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Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid…
A method of defining the complex structure(moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the…
We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the…
Dynamics of hydrogen atom driven by microwave field of arbitrary polarization is approximated by the discrete mapping. The map describes the change of dynamical variables from an aphelion or a perihelion to the next one. The results are…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential is studied. It is shown that if the pair potential allows for a discontinuous reduction of the…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…
We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex…
Understanding and mapping extreme heat is critical for risk management and public health planning, particularly in regions with complex terrain and heterogeneous climate. We present a case study of extreme heat in the Four Corners region of…
The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an…
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
We explore the initial conditions in short-time critical dynamics to propose a new method to evaluate the dynamic exponent z. Estimates are obtained with high precision for 2D Ising model and 2D Potts model for three and four states by…
We derive an interpolation version of constrained matrix Li-Yau-Hamilton estimate on K\"ahler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a K\"ahler manifold with fixed K\"ahler…
This is a comprehensive review on the perturbative hot QCD including the recent developments. The main body of the review is concentrated upon dealing with physical quantities like reaction rates. Contents: \S1. Introduction, \S2.…
Continuous and discrete models for firefighting problems are well-studied in Theoretical Computer Science. We introduce a new, discrete, and more general framework based on a hexagonal cell graph to study firefighting problems in varied…
We consider dynamical black hole formation from a collapsing fluid described by a symmetric and flat FRW metric. Using the Hamilton-Jacobi method the local Hawking temperature for the formed trapping/apparent horizon is calculated. The…
Reactive flows in confined spaces involve complex flame-wall interaction (FWI). This work aims to gain more insights into the physics of the premixed near-wall flame and the wall heat flux as an important engineering relevant quantity. Two…
We test on the 2+1 dimensional black hole the quantization method that we have previously proposed in four dimensions. While in the latter case the horizon dynamics is described, at the effective level, by the action of a relativistic…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…
The paper is devoted to study the space of multiplicative maps from the Eilenberg-MacLane spectrum $H\Z$ to an arbitrary ring spectrum $R$. We try to generalize the approach of Schwede from "Formal groups and stable homotopy of commutative…