The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.We investigate a model of magnetic friction with the infinite-range interaction by mean-field analysis and a numerical simulation, and compare its behavior with that of the short-range model that we considered previously [Komatsu, Phys. Rev. E 100, 052130 (2019)2470-004510.1103/PhysRevE.100.052130]. This infinite-range model always obeys the Stokes law when the temperature is higher than the critical value, T_c, whereas it shows a crossover or transition from the Dieterich-Ruina law to the Stokes law when the temperature is lower than T_c. Considering that the short-range model in our previous study shows a crossover or transition irrespective of whether the temperature is above or below the equilibrium transition temperature, the behavior in the high-temperature state is the major difference between these two models.Exact four-photon resonance of collinear planar laser pulses is known to be prohibited by the classical dispersion law of electromagnetic waves in plasma. We show here that the renormalization produced by an arbitrarily small relativistic electron nonlinearity removes this prohibition. The laser frequency shifts in collinear resonant four-photon scattering increase with laser intensities. For laser pulses of frequencies much greater than the electron plasma frequency, the shifts can also be much greater than the plasma frequency and even nearly double the input laser frequency at still small relativistic electron nonlinearities. This may enable broad range tunable lasers of very high frequencies and powers. Since the four-photon scattering does not rely on the Langmuir wave, which is very sensitive to plasma homogeneity, such lasers would also be able to operate at much larger plasma inhomogeneities than lasers based on stimulated Raman scattering in plasma.Kink-antikink scattering in nonintegrable field theories like ϕ^4 theory is still rather poorly understood beyond brute-force numerical calculations, even after several decades of investigation. Recently, however, some progress has been made based on the introduction of certain self-dual background fields in these field theories which imply both the existence of static kink-antikink solutions of the Bogomol'nyi type and the possibility of an adiabatic scattering (moduli space approximation). Here we continue and generalize these investigations by introducing a one-parameter family of models interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model with the self-dual background field and the original ϕ^4 theory. More concretely, we study kink-antikink scattering in a parameter range between the limit of no static force (BPS limit) and the regime where the static interaction between kink and antikink is small (non-BPS regime). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up.  https://www.selleckchem.com/products/OSI-906.html  We show that the thin, precisely localized spectral wall which forms in the limit of no static force broadens in a well-defined manner when a static force is included, giving rise to what we call a thick spectral wall. This phenomenon results from the appearance of a stationary saddle point solution where the acceleration of the solitons owing to the attractive force is compensated by the dynamics of the sufficiently excited mode. Thus, this barrier shows up before the mode crosses the mass threshold.Hydrogels are sponge-like materials that can absorb or expel significant amounts of water. Swelling up from a dried state, they can swell up more than a hundredfold in volume, with the kinetics and the degree of swelling depending sensitively on the physicochemical properties of both the polymer network and the aqueous solvent. In particular, the presence of dissolved macromolecules in the background liquid can have a significant effect, as the macromolecules can exert an additional external osmotic pressure on the hydrogel material, thereby reducing the degree of swelling. In this paper, we have submerged dry hydrogel particles in polymer solutions containing large and small macromolecules. Interestingly, for swelling in the presence of large macromolecules we observe a concentration-dependent overshoot behavior, where the particle volume first continuously increases toward a maximum, after which it decreases again, reaching a lower, equilibrium value. In the presence of smaller macromolecules we do not obsey.Langevin dynamical simulations are performed to study the depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate. From the diagnostics of the sixfold coordinated particles P_6 and the collective drift velocity V_x, three different states appear, which are the pinning, disordered plastic flow, and moving ordered states. It is found that the depth of the substrate is able to modulate the properties of the depinning phase transition, based on the results of P_6 and V_x, as well as the observation of hysteresis of V_x while increasing and decreasing the driving force monotonically. When the depth of the substrate is shallow, there are two continuous phase transitions. When the potential well depth slightly increases, the phase transition from the pinned to the disordered plastic flow states is continuous; however, the phase transition from the disordered plastic flow to the moving ordered states is discontinuous. When the substrate is even deeper, the phase transition from the pinned to the disordered plastic flow states changes to discontinuous.