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In geometrothermodynamics (GTD), to study the geometric properties of the equilibrium space three thermodynamic metrics have been proposed so far. These metrics are obtained by using the condition of Legendre invariance and can be computed…
Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly…
By considering the B-field dynamical and studying its interaction with Ramond-Ramond (RR) background we observe the breaking of the B-field gauge symmetry in the effective action. This effect takes place due to non-perturbative coupling of…
The notion that the geometry of spacetime is given by the moduli space of 0-branes is examined in four examples of Calabi-Yau threefolds. An important consideration when determining the moduli space of D-branes is the stability condition…
We study the instability of bound states for abstract nonlinear Schr\"{o}dinger equations. We prove a new instability result for a borderline case between stability and instability. We also reprove some known results in a unified way.
We study the low energy dynamics of a single Dp-brane carrying sufcient large number of D0-brane charges in type IIA theory. We assume the D-brane topology to be $R \times \mathcal{M}_{2n} $ , where $\mathcal{M}_{2n}$ is a closed manifold…
This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes…
We present finite temperature solutions describing N_c D5 branes wrapped on the S^2 of the resolved conifold in the presence of N_f flavor brane sources and their backreaction, i.e. N_f/N_c ~ 1. In these solutions the dilaton does not blow…
Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences…
The intrinsic uncertainty of fluid properties, including the equation of state, viscosity, and thermal conductivity, on boundary layer stability has scarcely been addressed. When a fluid is operating in the vicinity of the Widom line…
Gravitational thermodynamics and gravitoscalar thermodynamics with $S^2 \times \mathbb{R}$ boundary geometry are investigated through the partition function, assuming that all Euclidean saddle point geometries contribute to the path…
Theory of the influence of the thermal fluctuations on the electric transport beyond linear response in superconductors is developed within the framework of the time dependent Ginzburg - Landau approach. The I - V curve is calculated using…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
The first goal of this paper is to study necessary and sufficient conditions to obtain the attainability of the \textit{fractional Hardy inequality } $$\Lambda_{N}\equiv\Lambda_{N}(\Omega):=\inf_{\{\phi\in \mathbb{E}^s(\Omega, D), \phi\neq…
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…
The temporal instability of stably stratified flow was investigated by analyzing the Taylor-Goldstein equation theoretically. According to this analysis, the stable stratification $N^2\geq0$ has a destabilization mechanism, and the flow…
We present a new method to detect Fermi surface instabilities for interacting systems at finite temperature. We first apply it to a list of cases studied previously, recovering already known results in a very economic way, and obtaining…
The stability of a rapid dynamic crack in a two dimensional infinite strip is studied in the framework of Linear Elasticity Fracture Mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack…
Mixtures of near-symmetric oppositely charged components with strong attractive short range interactions exhibit ordered lamellar phases at low temperatures. In the strong segregation limit the state of these systems can be described by the…
A long elastic cylinder, radius $a$ and shear-modulus $\mu$, becomes unstable given sufficient surface tension $\gamma$. We show this instability can be simply understood by considering the energy, $E(\lambda)$, of such a cylinder subject…