We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase diagram of the mixture of large and small particles in the large-dimension limit where the mean-field theory becomes exact. When the size ratio of particles is beyond a critical value, the theory predicts three distinct glass phases; (i) the one-step replica symmetery breaking (1RSB) double glass where both components vitrify simultaneously, (ii) the 1RSB single glass where only large particles are frozen while small particles remain mobile, and (iii) a glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.While the majority of fusion energy research is focused on magnetic confinement, there have been several alternative confinement methods aimed at the development of smaller and less expensive reactors. A number of these alternative reactors are based on a spherically convergent beam of recirculating ions and include designs such as inertial electrostatic confinement (IEC), multigrid IEC, and the periodically oscillating plasma sphere concept. Here, a fully time-dependent GPU-based Vlasov solver was developed in order to study these spherically convergent devices. This code solves the Vlasov equation for a spherically symmetric system using a finite-volume method with a modified flux to account for electrode transparency. The solver accounts for secondary electron emission, interactions between the charged particles, and collisional effects such as ionization and charge exchange. This code was used to investigate a system similar to the ion-injected device described by Hirsch (see [R. L. Hirsch, J. Appl. Phys.een the ion beam and deuterium embedded on the inner surface of the cathode.The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. https://www.selleckchem.com/products/fx11.html We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates K(k,l)=1/k+1/l. In this case, it is possible to determine the behavior of large-size aggregates in the limit of large times in a way that allows a highly detailed analysis of the behavior of the system. This is the so-called scaling limit, in which the cluster size distribution collapses to a function of the ratio of the cluster size to a time-dependent typical size. The results confirm the far more general results of earlier work concerning a general scaling theory for so-called reaction rates of Type III, which are characterized by the property that aggregates of very different sizes react faster than comparable aggregates of similar sizes. For these, the cluster size distribution decays rapidly to zero both for sizes much larger and much smaller than the typical size, and is thus often described as being "bell-shaped". For clusters much larger than the typical size, however, an unexpected subleading correction is discovered. Finally, several results going beyond the scope of the scaling limit are obtained in particular the behavior of concentrations for fixed cluster size in the large-time limit and the large-size behavior for clusters at a fixed time. The latter again shows subleading deviations from the expected behavior.Diffusion-limited aggregation (DLA) has served for 40 years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references, no exact result for the fractal dimension D of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane D=3/2. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit, and a well-defined fractal dimension. Mathematical proofs of the main results are available in N. Berger, E. B. Procaccia, and A. Turner, Growth of stationary Hastings-Levitov, arXiv2008.05792.Although many previous studies have focused on the Brazil nut effect, segregation in a self-gravitating circular aggregate remains relatively unexplored. In this paper, size segregation in a two-dimensional assembly of grains in a circular geometry is studied through discrete element method (DEM) numerical simulations. We show that radial segregation within an asteroid submitted to periodic perturbations is not limited to the surface but also occurs in its core. The characteristic time and the overall efficiency of the segregation mechanism are studied as the intensity of the perturbation, the frictional properties, and rotational freedom of individual grains are varied.