An entirely analytical cosmological model

The purpose of the present study is to show that in a particular cosmological model, with an affine equation of state, one can obtain, besides the background given by the scale factor, Hubble and deceleration parameters, a representation in terms of scalar fields and, more important, explicit mathematical expressions for the density contrast and the power spectrum. Although the model so obtained is not realistic, it reproduces features observed in some previous numerical studies and, therefore, it may be useful in the testing of numerical codes and as a pedagogical tool.Comment: 4 pages (revtex4), 4 figure

Analytical solutions for the Rabi model

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 because it is hard to find a second conserved quantity besides the energy. Here we present a unitary transformation to map this unsolvable Rabi model into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, these explicit results agree well with the direct numerical simulations in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of Bloch-Siegert in the circuit quantum electrodynamics with the ultrastrong coupling can be explained perfectly. Our results have the potential application in the solid-state quantum information processing.Comment: 5 pages, 4 figure

Analytical approximation for single-impurity Anderson model

We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomic problem of the Anderson impurity model has a degenerate ground state, so the application of the perturbation theory is not straightforward. We construct a special approach dealing with symmetry-broken ground state of the renormalized atomic problem. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. Most of the Kondo-physics is reproduced: logarithmic contributions to the self energy arise, Kondo-like peak at the Fermi level appears, and the Friedel sum rule is fulfilled. Our approach describes also renormalization of atomic resonances due to hybridization with a conduction band. A generalization of the proposed scheme to a multi-orbital case can be important for the realistic description of correlated solids.Comment: 6 pages, 5 figure

Geosynthetic-encased stone columns: analytical calculation model

This paper presents a newly developed design method for non-encased and encased stone columns. The developed analytical closed-form solution is based on previous solutions, initially developed for non-encased columns and for non-dilating rigid-plastic column material. In the present method, the initial stresses in the soil/column are taken into account, with the column considered as an elasto-plastic material with constant dilatancy, the soil as an elastic material and the geosynthetic encasement as a linear-elastic material. To check the validity of the assumptions and the ability of the method to give reasonable predictions of settlements, stresses and encasement forces, comparative elasto-plastic finite element analyses have been performed. The agreement between the two methods is very good, which was the reason that the new method was used to generate a parametric study in order to investigate various parameters, such as soil/column parameters, replacement ratio, load level and geosynthetic encasement stiffness on the behaviour of the improved ground. The results of this study show the influence of key parameters and provide a basis for the rational predictions of settlement response for various encasement stiffnesses, column arrangements and load levels. The practical use of the method is illustrated through the design chart, which enables preliminary selection of column spacing and encasement stiffness to achieve the desired settlement reduction for the selected set of the soil/column parameters. (C) 2010 Elsevier Ltd. All rights reserved

COBE vs Cosmic Strings: An Analytical Model

We construct a simple analytical model to study the effects of cosmic strings on the microwave background radiation. Our model is based on counting random multiple impulses inflicted on photon trajectories by the string network between the time of recombination and today. We construct the temperature auto-correlation function and use it to obtain the effective power spectrum index n, the rms-quadrupole-normalized amplitude $Q_{rms-PS}$ and the rms temperature variation smoothed on small angular scales. For the values of the scaling solution parameters obtained in Refs.\cite{bb90},\cite{as90} we obtain $n=1.14 \pm 0.5$, $Q_{rms-PS}=(4.5\pm 1.5) G\mu$ and $({{\Delta T}\over T})_{rms}=5.5 G\mu$. Demanding consistency of these results with the COBE data leads to $G\mu=(1.7 \pm 0.7)\times 10^{-6}$ (where $\mu$ is the string mass per unit length), in good agreement with direct normalizations of $\mu$ from observations.Comment: 12 pages, 5 figures (available upon request), use late

Analytical Model of TCP Relentless Congestion Control

We introduce a model of the Relentless Congestion Control proposed by Matt Mathis. Relentless Congestion Control (RCC) is a modification of the AIMD (Additive Increase Multiplicative Decrease) congestion control which consists in decreasing the TCP congestion window by the number of lost segments instead of halving it. Despite some on-going discussions at the ICCRG IRTF-group, this congestion control has, to the best of our knowledge, never been modeled. In this paper, we provide an analytical model of this novel congestion control and propose an implementation of RCC for the commonly-used network simulator ns-2. We also improve RCC with the addition of a loss retransmission detection scheme (based on SACK+) to prevent RTO caused by a loss of a retransmission and called this new version RCC+. The proposed models describe both the original RCC algorithm and RCC+ improvement and would allow to better assess the impact of this new congestion control scheme over the network traffic.Comment: Extended version of the one presented at 6th International Workshop on Verification and Evaluation of Computer and Communication Systems (Vecos 2012

Degenerate Landau-Zener model: Exact analytical solution

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1

An analytical model for the influence of contact resistance on thermoelectric efficiency

An analytical model is presented that can account for both electrical and hot and cold thermal contact resistances when calculating the efficiency of a thermoelectric generator. The model is compared to a numerical model of a thermoelectric leg, for 16 different thermoelectric materials, as well as the analytical models of Ebling et. al. (2010) and Min \& Rowe (1992). The model presented here is shown to accurately calculate the efficiency for all systems and all contact resistances considered, with an average difference in efficiency between the numerical model and the analytical model of $-0.07\pm0.35$ pp. This makes the model more accurate than previously published models. The maximum absolute difference in efficiency between the analytical model and the numerical model is 1.14 pp for all materials and all contact resistances considered.Comment: 8 pages, 5 figure