In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation.

Derivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperatureT. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used.

We consider the generalization of discrete de la Vallée Poussin means on the square, obtained via tensor product by the univariate case. Pros and cons of such a kind of filtered approximation are discussed. In particular, under simple, we get near-best discrete approximation polynomials in the space of all locally continuous functions on the square with possible algebraic singularities on the boundary, equipped with the weighted uniform norm. In the four Chebychev cases, these polynomials also interpolate the function.

The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equation, we show that when adsorbed at a fluid interface, an active colloid experiences a net torque even in the absence of a viscosity contrast between the two adjacent fluids.

Bicontinuous interfacially jammed emulsion gels ("bijels") represent a new class of soft materials made of a densely packed monolayer of solid particles sequestered at the interface of a bicontinuous fluid. Their mechanical properties are relevant to many applications, such as catalysis, energy conversion, soft robotics, and scaffolds for tissue engineering. While their stationary bulk properties have been covered in depth, much less is known about their behavior in the presence of an external shear.

We study the formation of singularities for the problem {u(t) = [phi(u)](xx) + epsilon[psi(u)](txx) in Omega x (0, T) phi(u) + epsilon[psi(u)](t) = 0 in partial derivative Omega x(0, T) u = u(0) >= 0 in Omega x {0}, where epsilon and Tare positive constants, Omega a bounded interval, u(0) a nonnegative Radon measure on Omega, phi a nonmonotone and nonnegative function with phi(0) = phi(infinity) = 0, and psi an increasing bounded function. We show that if u(0) is a bounded or continuous function, singularities may appear spontaneously.

?1-Antitrypsin (AAT) encoded by the SERPINA1 gene is an acute-phase protein synthesized in the liver and secreted into the circulation. Its primary role is to protect lung tissue by inhibiting neutrophil elastase. The Z allele of SERPINA1 encodes a mutant AAT, named ATZ, that changes the protein structure and leads to its misfolding and polymerization, which cause endoplasmic reticulum (ER) stress and liver disease through a gain-of-function toxic mechanism.

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission.