Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Comparison of different methods for variable selection

In chemistry for chemical analysis of a multi-component sample or quantitative structure-activity/property relationship (QSAR/QSPR) studies, variable selection is a key step. In this study, comparisons between different methods were performed. These methods include three classical methods such as forward selection, backward elimination and stepwise regression; orthogonal descriptors; leaps-and-bounds regression and genetic algorithm. Thirty-five nitrobenzenes were taken as the data set. From these structures quantum chemical parameters, topological indices and indicator variable were extracted as the descriptors for the comparisons of variable selections. The interesting results have been obtained. (C) 2001 Elsevier Science B.V. All rights reserved.

A comparison between classical techniques and eigenstructure assignment in the design of a longitudinal instrument landing system

Although modern control techniques such as eigenstructure assignment have been given extensive coverage in control literature there is a reluctance to use them in practice as they are often not believed to be as `visible' or as simple as classical methods. A simple aircraft example is used, and it is shown that eigenstructure assignment can be used easily to produce a more viable controller than with simple classical techniques.

A comparison among different spectrum compatible earthquake simulation methods

The need for the simulation of spectrum compatible earthquake time histories has existed since earthquake engineering for complicated structures began. More than the safety of the main structure, the analysis of the equipment (piping, racks, etc.) can only be assessed on the basis of the time history of the floor in which they are contained. This paper presents several methods for calculating simulated spectrum compatible earthquakes as well as a comparison between them. As a result of this comparison, the use of the phase content in real earthquakes as proposed by Ohsaki appears as an effective alternative to the classical methods. With this method, it is possible to establish an approach without the arbitrary modulation commonly used in other methods. Different procedures are described as is the influence of the different parameters which appear in the analysis. Several numerical examples are also presented, and the effectiveness of Ohsaki's method is confirmed.

Physics-inspired methods for networking and communications

Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior into simple local interactions. Thus, large-scale problems can be solved or approximated in a distributed manner with iterative lightweight local messaging. This survey discusses how statistical physics methodology can provide efficient solutions to hard network problems that are intractable by classical methods. We highlight three typical examples in the realm of networking and communications. In each case we show how a fundamental idea of statistical physics helps solve the problem in an efficient manner. In particular, we discuss how to perform multicast scheduling with message passing methods, how to improve coding using the crystallization process, and how to compute optimal routing by representing routes as interacting polymers.

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Integrated surface-ground water modeling in wetlands with improved methods to simulate vegetative resistance to flow

In topographically flat wetlands, where shallow water table and conductive soil may develop as a result of wet and dry seasons, the connection between surface water and groundwater is not only present, but perhaps the key factor dominating the magnitude and direction of water flux. Due to their complex characteristics, modeling waterflow through wetlands using more realistic process formulations (integrated surface-ground water and vegetative resistance) is an actual necessity. This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%. The coupling of FLO-2D model with MODFLOW-2005 model and the incorporation of the dynamic effect of flow resistance due to vegetation performed in the new modeling tool WHIMFLO-2D is an important contribution to the field of numerical modeling of hydrologic flow in wetlands.

Integrated Surface-Ground Water Modeling in Wetlands With Improved Methods to Simulate Vegetative Resistance to Flow

This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%.

Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.

Cryptanalysis of block ciphers with overdefined systems of equations

Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds N r r. In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt’00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure. The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in N r> , with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.

Estimation of light interception in research environments: A joint approach using directional light sensors and 3D virtual plants applied to sunflower (Helianthus annuus) and Arabidopsis thaliana in natural and artificial conditions

Light interception is a major factor influencing plant development and biomass production. Several methods have been proposed to determine this variable, but its calculation remains difficult in artificial environments with heterogeneous light. We propose a method that uses 3D virtual plant modelling and directional light characterisation to estimate light interception in highly heterogeneous light environments such as growth chambers and glasshouses. Intercepted light was estimated by coupling an architectural model and a light model for different genotypes of the rosette species Arabidopsis thaliana (L.) Heynh and a sunflower crop. The model was applied to plants of contrasting architectures, cultivated in isolation or in canopy, in natural or artificial environments, and under contrasting light conditions. The model gave satisfactory results when compared with observed data and enabled calculation of light interception in situations where direct measurements or classical methods were inefficient, such as young crops, isolated plants or artificial conditions. Furthermore, the model revealed that A. thaliana increased its light interception efficiency when shaded. To conclude, the method can be used to calculate intercepted light at organ, plant and plot levels, in natural and artificial environments, and should be useful in the investigation of genotype-environment interactions for plant architecture and light interception efficiency. This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Heat-Capacity Measurements - Progress In Experimental-Techniques

The heat capacity of a substance is related to the structure and constitution of the material and its measurement is a standard technique of physical investigation. In this review, the classical methods are first analyzed briefly and their recent extensions are summarized. The merits and demerits of these methods are pointed out. The newer techniques such as the a.c. method, the relaxation method, the pulse methods, the laser flash calorimetry and other methods developed to extend the heat capacity measurements to newer classes of materials and to extreme conditions of sample geometry, pressure and temperature are comprehensively reviewed. Examples of recent work and details of the experimental systems are provided for each method. The introduction of automation in control systems for the monitoring of the experiments and for data processing is also discussed. Two hundred and eight references and 18 figures are used to illustrate the various techniques.

Conformationally restricted formyl methionyl tripeptide chemoattractants: a three-dimensional structure-activity study of analogs incorporating a C alpha,alpha-dialkylated glycine at position 2

The conformationally restricted CHO-L-Met-Xxx-L-Phe-OY (where Xxx = Aib, Ac3c, Ac5c, Ac6c, and Ac7c; Y = H, Me) tripeptides, analogs of the chemoattractant CHO-L-Met-L-Leu-L-Phe-OH, have been synthesized in solution by classical methods and fully characterized. Compounds were compared to determine the combined effect of backbone conformational preferences and side-chain bulkiness on the relation of three-dimensional structure to biological activity. Each peptide was tested for its ability to induce granule enzyme secretion from rabbit peritoneal polymorphonuclear leukocytes. In parallel, a conformational analysis on the CHO-blocked peptide and their tertbutyloxycarbonylated synthetic precursors was performed in the crystal state and in solution using X-ray diffraction, infrared absorption, and 1H nuclear magnetic resonance. The biological and conformational data are discussed in relation to the proposed model of the chemotactic peptide receptor of rabbit neutrophils.

S-matrix for magnons in the D1-D5 system

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS(3) x S-3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.