Related papers: Bubbling and regularity issues in geometric non-li…
In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…
Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
We explore phenomenological consequences of coupling a non-conformal scale-invariant theory to the standard model. We point out that, under certain circumstances, non-conformal scale-invariant theories have oscillating correlation functions…
In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau-Ginzburg (LG) models for critical and unstable fluids (e.g.…
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review describes a unified theoretical framework, the loop space…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
We use a full general relativistic framework to study the self-similar expansion of bubbles of the stable phase into a flat Friedmann-Lema\^itre-Robertson-Walker Universe in a first order phase transition in the early Universe. With a…
We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler-Lagrange equation of a natural Riemaniann variational problem of geometric interest. New uniqueness results for the entire…
Some nonperturbative aspects of Euclidean Yang-Mills theories in four dimensions, quantized in the Landau gauge, are analytically studied. In particular, we investigate the dynamical mass generation for the gluons due to the presence of…
A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases,…
We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the short time solution in the $L^q$-setting. Moreover, we give a…
In this paper we review some properties for the evolving wormhole solution of Einstein equations coupled with nonlinear electrodynamics. We integrate the geodesic equations in the effective geometry obeyed by photons; we check out the weak…