scholarly journals Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution

2020 ◽  
Vol 16 (4) ◽  
pp. 543-555
Author(s):  
C.C. Lim ◽  
Keyword(s):  
Mean Field ◽  
Gaussian Model ◽  
Closed Form Solution ◽  
Spherical Model ◽  
Form Solution ◽  
Critical Temperatures ◽  
Barotropic Flow ◽  
New Energy ◽  
Physical Principles ◽  
Method Of Steepest Descent

A new energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow on a sphere is introduced and solved exactly for phase transitions to quadrupolar vortices when the kinetic energy level is high. Unlike the Kraichnan theory, which is a Gaussian model, we substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based on sound physical principles. This yields a spherical model with zero total circulation, a microcanonical enstrophy constraint and a canonical constraint on energy, with angular momentum fixed to zero. A closed-form solution of this spherical model, obtained by the Kac – Berlin method of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking quadrupolar vortices. This model and its results differ from previous solvable models for related phenomena in the sense that they are not based on a mean-field assumption.

Closed-Form Solution for Defaultable Bond Options under a Two-Factor Gaussian Model for Risky Rates Modeling

2020 ◽  
Vol 28 (2) ◽  
pp. 88-103 ◽  
Author(s):  
Vincenzo Russo ◽  
Rosella Giacometti ◽  
Frank J. Fabozzi
Keyword(s):  
Closed Form ◽  
Gaussian Model ◽  
Closed Form Solution ◽  
Form Solution ◽  
Defaultable Bond ◽  
Bond Options

Approximate Solutions

2020 ◽  
pp. 106-158
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Random Walk ◽  
Mean Field ◽  
Gaussian Model ◽  
Spherical Model ◽  
Approximate Solutions ◽  
Field Approximation ◽  
Approximation Schemes ◽  
Mean Field Approximation ◽  
Exactly Solvable ◽  
The Subject

Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical properties of the spherical model.

scholarly journals A CLOSED-FORM SOLUTION FOR A QUEUEING MODEL OF ENERGY EFFICIENT ETHERNET LINKS

2021 ◽  
Vol 37 (4) ◽  
pp. 453-464
Author(s):  
Đỗ Văn Tiến ◽  
Csaba Rotter
Keyword(s):  
Low Power ◽  
Closed Form ◽  
Energy Efficient ◽  
Closed Form Solution ◽  
Compound Poisson Process ◽  
Form Solution ◽  
Queueing Model ◽  
Efficient Operation ◽  
New Energy ◽  
Save Energy

To save energy consumption of Ethernet switches, IEEE has standardized a new energy-efficient operation for Ethernet links with a low-power state and transition mechanisms between the high-power state for transporting traffic and the low-power state.In this paper, we propose a queueing model with the Markov Modulated Compound Poisson Process that is able to characterize backbone packet traffic. We derive a closed-form solution for the stationary distribution of the proposed queueing model. We show that our model can capture an entire system where the transition times are constant.

scholarly journals European Option Based on Least-Squares Method under Non-Extensive Statistical Mechanics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 933
Author(s):  
Limin Liu ◽  
Yingying Cui
Keyword(s):  
Statistical Mechanics ◽  
Least Squares ◽  
Least Squares Method ◽  
Gaussian Model ◽  
Closed Form Solution ◽  
Least Square Method ◽  
Form Solution ◽  
Least Square ◽  
European Options ◽  
Non Gaussian

This paper is devoted to the study of the pricing of European options under a non-Gaussian model. This model follows a non-extensive statistical mechanics which can better describe the fractal characteristics of price movement in the financial market. Moreover, we present a simple but precise least-square method for approximation and obtain a closed-form solution of the price of European options. The advantages of this technique are illustrated by numerical simulation, which shows that the least-squares method is better compared with Borland’s two methods in 2002 and 2004.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

A Simple Closed-Form Solution of Bending Stiffness for Laminated Composite Tubes

2000 ◽  
Vol 19 (4) ◽  
pp. 278-291 ◽  
Author(s):  
WEN S. CHAN ◽  
KAZIM C. DEMIRHAN
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Laminated Composite ◽  
Bending Stiffness ◽  
Form Solution ◽  
Composite Tubes
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