptotic interfacial motion is derived using this approach. A comparison with calculations carried out by the weakly nonlinear analysis is performed for various Atwood numbers and the validity of the renormalization group approach is discussed. We show that this approach suppresses the divergence in the perturbative solutions obtained by the weakly nonlinear analysis and provides better approximations for the growth rate of bubbles and spikes and interfacial profiles at the asymptotic nonlinear stage without requiring the use of Padé approximants.

Some years ago, Prigogine minimum entropy production principle was generalized by Lebon and Dauby to account for the nonlocal heat transport equation derived by Guyer and Krumhansl. Here, this criterion is extended to incorporate the effects of heat slip flow along the walls. This formulation is shown to be useful for the description of steady heat flow in nanosystems, where the heat slip flow plays a decisive role.

It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control [T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 090602 (2010)]. The presence of feedback control in physical systems should modify both the Jarzynski equality and the detailed fluctuation theorem [K. H. Kim and H. Qian, Phys. Rev. E 75, 022102 (2007)]. However, the generalized Jarzynski equality under forward feedback control has been proved by considering that the physical systems under feedback control should locally satisfy the detailed fluctuation theorem. We use the same formalism and derive the generalized detailed fluctuation theorem for nonequilibrium driven systems under feedback control. We find that the feedback control in a physical system should preserve the detailed fluctuation theorem if the system has the same feedback information measure in forward and reverse directions.

We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest-neighbor hopping and interaction, and next-nearest-neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.

We have considered heat conduction in a one-dimensional mass-disordered harmonic chain of $N$ particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current autocorrelation function in the nonequilibrium steady state (NESS) is obtained in terms of nonequilibrium phonon Green’s functions. The time integral of the correlation function gives expected result, both in nonequilibrium as well as equilibrium cases. Using the form of this correlation function we show that asymptotic system size dependence of current fluctuation in NESS for a mass-disordered harmonic chain is $N^{-\alpha }$ for different boundary conditions. For free and fixed boundary conditions we get $\alpha =1/2$ and 3/2, respectively, while for pinned case the fluctuation decays exponentially with system size.

In this work discrete element modeling (DEM) was applied to the flow of granular jets against a target. The resulting sheetlike or conelike formations under different conditions are described and explained by means of kinetic analysis. A qualitative and quantitative comparison with experimental results [Cheng et al., Phys. Rev. Lett. 93, 188001 (2007)] provides interesting insights in the theoretical treatment of the head-on collision of granular jets. Results presented in this paper provide a theoretical description of this type of physical system. However, there still exist obstacles in obtaining quantitative results.

We study the phase behavior of bowl-shaped particles using computer simulations. These particles were found experimentally to form a metastable wormlike fluid phase in which the bowl-shaped particles have a strong tendency to stack on top of each other [M. Marechal et al., Nano Lett. 10, 1907 (2010)]. In this work, we show that the transition from the low-density fluid to the wormlike phase has an interesting effect on the equation of state. The simulation results also show that the wormlike fluid phase transforms spontaneously into a columnar phase for bowls that are sufficiently deep. Furthermore, we describe the phase behavior as obtained from free energy calculations employing Monte Carlo simulations. The columnar phase is stable for bowl shapes ranging from infinitely thin bowls to surprisingly shallow bowls. Aside from a large region of stability for the columnar phase, the phase diagram features four novel crystal phases and a region where the stable fluid contains wormlike stacks.

We report the results of x-ray photon correlation spectroscopy (XPCS) experiments on multilayers of a photosensitive azo-polymer which can be softened by photoisomerization. Time correlation functions have been measured at different temperatures and momentum transfers $\left(q\right)$ and under different illumination conditions (dark, UV or visible). The correlation functions are well described by the Kohlrausch-Williams-Watts (KWW) form with relaxation times that are proportional to $q^{-1}$. The characteristic relaxation times follow the same Vogel-Fulcher-Tammann law describing the bulk viscosity of this polymer. The out-of-equilibrium relaxation dynamics following a UV photoperturbation are accelerated, which is in agreement with a fluidification effect previously measured by rheology. The transient dynamics are characterized by two times correlation function, and dynamical heterogeneity is evidenced by calculating the variance $\chi$ of the degree of correlation as a function of ageing time. A clear peak in $\chi$ appears at a well defined time ${\tau }_{\text{C}}$ which scales with $q^{-1}$ and with the ageing time, in a similar fashion as previously reported in colloidal suspensions [O. Dauchot et al., Phys. Rev. Lett. 95, 265701 (2005)]. From an accurate analysis of the correlation functions we could demonstrate a temperature and light dependent cross-over from compressed KWW to simple exponential behavior.

Dynamic force spectroscopy (DFS) has become a well-established method for characterizing bond strength, yet may also be useful for examining more complex phenomena such as dynamic processes or multiple reaction pathways. Here, we analyze the case where contact between an atomic force microscopy (AFM) tip and the sample induces sample reorganization during testing. Surface contact often causes molecular rearrangement in soft materials, which could also result in an altered reaction energy landscape. We model this situation by allowing the energy barrier position and magnitude to be time-dependent functions with a characteristic time scale $\tau$. We find dynamic energy barriers result in two linear regimes with a dramatic transition near $t=\tau$ in the DFS analysis. The sharp transition region is a hallmark of a moving energy barrier and indicates the time scale of reorganization. These results illustrate that DFS may be useful to monitor dynamic transitions and also highlight the importance of extending the loading rate range used in DFS studies.

Ribosome is a molecular machine that moves on a messenger RNA (mRNA) track while, simultaneously, polymerizing a protein using the mRNA also as the corresponding template. We define, and analytically calculate, two different measures of the efficiency of this machine. However, we argue that its performance is evaluated better in terms of the translational fidelity and the speed with which it polymerizes a protein. We define both these quantities and calculate these analytically. Fidelity is a measure of the quality of the products, while the total quantity of products synthesized in a given interval depends on the speed of polymerization. We show that for synthesizing a large quantity of proteins, it is not necessary to sacrifice the quality. We also explore the effects of the quality control mechanism on the strength of mechanochemical coupling. We suggest experiments for testing some of the ideas presented here.

A transfer matrix method is described for the conformational spread (CS) model of allosteric cooperativity within a one-dimensional arrangement of four-state binding sites. Each such binding site can realize one of two possible conformational states. Each of these states can either bind ligand or not bind ligand. Thus, analytical expressions that are exact within the context of the CS model are derived for the grand partition function, for the mean fraction of binding sites occupied by ligand versus ligand concentration, and for the mean fraction of binding sites in a given allosteric state versus ligand concentration. The utility of our analytical results is demonstrated by least-mean-square fitting of prior experimental results obtained on the bacterial flagellar motor for the fraction of FliM/FliG/FliN complexes with CheY-P bound [V. Sourjik and H. C. Berg, Proc. Natl. Acad. Sci. U.S.A. 99, 12669 (2002)] and for the cw bias [P. Cluzel et al., Science 287, 1652 (2000)], which plausibly may be identified as the fraction of protomers realizing state 2. Finally, the relationships between our analytical results and the classical Monod-Wyman-Changeaux, Koshland-Nemethy-Filmer, and McGhee-Von Hippel treatments of allosteric cooperativity are elucidated, as is the connection to an earlier approximate analytical treatment of the CS model.

Indirect reciprocity is one of the key mechanisms for the evolution of cooperation. It relies on mutual monitoring and assessments, i.e., individuals collect information about the past behavior of others and judge whether that behavior is “good” or “bad.” A player will not be helped if labeled with a bad image. There are many ways for assessing others, each of which can be interpreted as an elementary form of a moral sense (i.e., a view on what is good or bad). The information can be either public or private: private information can lead to mismatches between the opinions of individuals even when they share the same moral sense. In this paper, the effect of private information on the best-known assessment rules is investigated. In order to calculate payoffs, the concept of an image matrix is introduced. It describes who is good in the eyes of whom, and its time evolution is given by a probabilistic Boolean automaton. In contrast to the public information case, private information leads to the collapse of the sterner assessment rule. Alternatively, stable polymorphisms may subsist, with the milder rule and a more simple-minded rule coexisting together with unconditional cooperators; thus, cooperation can be sustained by indirect reciprocity even in the absence of public information.

Although the definition of deterministic chaos in the sense of Devaney is often employed for investigating dynamical systems, it has been rarely used for identifying deterministic chaos from time series. In this paper, we develop a set of methods that infers whether a given time series is consistent with deterministic chaos in the sense of Devaney or not. We define weaker notions of the three properties of Devaney’s chaos which can be checked using a given time series of a finite length. We apply these methods for artificial and real data.

We study the family of steady shapes which arise when a magnetic liquid droplet is confined in a rotating Hele-Shaw cell and subjected to an azimuthal magnetic field. Two different scenarios are considered: first, the magnetic fluid is assumed to be a Newtonian ferrofluid, and then it is taken as a viscoelastic magnetorheological fluid. The influence of the distinct material properties of the fluids on the ultimate morphology of the emerging stationary patterns is investigated by using a vortex-sheet formalism. Some of these exact steady structures are similar to the advanced time patterns obtained by existing time-evolving numerical simulations of the problem. A weakly nonlinear approach is employed to examine this fact and to gain analytical insight about relevant aspects related to the stability of such exact stationary solutions.

Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctuation theorems for perturbed nonequilibrium steady states are unified and arise as particular cases of this general result. In particular, we show that the joint probability distribution of the system and reservoir trajectory entropies satisfy a detailed fluctuation theorem valid for all times.

We investigate the complex spatiotemporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining different scaling relationships among the involved critical exponents depending on how far from or close to a critical point the system is. Our scaling arguments are very general and connect local and global magnitudes through several scaling relationships. We expect our results to be applicable in a wide range of systems exhibiting interface kinetic roughening driven by avalanches of local activity, either critical or not. As an example we apply the scaling theory to analyze avalanches and roughening of forced-flow imbibition fronts in excellent agreement with phase-field numerical integrations.

We report on the anisotropic electrohydrodynamic states formed over a wide temperature range $\left(\sim 45°\text{C}\right)$ in a planarly aligned bent-core nematic liquid crystal driven by fields of frequency in the range 0.1 Hz–1 MHz. Three different primary bifurcation scenarios are generated in the voltage-frequency $\left(V\text{−}f\right)$ plane, depending on the temperature $T$. These, under increasing $T$, are characterized by the pattern sequences (i) in-plane longitudinal rolls $\left(\text{ILR}\right)\to \text{in-plane}$ normal rolls 1 (INR1), (ii) Williams rolls $\left(\text{WR}\right)\to \text{ILR}\to \text{INR}1$, and (iii) $\text{WR}\to \text{INR}2\to \text{INR}1$. Temperature-induced $\text{ILR}\to \text{INR}2$ transition, the first example of its kind, points to elastic anisotropy as possibly the determining factor in wave vector selection. In the ILR and INR states, at threshold, the director modulations are predominantly azimuthal, and the streamlines, mainly normal to the wave vector, lie in the sample plane. Well above threshold, growing director deviations lead to narrow disclination loops that evolve in regular arrays, with their area density being exponential in voltage. The defects drift in a coordinated manner along the flow lines with a speed that scales nonlinearly with voltage; they mediate in the eventual occurrence of turbulence. The current theories of anisotropic convection based on static electrical parameters fail to account for the observed high-frequency instabilities. The study includes (i) a quantitative characterization of the critical parameter functions $V_{\text{c}}\left(f\right)$, $V_{\text{c}}\left(T\right)$, $q_{\text{c}}\left(f\right)$, and $q_{\text{c}}\left(T\right)$, with $q_{\text{c}}$ denoting the critical pattern wave number, and (ii) measurement of electrical and elastic parameters of relevance to electroconvection; the latter show anomalous features supporting the cluster hypothesis.

A detailed study has been performed for mixtures of octyloxycyanobiphenyl (8OCB) and nonyloxycyanobiphenyl (9OCB) liquid crystals and nine of their mixtures by means of high-resolution adiabatic scanning calorimetry. The isotropic to nematic transitions are weakly first order with latent heat values in the range usually encountered for this transition in other liquid crystals. With the exception of pure 8OCB, for which only an upper limit of $1.8\text{J}{\text{kg}}^{-1}$ for the latent heat could be established, finite latent heats have been obtained for the nematic to smectic-$A$ transition of all the mixtures and of pure 9OCB. The concentration dependence of their latent heats could be well fitted with a crossover function consistent with a mean-field free-energy expression that has a nonzero cubic term induced by the Halperin-Lubensky-Ma (HLM) coupling between the smectic-$A$ order parameter and the orientational director fluctuations. Clearly first-order transitions with measurable latent heats are found for mole fractions of 9OCB in the mixtures where the effective critical exponent for the specific-heat capacity has substantially lower values than the tricritical one (0.5). This is qualitatively different from what has been observed so far in other liquid-crystal systems and yields strong experimental evidence from a calorimetric experiment for the HLM coupling between the smectic-$A$ order parameter and the director orientation fluctuations.

Living organisms use waves that propagate through excitable media to transport information. ${\text{Ca}}^{2+}$ waves are a paradigmatic example of this type of processes. A large hierarchy of ${\text{Ca}}^{2+}$ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, ${\text{Ca}}^{2+}$ release occurs trough inositol 1,4,5-trisphosphate receptors $\left({\text{IP}}_3\text{Rs}\right)$ which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of ${\text{IP}}_3\text{R}$’s that replicates the experimental observations reported in [D. Fraiman et al., Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the ${\text{IP}}_3$ concentration is increased.