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I present a general discussion of the evolution and model-dependence of both the linear and nonlinear power spectrum of density fluctuations. The features of the linear power spectrum in cosmological models with cold dark matter (CDM) and…
We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Benard convection.…
Cold Dark Matter (CDM) has become the standard modern theory of cosmological structure formation. Its predictions appear to be in good agreement with data on large scales, and it naturally accounts for many properties of galaxies. But…
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…
We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic…
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
An approach to understanding the light scalar meson phenomenology is briefly reviewed.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
Out of the many exciting results obtained with the lattice approach to QCD under extreme conditions, I discuss a few selected items related to chiral symmetry: the chiral condensate as an approximate order parameter, meson screening masses,…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
We review the theory of polarized structure functions measured in deep-inelastic lepton-nucleon scattering, focusing on the most recent developments. We concentrate on the structure function $g_1$, emphasizing the phenomenological problems…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist…
The general parameterization of the quark-quark correlation function for a spin-1/2 hadron is considered. The presence of the Wilson line ensuring color gauge invariance of the correlator induces structures that were not given explicitly in…
Using an unambiguous characterization of Trace Anomalies a general proof of matching for Type A and B anomalies in the broken phases of Conformal Field Theories is given. The general constraints on amplitudes of energy-momentum tensors and…
This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…