Related papers: Soft matter and fractional mathematics: insights i…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
We analyze statistically the energization of particles in a large scale environment of strong turbulence that is fragmented into a large number of distributed current filaments. The turbulent environment is generated through strongly…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with $q$-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints…
We study a noninteracting supersymmetric model in an expanding FRW spacetime. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density. A short distance cutoff of the order of Planck length provides a scale…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on…
Soft condensed matter physics is the study of materials, such as fluids, liquid crystals, polymers, colloids, and emulsions, that are ``soft" to the touch. This article will review some properties, such as the dominance of entropy, that are…
The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this…
This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive…
The space-time metric is widely believed to be subject to stochastic fluctuations induced by quantum gravity at the Planck scale. This work is based on two different phenomenological approaches being currently made to this topic, and…
Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We…
Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between…