Molecular dynamics simulations of crystallization in a supercooled liquid of Lennard-Jones particles with different range of attractions shows that the inclusion of the attractive forces from the first, second, and third coordination shell increases the trend to crystallize systematic. The bond order Q_6 in the supercooled liquid is heterogeneously distributed with clusters of particles with relative high bond order for a supercooled liquid, and a systematic increase of the extent of heterogeneity with increasing range of attractions. The onset of crystallization appears in such a cluster, which together explains the attractive forces influence on crystallization. The mean-square displacement and self-diffusion constant exhibit the same dependence on the range of attractions in the dynamics and shows, that the attractive forces and the range of the forces plays an important role for bond ordering, diffusion, and crystallization.We devise a general method to extract weak signals of unknown form, buried in noise of arbitrary distribution.  https://www.selleckchem.com/products/Nolvadex.html  Central to it is signal-noise decomposition in rank and time only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N points in a data sequence. We show that rank, averaged across jointly indexed series of noisy data, tracks the underlying weak signal via a simple relation, for all noise distributions. We derive an exact analytic, distribution-independent form for the discrete covariance matrix of cumulative distributions for independent and identically distributed noise and employ its eigenfunctions to extract unknown signals from single time series.This article proposes a phase-field-simplified lattice Boltzmann method (PF-SLBM) for modeling solid-liquid phase change problems within a pure material. The PF-SLBM consolidates the simplified lattice Boltzmann method (SLBM) as the flow solver and the phase-field method as the interface tracking algorithm. Compared with conventional lattice Boltzmann modelings, the SLBM shows advantages in memory cost, boundary treatment, and numerical stability, and thus is more suitable for the present topic which includes complex flow patterns and fluid-solid boundaries. In contrast to the sharp interface approach, the phase-field method utilized in this work represents a diffuse interface strategy and is more flexible in describing complicated fluid-solid interfaces. Through abundant benchmark tests, comprehensive validations of the accuracy, stability, and boundary treatment of the proposed PF-SLBM are carried out. The method is then applied to the simulations of partially melted or frozen cavities, which sheds light on the potential of the PF-SLBM in resolving practical problems.Several studies have investigated the dynamics of a single spherical bubble at rest under a nonstationary pressure forcing. However, attention has almost always been focused on periodic pressure oscillations, neglecting the case of stochastic forcing. This fact is quite surprising, as random pressure fluctuations are widespread in many applications involving bubbles (e.g., hydrodynamic cavitation in turbulent flows or bubble dynamics in acoustic cavitation), and noise, in general, is known to induce a variety of counterintuitive phenomena in nonlinear dynamical systems such as bubble oscillators. To shed light on this unexplored topic, here we study bubble dynamics as described by the Keller-Miksis equation, under a pressure forcing described by a Gaussian colored noise modeled as an Ornstein-Uhlenbeck process. Results indicate that, depending on noise intensity, bubbles display two peculiar behaviors when intensity is low, the fluctuating pressure forcing mainly excites the free oscillations of the bubble, and the bubble's radius undergoes small amplitude oscillations with a rather regular periodicity. Differently, high noise intensity induces chaotic bubble dynamics, whereby nonlinear effects are exacerbated and the bubble behaves as an amplifier of the external random forcing.Mushroom species display distinctive morphogenetic features. For example, Amanita muscaria and Mycena chlorophos grow in a similar manner, their caps expanding outward quickly and then turning upward. However, only the latter finally develops a central depression in the cap. Here we use a mathematical approach unraveling the interplay between physics and biology driving the emergence of these two different morphologies. The proposed growth elastic model is solved analytically, mapping their shape evolution over time. Even if biological processes in both species make their caps grow turning upward, different physical factors result in different shapes. In fact, we show how for the relatively tall and big A. muscaria a central depression may be incompatible with the physical need to maintain stability against the wind. In contrast, the relatively short and small M. chlorophos is elastically stable with respect to environmental perturbations; thus, it may physically select a central depression to maximize the cap volume and the spore exposure. This work gives fully explicit analytic solutions highlighting the effect of the growth parameters on the morphological evolution, providing useful insights for novel bio-inspired material design.To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small.