Related papers: On Scaling Laws for Multi-Well Nucleation Problems…
Scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action and do not lead to conservation laws. Nevertheless, by an extension of Noether's theorem, scaling symmetries lead to useful {\em…
The response of masonry structures to explosions can be hardly investigated relying only on numerical and analytical tools. Experimental tests are of paramount importance for improving the current comprehension and validate existing models.…
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
Energy functionals describing phase transitions in crystalline solids are often non-quasiconvex and minimizers might therefore not exist. On the other hand, there might be infinitely many gradient Young measures, modelling microstructures,…
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…
We discuss nonperturbative radiation for a recently introduced class of infrared safe event shape weights, which describe the narrow-jet limit. Starting from next-to-leading logarithmic (NLL) resummation, we derive an approximate scaling…
We use continuum elasticity theory to revise scaling laws for radial breathing-like and shear-like vibration modes in quasi-2D nanostructures including finite-width nanoribbons and finite-size thin circular discs. Such modes can be observed…
The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between…
Passive scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the…
Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely…
Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly…
We introduce a new shell model of turbulence which exhibits improved properties in comparison to the standard (and very popular) GOY model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular…
Large-scale inhomogeneities and anisotropies are modeled using the Long Wavelength Iteration Scheme. In this scheme solutions are obtained as expansions in spatial gradients, which are taken to be small. It is shown that the choice of…
We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general…
As pointed out by Linus Pauling in his classic work on the relationship between crystal packing and ionic radius ratio, a difference in atomic size can be accommodated more readily by an ordered structure than by a disordered one. Because…
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in…
A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Gr\"{u}neisen equation of state, the Wilkins…
We present a unified theoretical and numerical framework for self-similar multi-shock implosions achieving ultrahigh compression in a uniform solid spherical target. Extending the classical Guderley model to N stacked, spherically…
From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the…
We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement…