Transitions between different condensed phases, molecular conformations, chemical compositions, or spatiotemporal patterns play important roles in many branches of natural science and at the same time incur serious challenges in their precise characterization. We design an approach for computing connecting orbits bridging steady states based on the renormalization group analysis. The technique is successfully applied to several interesting examples and good analytic results are obtained in a systematic and unified way.

We consider small dynamical networks of coupled oscillators for which the network topology is unknown and try to use partial knowledge of the oscillators' dynamics to estimate both the network couplings and the states of the nodes. We focus on the case where the state time evolution from only one oscillator is available. We propose an adaptive strategy that uses synchronization between the true network and a replica network in order to estimate both the couplings and the states. The adaptive scheme is tested with several modules of coupled oscillators. We consider the effects of small mismatches in the parameters of the individual oscillators and we propose an alternative version of the strategy that is suitable to handle noise in the received signal.

Acceleration and focusing of high-energy proton beams from fast-ignition (FI) -related hemisphere-cone assembled targets have been numerically studied by hybrid particle-in-cell simulations and compared with those from planar-foil and open-hemisphere targets. The whole physical process including the laser-plasma interaction has been self-consistently modeled for 15 ps, at which time the protons reach asymptotic motion. It is found that the achievable focus of proton beams is limited by the thermal pressure gradients in the co-moving hot electrons, which induce a transverse defocusing electric field that bends proton trajectories near the axis. For the advanced hemisphere-cone target, the flow of hot electrons along the cone wall induces a local transverse focusing sheath field, resulting in a clear enhancement in proton focusing; however, it leads to a significant loss of longitudinal sheath potential, reducing the total conversion efficiency from laser to protons.

If two half spaces are in contact, there exists a formal mathematical relation between the electrical contact resistance and the incremental elastic compliance. Here, this relation is extended to the contact of finite bodies. In particular, it is shown that the additional resistance due to roughness of the contacting surfaces (the interface resistance) bears a similar relation to the additional compliance as that obtained for the total resistance in the half-space problem.

The full gyrokinetic electrostatic linearized Landau collision operator is calculated including the equilibrium operator, which represents the effect of collisions between gyrokinetic Maxwellian particles. First, the equilibrium operator describes energy exchange between different plasma species, which is important in multiple ion-species plasmas. Second, the equilibrium operator describes drag and diffusion of the magnetic field aligned component of the vorticity associated with the $\mathit{E}\times \mathit{B}$ drift. Therefore, a correct description of collisional effects in turbulent plasmas requires the equilibrium operator, even for like-particle collisions.

A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate an improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean-field approaches to inverse Ising problems. The proposed susceptibility propagation is robust for various network structures, and it is reduced to the ordinary susceptibility propagation and to the adaptive Thouless-Anderson-Palmer equation in special cases.

We present results for pattern formation and related dynamics in the two-dimensional complex Ginzburg-Landau equation. Both single and multispiral morphologies have been considered. For the former, Hagan's solution has been tested. In case of the multispiral morphology, at a late time, depending upon certain parameter values, the dynamics is found to be frozen. However, upon introduction of disorder in these parameters the frozen dynamics is observed to be unlocked. This latter result is counterintuitive considering our current knowledge of dynamics in disorder systems. We also present results for the role of shocks (the regions where Hagan's solution is violated) in the multispiral dynamics. It is observed that the suppression of the order-parameter amplitude, in this region, to the value allowed by Hagan's single-spiral solution, also unlocks the dynamical freezing. In this case, both the pattern and dynamics are observed to be very similar to the the dynamical $XY$ model.

We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the $q$-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of $q$. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.

We obtain the exact solution of the bond-percolation thresholds with inhomogeneous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in the spin-glass theory. Our formulation is a more straightforward way than that of a very recent study on the same problem [R. M. Ziff et al., J. Phys. A: Math. Theor. 45, 494005 (2012)]. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices rather than the square lattice.

We have considered a one-dimensional coagulation-decoagulation system of classical particles on a finite lattice with reflecting boundaries. It is known that the system undergoes a phase transition from a high-density to a low-density phase. Using a matrix product approach we have obtained an exact expression for the average entropy production rate of the system in the thermodynamic limit. We have also performed a large-deviation analysis for fluctuations of entropy production rate and particle current. It turns out that the characteristics of the kink in the large deviation function can be used to spot the phase transition point. We have found that for very weak driving field (when the system approaches its equilibrium) and also for very strong driving field (when the system is in the low-density phase) the large deviation function for fluctuations of entropy production rate is almost parabolic, while in the high-density phase it prominently deviates from Gaussian behavior. The validity of the Gallavotti-Cohen fluctuation relation for the large deviation function for particle current is also verified.

The phase diagrams of the three-state Ghatak-Sherrington spin-glass (or random Blume-Capel) model are obtained in mean-field theory with replica symmetry in order to study the effects of a ferromagnetic bias and finite random connectivity in which each spin is connected to a finite number of other spins. It is shown that inverse melting from a ferromagnetic to a low-temperature paramagnetic phase may appear for small but finite disorder and that inverse freezing appears for large disorder. There can also be a continuous inverse ferromagnetic to spin-glass transition.

We perform a systematic statistical investigation of the effect of harmonic boundary vibrations on a sheared granular layer undergoing repetitive, fully dynamic stick-slip motion. The investigation is performed using two-dimensional discrete element method simulations. The main objective consists of improving the understanding of dynamic triggering of slip events in the granular layer. Here we focus on how the vibration amplitude affects the statistical properties of the triggered slip events. The results provide insight into the granular physical controls of dynamic triggering of failure in sheared granular layers.

Gas-liquid critical parameters of charged soft dumbbells (CSDs) as function of the site-to-site separation on the dumbbells, $d$, obtained on the basis of molecular dynamics computer simulation are presented. A mean field theoretical description is developed, which explains the results at small and large $d$, respectively. We note that in the limit $d\to 0$ the CSD system exhibits gas-liquid phase separation solely driven by repulsion and dipole-dipole interaction. If the dumbbell bond is eliminated the CSD system becomes similar to the restricted primitive model of ionic fluids with hard core repulsion replaced by soft repulsion. We obtain the gas-liquid critical parameters for this model and discuss their relation to the CSD system.

We report the measurements of the temperature variations of the flexoelastic coefficient ($e^{*}/K$) of a host calamitic liquid crystal (RO) and its mixture with two guest bent-core (BC-120 and BC-60) liquid crystals. The bent-core (BC) molecules have different core structures and bend angles; namely, $\theta \simeq {120}^{\circ }$ and $\simeq {60}^{\circ }$, respectively. We find that $e^{*}/K$ is independent of temperature and decreases rapidly with increasing concentration of BC-120 molecules and changes sign from positive to negative. In mixtures with BC-60, $e^{*}/K$ is always positive and its concentration-dependent variation is not unique. At 7M% it is significantly large (three times) near the nematic-isotropic transition and decreases strongly with reducing temperature. Dielectric measurement suggests antagonistic orientation of the dipole axes (arrow axes) of the two BC molecules in the host liquid crystal, and based on this, the opposite sign of $e^{*}/K$ is explained.

In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the $n$-fold Darboux transformation of this system. This $n$-fold Darboux transformation implies the determinant representation of $n$th solutions of $(E^{\left[n\right]},p^{\left[n\right]},{\eta }^{\left[n\right]})$ generated from the known solution of $(E,p,\eta )$. The determinant representation of $(E^{\left[n\right]},p^{\left[n\right]},{\eta }^{\left[n\right]})$ provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for $p$ and $\eta$ has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters $\alpha$ and $\beta$, we generate a rogue wave shape.

The refined similarity hypotheses (RSH) and their extension to passive scalar (RSH-P) are tested experimentally using simultaneous velocity and scalar data in a turbulent jet. Different from the single-point hot-wire probe in a previous experimental test, a combined particle image velocimetry and planar laser induced fluorescence technique enable us to obtain the test data without applying Taylor's hypothesis. RSH is successfully validated with direct examinations of its three hypotheses. RSH-P is partially supported, where the hypothesis of independent behavior of the stochastic variable ${\upsilon }_{\theta }$ is not supported. The conditional probability density functions (PDFs) of $\upsilon$ and ${\upsilon }_{\theta }$ cannot be described by Gaussian distributions when ${\mathrm{Re}}_{\mathrm{r}}<5$ for $\upsilon$ and ${\mathrm{Re}}_{\mathrm{r}}<300$ for ${\upsilon }_{\theta }$, and their Gaussian peaks converge when ${\mathrm{Re}}_{\mathrm{r}}>100$ for $\upsilon$ and ${\mathrm{Re}}_{\mathrm{r}}>1000$ for ${\upsilon }_{\theta }$. In addition, the bimodal behavior of the PDFs and oscillations at small $r$ in previous experimental tests are not observed in this study.

In spite of the widespread use of optical tweezers as a quantitative tool to measure small forces, there exists no unambiguous and simple experimental method for either validating its theoretically predicted form or empirically parameterizing it over the entire range. This problem is addressed by studying the transition of a colloidal particle between two spatially separated optical traps. The transition as a function of the relative intensity of the traps and the separation between them reveals a formal resemblance to the “butterfly catastrophe” which also maps onto to phase transitions observed, for example, in ferroelectrics on a phenomenological level. The method has been used to experimentally determine the force-displacement curve for an optical trap over its entire range.

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But, in contrast to mutual information, redundant information denotes information that is shared about the outcome of a third variable. Formalizing this concept, and being able to measure it, is required for the non-negative decomposition of mutual information into redundant and synergistic information. Previous attempts to formalize redundant or synergistic information struggle to capture some desired properties. We introduce a new formalism for redundant information and prove that it satisfies all the properties necessary outlined in earlier work, as well as an additional criterion that we propose to be necessary to capture redundancy. We also demonstrate the behavior of this new measure for several examples, compare it to previous measures, and apply it to the decomposition of transfer entropy.

In this work, we study the critical behavior of second-order points, specifically the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions [the axial-next-nearest-neighbor Ising (ANNNI) model], using time-dependent Monte Carlo simulations. We use a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time: ${\langle M\rangle }_{m_0=1}\sim t^{-\beta /\nu z}$, which is expected of simulations starting from initially ordered states. We obtain original results for the dynamic critical exponent $z$, evaluated from the behavior of the ratio $F_2\left(t\right)={\langle M^2\rangle }_{m_0=0}/{\langle M\rangle }_{m_0=1}^2\sim t^{3/z}$, along the critical line up to the LP. We explore all the critical exponents of the LP in detail, including the dynamic critical exponent $\theta$ that characterizes the initial slip of magnetization and the global persistence exponent ${\theta }_g$ associated with the probability $P\left(t\right)$ that magnetization keeps its signal up to time $t$. Our estimates for the dynamic critical exponents at the Lifshitz point are $z=2.34\left(2\right)$ and ${\theta }_g=0.336\left(4\right)$, values that are very different from those of the three-dimensional Ising model (the ANNNI model without the next-nearest-neighbor interactions at the $z$ axis, i.e., $J_2=0$), i.e., $z\approx 2.07$ and ${\theta }_g\approx 0.38$. We also present estimates for the static critical exponents $\beta$ and $\nu$, obtained from extended time-dependent scaling relations. Our results for static exponents are in good agreement with previous works.

We study the $\pm J$ three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The $\pm J$ random exchange is applied on the $xy$ planes, whereas, in the $z$ direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0;p_{xy}=0.176$). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent $1/\nu =1.463\left(3\right)$, and a collapse analysis of magnetization data gives an estimate of $\beta /\nu =0.516\left(7\right)$. These results are in agreement with previous papers and, in particular, with those of the isotropic $\pm J$ three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.