相关论文: Analytical Solutions in the Two-cavity Coupling Pr…
We present a manifestly duality covariant formulation of the composite non-BPS and almost-BPS systems of multi-centre black hole solutions in four dimensions. The method of nilpotent orbits is used to define the two systems in terms of…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
We theoretically study a cavity filled with atoms, which provides the optical-mechanical interaction between the modified cavity photonic field and a movable mirror at one end. We show that the cavity field ``dresses'' these atoms,…
The Homotopy Analysis Method (HAM) is a useful method to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein-Weyl gravity coupled with Maxwell field, and obtain…
Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the…
This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…
We describe a realistic scheme for coupling atoms or other quantum emitters with an array of coupled optical cavities. We consider open Fabry-Perot microcavities coupled to the emitters. Our central innovation is to connect the…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly…
The mode profile of a coupled optical cavity often exhibits a resonant doublet, which arises from the strong coupling between its sub-cavities. Traditional readout methods rely on setting fields of different frequencies to be resonant in…
We have developed the mode matching technique that is based on the using the eigenmodes of circular cavities and the eigenwaves of circular waveguides as the basic functions for calculation the properties of nonuniform disc-loaded…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\chi_2$ type nonlinearity as well as two mode…
In this paper, we develop a differential-topological method to yield explicit real analytic solutions $v$ to the divergence equation $div_{\mathbb{R}^n} v = f$ on any annali $A(R_1 ,R_2) = \{ x \in \mathbb{R}^n : R_1 < |x| < R_2\}$, with $n…
We derive a charged black hole solution in four dimensions described by $SL(2,R)\times SU(2)\times U(1)/U(1)^2$ WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact to all orders in…
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
In this paper, we use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions for the collinear four- body problem in both the decoupled case and the coupled case. All…