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The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not converge to the known TUR in the overdamped limit. Furthermore, it was found that there are restrictions for a TUR to hold such as the absence of a magnetic field. In this article we first analyze the properties of driven free diffusion in the underdamped regime and show that it inherently violates the overdamped TUR for finite times. Based on numerical evidence, we then conjecture a bound for one-dimensional driven diffusion in a potential which is based on the result for free diffusion. This bound converges to the known overdamped TUR in the corresponding limit. Moreover, the conjectured bound holds for observables that involve higher powers of the velocity as long as the observable is odd under time reversal. Finally, we address the applicability of this bound to underdamped dynamics in higher dimensions.We derive generalized Fokker-Planck equations (FPEs) based on two nonextensive entropy measures S_± that depend exclusively on the probability. These entropies have been originally obtained from the superstatistics framework, therefore they regard nonequilibrium systems outlined by a long-term stationary state in view of a spatiotemporally fluctuating intensive quantity. Moreover, entropies S_± as well as Boltzmann-Gibbs (BG) entropy S_B both pertain to the same asymptotical equivalence class, thus suggesting that S_± could depict a consistent thermodynamic generalization of BG. For these reasons, we assert that transport phenomena to be accounted for by our models shall coincide with the portrait given by the conventional FPEs for systems comprehending short-range interactions or a high number of accessible microstates, whereas, for systems composed of a small number of microstates, or those with long-range interactions, the governing equations of motion are to be the FPEs here derived, as long as the system fulfills the attributes mentioned above. We discuss the anomalous diffusion exhibited by the two generalized FPEs and also present some numerical applications. In particular, we find that there are models regarding biological sciences, for the study of congregation and aggregation behavior, the structure of which coincides with the one of our models.Understanding of multiphase flow in porous media is important for a wide range of applications such as soil science, environmental remediation, energy resources, and CO_2 sequestration. This phenomenon depends on the complex interplay between the fluid and solid forces such as gravitational, capillary, and viscous forces, as well as wettability of the solid phase. Such interactions along with the geometry of the medium give rise to a variety of complex flow regimes. Although much research has been done in the area of wettability, its mechanical effect is not well understood, and it continues to challenge our understanding of the phenomena on macroscopic and microscopic scales. In this paper, therefore, the effect of wettability on the deformation of porous media and fluid-fluid patterns is studied through a series of three-dimensional (3D) simulations. selleck chemicals To this end, the discrete element method (DEM) and volume of fluid (VOF) are coupled to accurately model free-surface flow interaction in a cylindrical pack of spheres. The fluid-particle interactions are modeled by exchanging information between DEM and VOF, while the effect of wettability is considered to study how it controls fluid displacement. The results indicate that the drag force and deformation in the pack vary with the change in wettability and capillary number. To demonstrate the effect of both wettability and capillary number, a series of numerical experiments were conducted with two capillary numbers and three wettability conditions. Our results show that the drag force was greatest for near extreme wettability conditions, which resulted in a larger deformation.Individual fire ants are inherently active as they are living organisms that convert stored chemical energy into motion. However, each individual ant is not equally disposed to motion at any given time. In an active aggregation, most of the constituent ants are active, and vice versa for an inactive aggregation. Here we look at the role activity plays on the nonlinear mechanical behavior of the aggregation through large amplitude oscillatory shear measurements. We find that the level of viscous nonlinearity can be decreased by increasing the activity or by increasing the volume fraction. In contrast, the level of elastic nonlinearity is not affected by either activity or volume fraction. We interpret this in terms of a transient network with equal rates of linking and unlinking but with varying number of linking and unlinking events.A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation permits the consideration of arbitrary polymer chain behaviors when interactions among chains may be neglected. This careful treatment highlights the naturally occurring correspondence between single-chain mechanical behavior and the equilibrium distribution of chains in the network, as well as the correspondences between different single-chain thermodynamic ensembles. We demonstrate these important distinctions with the extensible freely jointed chain model. This statistical mechanical theory is then extended to the continuum scale, where we utilize traditional macroscopic constitutive theory to ultimately retrieve the Cauchy stress in terms of the deformation and polymer network statistics. Once again using the extensible freely jointed chain model, we illustrate the importance of the naturally occurring statistical correspondences through their effects on the stress-stretch response of the network. We additionally show that these differences vanish when the number of links in the chain becomes sufficiently large enough, and discuss why certain methods perform better than others before this limit is reached.