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There are strong correlations between the three structural properties of elliptical galaxies -- stellar mass, velocity dispersion and size -- in the form of a tight "fundamental plane" and a "scaling relation" between each pair. Major…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a non-equilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of…
We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…
We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under general assumptions using De Giorgi's minimizing movement scheme.…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…
We elaborate on the effective field theory (EFT) construction for dissipative open systems coupled to dynamical gravity, in light of recent developments on the EFT of dissipative hydrodynamics (HydroEFT). Our construction is based on the…
Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
We analytically study a one dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a $1/\ln t$…
We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural…
A unified classification framework for models of extended plasticity is presented. The models include well known micromorphic and strain gradient plasticity formulations. A unified treatment is possible due to the representation of strain…
A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa- Mima equation, but does not conserve enstrophy, and, as a…
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
A cosmic potential which can relax the vacuum energy is proposed in a framework of scalar-tensor gravity. In the phase of the gravity scalar field around the evolution with an approximate emergent conformal symmetry, we have obtained a set…
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough…
We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set $\Omega$ and a thin layer $\Sigma$ locally described by $\varepsilon h$, where $h$ is a positive function defined on the boundary…