Equilibrium properties of classical systems with long-range forces. BBGKY equation,neutrality, screening,and sum rules

We introduce a generalization of the BBGKY equation to define the equilibrium states for systems with long-range forces and study the properties of such states. We show that there are properties typical of short-range forces (shape independence, normal fluctuations, asymptotic behavior of correlation functions) and others which are typical of long-range forces (possible shape dependence, neutrality, sum rules and screening, abnormal fluctuations, boundedness of the internal electric field). If the force decreases at infinity faster than the Coulomb force, the properties will be those typical of short-range forces; on the other hand, if the force decreases at infinity as the Coulomb force or slower, the properties will be those typical of long-range forces.     

A remark on truncation schemes of cumulant hierarchies

We discuss some problems obtained by truncating a cumulant hierarchy at ordern > 2. We show that such a truncation scheme is not consistent witha in its whole range of definition nonnegative probability function.     

Confidence structures in decision making

Decision making is defined in terms of four elements: the set of decisions, the set of outcomes for each decision, a set-valued criterion function, and the decision maker's value judgment for each outcome. Various confidence structures are defined, which give the decision maker's confidence of a given decision leading to a particular outcome. The relation of certain confidence structures to Bayesian decision making and to membership functions in fuzzy set theory is established. A number of schemes are discussed for arriving atbest decisions, and some new types of domination structures are introduced.This research was partly supported by Project No. NR-047-021, ONR Contract No. N-00014-75-C-0569 with the Center for Cybernetic Studies, The University of Texas, Austin, Texas, and by ONR Contract No. N-00014-69-A-0200-1012 with the University of California, Berkeley, California.     

Systematic and statistical errors in quantitative evaluation using TLC and HPTLC. 2. Internal and external standard methods

The error propagation is given for routine analysis by in situ evaluation in TLC using the methods with internal or external standard. The internal standard method will need four different measurements of peak height or area, while the external standard method uses only two measurements. Therefore in the latter case the error of the spotting volume will cause errors in the determined concentration. By error propagation it can be shown, that the internal standard method gives better results, if the error in measuring peak height or area is less than the error of the spotting volume.     

Simply terminating rewrite systems with long derivations

A term rewrite system is called simply terminating if its termination can be shown by means of a simplification ordering. According to a result of Weiermann, the derivation length function of any simply terminating finite rewrite system is eventually dominated by a Hardy function of ordinal less than the small Veblen ordinal. This bound had appeared to be of rather theoretical nature, because all known examples had had multiple recursive complexities, until recently Touzet constructed simply (and even totally) terminating examples with complexities beyond multiple recursion. This was established by simulating the Hydra battle for all ordinal segments below the proof-theoretic ordinal of Peano arithmetic. By extending this result to the small Veblen ordinal we prove the huge bound of Weiermann to be sharp. As a spin-off we can show that total termination allows for complexities as high as those of simple termination. This paper is part of the authors doctoral dissertation project (under the supervision of Professor A. Weiermann at the University of Münster).The work on this paper was supported by DFG grant WE 2178/2–1 Mathematics Subject Classification (2000): 03D20, 68Q15, 68Q42     

Stabilization of the Hierarchy in Brane-World Scenarios

We consider a class of warped brane models with topology M ₄ × × S¹/Z ₂, where is a D₂-dimensional compact manifold, and two branes are placed at the orbifold fixed points. In a scenario where supersymmetry is broken not far below the cutoff scale, the hierarchy between the electroweak and the Planck scales is generated by a combination of the redshift and the large volume effects. We evaluate the effective potential induced by bulk scalar fields in these models and show that it can stabilize the moduli and the hierarchy without fine-tuning, provided that the internal space is flat. We also comment on the relation between these models and the five-dimensional scalar-tensor models that describe them classically when the compactification scale is small.     

Four Easy Ways to a Faster FFT

The Fast Fourier Transform (FFT) was named one of the Top Ten algorithms of the 20th century , and continues to be a focus of current research. A problem with currently used FFT packages is that they require large, finely tuned, machine specific libraries, produced by highly skilled software developers. Therefore, these packages fail to perform well across a variety of architectures. Furthermore, many need to run repeated experiments in order to re-program their code to its optimal performance based on a given machine's underlying hardware. Finally, it is difficult to know which radix to use given a particular vector size and machine configuration. We propose the use of monolithic array analysis as a way to remove the constraints imposed on performance by a machine's underlying hardware, by pre-optimizing array access patterns. In doing this we arrive at a single optimized program. We have achieved up to a 99.6% increase in performance, and the ability to run vectors up to 8388608 elements larger, on our experimental platforms. Preliminary experiments indicate different radices perform better relative to a machine's underlying architecture.     

Approximating the Approximant: A Numerical Code for Polynomial Compression of Discrete Integral Operators

The action of various one-dimensional integral operators, discretized by a suitable quadrature method, can be compressed and accelerated by means of Chebyshev series approximation. Our approach has a different conception with respect to other well-known fast methods: its effectiveness rests on the smoothing effect of integration, and it works in linear as well as nonlinear instances, with both smooth and nonsmooth kernels. We describe a Matlab toolbox which implements Chebyshev-like compression of discrete integral operators, and we present several numerical tests, where the basic O(n ²) complexity is shown to be reduced to O(mn), with mn.     

Crack Detection in an Embedded Spindle using Broadband Modal Excitation

This paper demonstrates a methodology for detecting cracks in a metal spindle, which is housed within a military vehicle wheel end assembly. A finite element model is used to estimate the undamped natural frequencies of the raw spindle. Additional mass and stiffness is then added to a simplified model of the spindle to simulate sources of variability within the assembly. Spindles are tested outside the wheel end assembly to compare the responses of undamaged and cracked spindles. A hypothesis testing approach is developed to detect the presence of a crack based on damage indices involving the summation and multiplication of spectral energies. Experiments on wheel assemblies mounted on a vehicle with the vehicle lifted off the ground are performed to demonstrate that the wheel assemblies can be nondestructively evaluated to identify cracks of varying depths despite sources of variability due to the presence of the brake drum, lack of repeatability in the sensor attachment, and other issues.     

Solving the AKNS Hierarchy by Its Bilinear Form： Generalized Double Wronskian Solutions

Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.