Energy storage by compressed air

The feasibility of windpower energy storage by compressed air is considered. The system is comprised of a compressor, a motor, and a pump turbine to store air in caverns or aquifiers. It is proposed that storage of several days worth of compressed air up to 650 pounds per square inch can be used to push the aquifier up closer to the container dome and thus initiate piston action by simply compressing air more and more. More energy can be put into it by pressure increase or pushing back the water in the aquifier. This storage system concept has reheat flexibility and lowest cost effectiveness

On the Application of Liapunov’s Second Method to the Stability Analysis of Time-invariant Control Systems

The investigation of the stability properties of the equilibrium point of a control system poses various problems -which, even if conceptually very similar, vary greatly in difficulty and in the methods appropriate for their solutions. The first and easier problem is what we may call the stability analysis of a completely defined system: given a particular control system to decide what stability properties its equilibrium point has. The second problem deals with a system having a fixed configuration but with parameters whose numerical values are to be determined. The problem is to find the boundaries in the parameter space at which the stability properties of the system undergo a change. The third problem is that of synthesizing stable systems and its solution implies knowledge of necessary and sufficient conditions for the equilibrium point of the system to be stable. This problem is far from being solved and it is also doubtful if its practical solution will emerge from the classical theory of stability. In fact stability problems of this generality arise only in very general formulations like the synthesis of systems which are optimal in some sense. It should he easier to include stability among the other constraints that the system must satisfy, then investigate this property separately. Obviously then many problems about structural stability will arise, but the logical procedure will still be to find at least a fixed structure for the system, by various variational methods, and then to investigate its stability properties; in other words, to reduce the general problem to the second problem of our classification. In the present report, this problem will be investigated by means of the Second Method of Liapunov. The Second Method of Liapunov is essentially based upon the now classical Grande Memorie [1] that the Russian scientist published in I893. This method can, however, be thought of in different ways. The first way is as a general procedure for tackling the problem of stability of systems, a way of thinking, a policy, more than a well defined stability criterion: in this fashion, it has mostly been used in mathematical works. In the Soviet Union especially, this state of mind prevails also in the area of control theory, in other words, the Liapunov Second Method has been almost exclusively applied in order to develop some algebraic condition of stability. In other words, the Liapunov method has been applied to stability problems in order to find stability criteria applicable to certain classes of systems. On the contrary, we regard the Liapunov Second Method as a stability criterion, based upon certain theorems ( 3). The main aim of this work is to develop a method ( 5) for the construction of Liapunov functions for autonomous systems. This method in contrast to others will always yield a solution of the stability problem. The price we have to pay for assuring that the method always works is the restriction to a particular class of Liapunov functions, solutions of a partial differential equation (19) \u27which turns out to be the generalization of an analogous equation proposed by Zubov [2]. Since the solution of this partial differential equation is by no means elementary and since there exist very easy methods [3, 4, 5] which give the answer in many cases (but fail in others.’) the investigation of the stability by applying this new method is advisable only in the case in which these simpler methods have failed. In order to make this paper reasonably self-contained, a short outline of these three methods are given. [10] and a comparison between them is made. On the basis of this critical study of the available methods for constructing Liapunov functions, we shall suggest a scheme for attacking the stability problem

On the distribution of the nodal sets of random spherical harmonics

We study the length of the nodal set of eigenfunctions of the Laplacian on the \spheredim-dimensional sphere. It is well known that the eigenspaces corresponding to \eigval=n(n+\spheredim-1) are the spaces \eigspc of spherical harmonics of degree $n$, of dimension \eigspcdim. We use the multiplicity of the eigenvalues to endow \eigspc with the Gaussian probability measure and study the distribution of the \spheredim-dimensional volume of the nodal sets of a randomly chosen function. The expected volume is proportional to \sqrt{\eigval}. One of our main results is bounding the variance of the volume to be O(\frac{\eigval}{\sqrt{\eigspcdim}}). In addition to the volume of the nodal set, we study its Leray measure. For every $n$, the expected value of the Leray measure is $\frac{1}{\sqrt{2\pi}}$. We are able to determine that the asymptotic form of the variance is \frac{const}{\eigspcdim}.Comment: 47 pages, accepted for publication in the Journal of Mathematical Physics. Lemmas 2.5, 2.11 were proved for any dimension, some other, suggested by the referee, modifications and corrections, were mad

Soft matrix models and Chern-Simons partition functions

We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. We mainly rely on simple considerations based on orthogonal polynomials and the moment problem. In addition, some of these models are equivalent, by a simple mapping, to matrix models that appear in Chern-Simons theory. The models can be solved with q deformed orthogonal polynomials (Stieltjes-Wigert polynomials), and the deformation parameter turns out to be the usual $q$ parameter in Chern-Simons theory. In this way, we give a matrix model computation of the Chern-Simons partition function on $S^{3}$ and show that there are infinitely many matrix models with this partition function.Comment: 13 pages, 3 figure

High-energy gravitational scattering and black hole resonances

Aspects of super-planckian gravitational scattering and black hole formation are investigated, largely via a partial-wave representation. At large and decreasing impact parameters, amplitudes are expected to be governed by single graviton exchange, and then by eikonalized graviton exchange, for which partial-wave amplitudes are derived. In the near-Schwarzschild regime, perturbation theory fails. However, general features of gravitational scattering associated with black hole formation suggest a particular form for amplitudes, which we express as a black hole ansatz. We explore features of this ansatz, including its locality properties. These amplitudes satisfy neither the Froissart bound, nor apparently the more fundamental property of polynomial boundedness, through which locality is often encoded in an S-matrix framework. Nevertheless, these amplitudes do satisfy a macroscopic form of causality, expressed as a polynomial bound for the forward-scattering amplitude.Comment: 22 pages, harvmac. v2: minor correction

Charged particle environment of Titan during the T9 flyby

The ion measurements of the Cassini Plasma Spectrometer are presented which were acquired on 26 December 2005, during the T9 flyby at Titan. The plasma flow and magnetic field directions in the distant plasma environment of the moon were distinctly different from the other flybys. The near-Titan environment, dominated by ions of Titan origin, had a split signature, each with different ion composition; the first region was dominated by dense, slow, and cold ions in the 16-19 and 28-40 amu mass range, the second region contained only ions with mass 1 and 2, much less dense and less slow. Magnetospheric ions penetrate marginally into region 1, whereas the region-2 ion population is mixed. A detailed analysis has led us to conclude that the first event was due to the crossing of the mantle of Titan, whereas the second one very likely was a wake crossing. The split indicates the non-convexity of the ion-dominated volume around Titan. Both ion distributions are analysed in detail

Jacobi evolution of structure functions: convergence and stability

The Jacobi evolution method has been widely used in the QCD analysis of structure function data. However a recent paper claims that there are serious problems with its convergence and stability. Here we briefly review the evidence for the adequate convergence of the method; and show that there are errors in the above paper which undermine its conclusions.Comment: 6 pages revtex. Shortened version for publication. Some details are omitted, but are still accessible on hep-ph/9901253v

Asymptotics of skew orthogonal polynomials

Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials of random matrices. From there, asymptotics of the skew orthogonal polynomials are derived.Comment: 17 pages, Late

Solution of a Generalized Stieltjes Problem

We present the exact solution for a set of nonlinear algebraic equations $\frac{1}{z_l}= \pi d + \frac{2 d}{n} \sum_{m \neq l} \frac{1}{z_l-z_m}$. These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain \cite{dhar}. These equations are low $d$ (density) ``degenerations'' of more complicated transcendental equation of Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, $x_l = \sum_{m \neq l} 1/(x_l-x_m)$, familiar from Random Matrix theory. It is shown that the solutions of these set of equations is given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a ``Green's function'' and a saddle point technique we determine the asymptotic distribution of zeros.Comment: 19 pages, 4 figure

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review