Search

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Актуальность. В статье рассмотрены существующие подходы к актуальной задаче минимаксного сглаживания стационарного случайного процесса в условиях, когда наблюдаемый процесс является аддитивной смесью взаимно некоррелированных полезной составляющей и помехи, о спектральных плотностях которых имеется частичная информация в форме интервальных изменений их значений, а также их интервальные моментные неравенства, структурно содержащие одинаковые по абсолютной величине, небольшие симметричные отклонения неопределенности от заданных границ своих интервальных ограничений, которым они удовлетворяют. Дана точная постановка интервальной задачи линейного минимаксного сглаживания стационарного случайного процесса в условиях существования согласованной седловой точки интервальной согласованной функции Лагранжа. Цель статьи. Целью является изложение идеи решения задачи линейного минимаксного сглаживания стационарного случайного процесса с учетом интервальных моментных ограничений, которым удовлетворяют эти параметры. Метод. На базе предложенной идеи сформулирован и обоснован метод детерминизации, позволяющий решить задачу линейной минимаксной интерполяции при интервальной неопределенности параметров путем ее сведения к двум полностью определенным задачам оптимизации того же типа. Новизна. Сформулирована и доказана теорема, определяющая необходимое и достаточное условие существования решения выпуклой задачи линейной минимаксной интерполяции при интервальной неопределенности параметров в условиях существования согласованной седловой точки интервальной согласованной функции Лагранжа. Результат. Построен 4-шаговый алгоритм решения задачи линейного минимаксного сглаживания стационарного случайного процесса при интервальной неопределенности параметров путем ее сведения к двум полностью определенным задачам оптимизации того же типа. Используемый детерминизационный подход сводит решение игры с недетерминированными параметрами интервального типа к решению двух граничных игр с детерминированными стратегиями и функциями выигрыша с использованием аппарата интервальной арифметики в условиях существования согласованной седловой точки интервальной согласованной функции Лагранжа. Дается пример, иллюстрирующий предлагаемый метод анализа., Relevance. The article considers existing approaches to the actual problem of minimax smoothing of a stationary random process under conditions when the observed process is an additive mixture of mutually uncorrelated useful component and interference, the spectral densities of which have partial information in the form of interval changes in their values, as well as their interval moment inequalities, structurally containing the same absolute value, small symmetric deviations of uncertainty from the specified limits of their interval restrictions, which they satisfy. An exact statement of the interval problem of linear minimax smoothing of a stationary random process is given under the conditions of existence of a consistent saddle point of an interval consistent Lagrange function. Purpose. The aim of the article is to present the idea of solving the problem of linear minimax smoothing of a stationary random process, taking into account the interval moment constraints that these parameters satisfy. This idea is based on the rules of the mathematical theory of comparison of intervals which allows replace comparison of intervals and determinization of maximal and minimal interval by comparising their lower and upper bounds. Methods. On the basis of the the proposed idea the determinization method is formulated and justified that allows solving the problem of linear minimax interpolation with interval parameter uncertainty by reducing it to two fully defined optimization problems of the same type. Novelty. We formulate and prove a theorem that defines a necessary and sufficient condition for the existence of a solution to a convex linear minimax interpolation problem with interval parameter uncertainty under conditions of existence of a consistent saddle point of an interval consistent Lagrange function. Result. A 4-step algorithm for solving the problem of linear minimax smoothing of a stationary random process with interval parameter uncertainty is constructed by reducing it to two fully defined optimization problems of the same type. The proposed deterministic approach reduces the solution of a game with nondeterministic parameters of the interval type to the solution of two boundary games with deterministic strategies and winning functions using the apparatus of interval arithmetic under the conditions of the existence of a consistent saddle point of the interval consistent Lagrange function. An example illustrating the proposed method of analysis is given

This paper proposes a method to control microcracks in fragile samples of solid bodies. Rock samples were tested and analyzed to prove high performance and time efficiency as well as high sensitivity of the method.

In this paper we consider fractional higher-order stochastic differential equations of the form \[ \left ( \mu + c_\alpha \frac{d^\alpha } {dt^\alpha } \right )^\beta X(t) = \mathcal{E} (t) , \quad \mu >0,\; \beta >0,\; \alpha \in (0,1) \cup \mathbb{N} \] where $\mathcal{E} (t)$ is a Gaussian white noise. We obtain explicitly the covariance functions and the spectral densities of the stochastic processes satisfying the above equations.

The emergence of complex behavior out of simple elementary building blocks is a typical property of condensed matter systems. While the individual constituents may be well-studied, strongly interacting many-particle systems can give rise to novel collective behavior that can not be understood by considering the individual properties alone. Effective models are a powerful tool to handle this complexity: Instead of aiming at a full description a complex many-particle system on the high-energy scale, an effective model covers only those degrees of freedom which are essential for the low-energy physics. While the high-energy degrees of freedom are integrated out, they influence the low-energy degrees of freedom due to a renormalization of the effective coupling constants. In particular, the concept of the quasi-particle allows for the description of a strongly-interacting many-particle excitations in terms of a simple objects with similar degrees of freedom as a dispersive elementary particle, which gives rise to phenomena like quasi-particle bound states or quasi-particle decay. This thesis aims at the application and methodological improvement of a systematic and well-controlled framework to derive effective low-energy models, denoted as Continuous Unitary Transformations (CUT). In this method, a Hamiltonian is mapped continuously to an effective basis, in which the low-energy degrees of freedom can be interpreted as quasi-particles. Mathematically, the transformation is parametrized by a flow parameter and is represented as a differential equation, denoted as flow equation, while the direction of the transformation is controlled by the generator scheme. As foundation of our studies, we use the sCUT method, in which the types of possible interaction terms are fixed by a truncation scheme. In a common project, we established a new flavor of CUT, called epCUT. It allows us to derive the effective Hamiltonian in a perturbation series. In contrast to the already existent pCUT method, epCUT can handle system with a non-equidistant spectrum as well. Moreover, we discovered the deepCUT method, the non-perturbative twin of epCUT. While it bears large similarities to sCUT, it replaces the cumbersome definition of an appropriate truncation scheme by the order of the flow equation system. Compared to sCUT, deepCUT offers a larger robustness while the ambiguities of the truncation scheme are eliminated. My contribution comprises the computational, parallelized construction of the flow equation system as well. In another project, we investigated the breakdown of the conventional, particle-sorting generator schemes in system with strongly overlapping quasi-particle sub-spaces and identified the emergence of a spectrum unbounded from below due to truncation errors as origin of the divergence. As a testing ground, we used a system of two coupled bosonic degrees of freedom. To overcome these problems, we developed a family of three novel variational generator schemes, denoted as scalar, vectorial and tensorial optimization. After this, we investigated the dimerized, two-dimensional S=1/2 Heisenberg model with an emphasis on the quantum phase transition between a magnetically disordered and a magnetically ordered phase using sCUT. Parametrizing the starting point by a variational parameter, we were able to describe the spontaneous breaking of the SU(2) spin symmetry by CUT for the first time. We were able to calculate the ground state energy and the dispersion of triplons, and magnons, respectively, in both phases. However, we were not able to provide quantitative results for the spontaneous magnetization. Furthermore, we found a way to derive an optimal starting point for the integration of the flow equations that is independent on the particularities of the model and does not require a parametrization by a variational parameter. As a further application, we analyzed the S=1 Heisenberg chain by means of deepCUT. To this end, we mapped the system to an extended S=1/2 Heisenberg ladder with the help of a variational parameter. Using the variational generator schemes developed before, we were able to decouple the low-energy spectrum and to calculate spectral densities. In this investigation, we found an indication for a S=0 bound state. Furthermore, we were able to find some signs of spontaneous quasi-particle decay, but a quantitatively correct description is pending., Das Ganze ist mehr als die Summe seiner Teile - so ließe sich das Grundproblem der Physik kondensierter Materie in aller Kürze zusammenfassen. Auch wenn das Verhalten aller Grundbausteine im Detail bekannt ist, so können sich durch starke Wechselwirkungen vieler Teilchen untereinander neuartige, kollektive Phänomene ergeben, die sich durch das Studium der einzelnen Bestandteile nur schwerlich verstehen. Einen Ausweg aus dieser Problematik bieten effektive Modelle: Anstatt ein komplexes System mit vielen Freiheitsgraden auf hohen Energieskalen vollständig zu beschreiben, bildet ein effektives Modell nur die Freiheitsgrade ab, die bei niedrigen Energien wichtig sind. Hochenergetische Freiheitsgrade werden aus dem effektiven Modell weggelassen, ihre indirekten Auswirkungen auf niedrige Energien aber durch modifizierte, effektive Wechselwirkungen berücksichtigt. Als besonders hilfreich hat sich in der Festkörperphysik das Modell des Quasiteilchens erwiesen: Eine Anregung eines Systems vieler, stark wechselwirkender Teilchen wird durch ein Objekt beschrieben, das sich wie ein einzelnes Elementarteilchen bewegen, Bindungen eingehen und zerfallen kann. Die vorliegende Arbeit widmet sich dem Einsatz und der Verbesserung eines Verfahrens zur systematischen, kontrollierten Ableitung effektiver Niederenergiemodelle: Die Methode der kontinuierlichen, unitären Transformationen (englisch: Continuous Unitary Transformations, CUT). Hierbei wird der Hamiltonoperator eines physikalischen Systems kontinuierlich durch Lösen einer Differentialgleichung, der Flussgleichung, in eine effektive Darstellung überführt, bei der die Niederenergiefreiheitsgrade als Quasiteilchen interpretiert werden können. Die Art der Transformation wird hierbei über das Generatorschema der CUT gesteuert. Als Näherung geht in der sCUT (selbstähnliche CUT, englisch: self-similar CUT), der hier als Grundlage dienenden Variante, das Trunkierungsschema ein. Als methodische Verbesserung wurde in einem gemeinsamen Projekt eine neue Variante der CUT, genannt (erweiterte perturbative CUT, englisch: enhanced perturbative CUT), etabliert, die eine Beschreibung des effektiven Hamiltonoperators des Systems als Reihe im Sinne einer Störungsrechnung bis zu einer vorgegebenen erlaubt. Dieser Ansatz ist allgemeiner als die bereits existierende pCUT Methode (perturbative CUT, englisch: perturbative CUT), da sich auch Systeme mit nicht äquidistantem Energiespektrum behandeln lassen. Darüber hinaus wurde mit deepCUT (direkt ausgewertete epCUT, englisch: directly evaluated epCUT) eine verwandte, nichtperturbative Methode entdeckt, die der sCUT ähnelt, aber das komplizierte Trunkierungsschema durch die Ordnung im Sinne einer epCUT-Rechnung ersetzt. Die deepCUT zeichnet sich hierbei gegenüber der sCUT durch eine höhere Robustheit und geringere Mehrdeutigkeit aus. Einen besonderen Anteil meiner Arbeit nahm hierbei die rechnergestützte, parallelisierte Implementierung des Aufstellens der Flussgleichungen. In einem weiteren Projekt wurde das Versagen der bisher üblichen teilchensortierenden Generatoren in Systemen mit stark überlappenden Quasiteilchenräumen untersucht und das Auftreten eines zu niedrigen Energien unbeschränkten Spektrums als Ursache festgestellt. Als Beispielsystem dienten hierbei zwei gekoppelte bosonische Freiheitsgrade. Daraufhin entwickelten wir eine Familie aus drei neuartigen Generatorschemata, die skalare, vektorielle und tensorielle Optimierung, die diese Probleme umgehen. Danach untersuchten wir das dimerisierte, zweidimensionale S=1/2 Heisenberg mit besonderem Schwerpunkt auf dem Quantenphasenübergang zwischen der magnetisch ungeordneten und der magnetisch geordneten Phase mittels sCUT. Durch Parametrisierung des Startpunktes mit einem Variationsparameter gelang uns erstmals die Beschreibung der spontanen Brechung der kontinuierlichen SU(2) Spinsymmetrie mittels CUT. Wir konnten die Grundzustandsenergie und die Disperisionsrelationen der Triplonen und Magnonen in beiden Phasen bestimmen, erhielten jedoch keine zufriedenstellenden Resultate für die spontane Magnetisierung. Ferner entwickelten wir in einem verwandten, eindimensionalen System ein Verfahren, um modellunabhängig und ohne Parametrisierung durch einen Variationsparameter einen optimalen Startzustand zu wählen. Als weitere Anwendung analysierten wir die S=1 Heisenbergkette mittels deepCUT. Hierzu bildeten wir das System unter Einführung eines Variationsparameters auf eine S=1/2 Heisenbergkette ab. Unter Verwendung der zuvor entwickelten variationellen Generatorschemata gelang uns trotz des starken Überlapps zwischen Zwei- und Dreiteilchenraum die Entkopplung des Niederenergiespektrums und die Berechnung spektraler Dichten. Wir fanden hierbei Anhaltspunkte für einen gebundenen S=0 Zustand. Weiterhin konnten wir wichtige Merkmale für den Zerfall eines Triplons in zwei Triplonen nachweisen; eine vollständige und quantitative Beschreibung steht jedoch noch noch aus.

Quasi arithmetic and Archimedean functionals are used to build new classes of spectral densities for processes defined on any d-dimensional lattice $${\mathbb{Z}^d}$$ and random fields defined on the d-dimensional Euclidean space $${\mathbb{R}^d}$$ , given simple margins. We discuss the mathematical features of the proposed constructions, and show rigorously as well as through examples, that these new classes of spectra generalize celebrated classes introduced in the literature. Additionally, we obtain permissible spectral densities as linear combinations of quasi arithmetic or Archimedean functionals, whose associated correlation functions may attain negative values or oscillate between positive and negative ones. We finally show that these new classes of spectral densities can be used for nonseparable processes that are not necessarily diagonally symmetric.

A 0.2 mu s molecular dynamics simulation of ubiquitin in water is presented, which allows us to assess both the global tumbling in solution and the internal dynamics. The latter reveals slow motions outside the classical NMR timewindow, in agreement with recent RDC and cross-correlation measurements. Analysis of back-calculated relaxation rates using the classical NMR model-free approach reproduces the amplitudes of internal motions expressed in the order parameter, while it severely underestimates the corresponding time scales present in the simulation.

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities., Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000364

7 pp.-- PACS nrs.: 43.55.Br, 43.55.Cs.-- Comunicación presentada en los siguientes congresos: II Congreso Iberoamericano de Acústica. XXXI Congreso Nacional de Acústica – TecniAcústica 2000. II Jornadas Iberoamericanas de Ultrasonidos. II Congreso Ibérico de Acústica. EAA Symposium on Architectural Acoustics (Madrid, 16-20 Octubre 2000)., Publicado también en número especial de la Revista de Acústica, Vol. XXXI, año 2000., [EN] In 1965 A. Lara et al. described, in a short publication, the main acoustic characteristics of the reverberant room of the Instituto de Acústica. Since that time some changes have significantly improved its features. In parallel, international standards dealing with precision methods on measuring sound absorption and sound power have experienced a noteworthy progress and contains new requirements to fulfil by reverberant room facilities., In this work some recent characterisations of the above mentioned reverberant room are described. Reverberation time as a function of frequency is analysed regarding UNE EN 20354 (ISO 354) standard. Normal modes and spectral densities particularly in the low frequency range are described and compared to classical polynomial approaches. Analysis of diffusion covers most recent theories and proposed metrics, by using prospections along closed trajectories and fixed points. Practical conclusions are given of interest in sound power measurements and random vibration techniques in solids excited by airborne sound., [ES] Aparte del interés teórico que pueda tener un campo difuso, la utilidad práctica de disponer de una buena cámara reverberante se deriva de la sencillez experimental en la medición de la absorción sonora de materiales y objetos, de la potencia acústica de fuentes sonoras y de la exploración de vibraciones aleatorias en sólidos excitados por vía aérea. Es fundamental por consiguiente alcanzar grados suficientes de aproximación a la situación ideal de difusión. Las normas internacionales de medición tratan de establecer condiciones mínimas de aproximación y se han investigado y desarrollado magnitudes de razonable fácil determinación que garanticen un adecuado cumplimiento., Lara et al. presentaron en el Congreso Internacional de Acústica, celebrado en Lieja en 1965, las características y propiedades de la cámara reverberante del Instituto de Acústica del CSIC. Desde entonces se han realizado nuevos tratamientos que han producido indudables mejoras en su comportamiento. Paralelamente las normas de medición de las distintas magnitudes medibles en estos recintos han progresado notablemente tanto en la definición como en los niveles de exigencias de las prestaciones exigibles a estos recintos. La teoría de campos acústicos difusos también ha experimentado un gran progreso y se han desarrollado y propuesto nuevas y mas fundamentadas métricas para la medida del grado de difusión de un recinto concreto., Parece pues un buen momento para difundir las propiedades actuales de la citada cámara reverberante del IA-CSIC, a la luz del grado actual de progreso teórico y normativo. Este es el objetivo del presente trabajo., El presente trabajo ha contado con la financiación del Plan Nacional de I+D nº AMB 98-1029-C04-01 y con la del contrato de investigación "Respuesta dinámica vibratoria de estructuras aerospaciales sometidas a excitaciones acústicas de alta intensidad, por vía aérea" entre CASA y el Instituto de Acústica.

During the last years several papers utilizing the Random Decrement transform as a basis for extraction of modal parameters from the response of linear systems subjected to unknown ambient loads have been presented. Although the Random Decrement technique was developed in a decade starting from the introduktion in 1968 the technique seems still to be attractive. This is probably due to the simplicity and the speed of the algorithm and the fact that the theory of the technique has been extended by introducing statistical measures such as correlation functions or spectral densities. The purpose of this paper is to present a state-of-the-art description of the Random Decrement technique where the statistical theory is outlined and examples are given. But also new results such as estimation of frequency response functions and quality assessment are introduced. Special attention is given to the theoretical background for the application of the Random Decrement transform to ambient measurements.

Liquid crystal phases are typically formed by molecules having several degrees of internal freedom. These systems exhibit, therefore, complex dynamics, with internal motions superimposed on the rot...

By considering Fokker-Planck equation in the asymptotic limit, that is when strong potential act on the particles, a simplified description of its solutions is achievable. The asymptotic behaviour of the Fokker-Planck equation is analyzed for one-dimensional motions in the context of the correlation functions formalism. Much emphasis is placed on the single-minimum potential and analytical relations are derived in all the range of friction, from the zero-friction limit where the process of velocity relaxation is absent, to the diffusional regime. The planar rotator is used as a test case for comparing the asymptotic form of the spectral densities with the numerical solution of the Fokker-Planck operator. By incorporating known results of the theory of activated rate processes, the analysis is extended to multiminima potentials

Une analyse probabiliste de la cinétique des réacteurs permet de décrire le comportement aléatoire des fluctuations, de certaines grandeurs physiques autour de leur valeur moyenne. Ces fluctuations peuvent être caractérisées, par exemple, par leur densité spectrale. Dans ce travail, les populations des neutrons, des précurseurs et la température du combustible sont considérées comme des grandeurs aléatoires. Le processus décrivant le comportement du réacteur, qui est considéré comme ponctuel, est supposé markovien, ce qui permet de le décrire par l'équation de Chapman-Kolmogoroff. Les approximations de Fokker-Planck et de Langevin permettent de déterminer les densités spectrales énergétiques neutronique et thermique, ainsi que celle d'interaction neutrons-température du combustible. Une analyse de ces dernières est effectuée afin de déterminer les domaines dans lesquels certains paramètres, comme la puissance du réacteur, le coefficient d'échange thermique et le coefficient de température du combustible, ont une influence. Le temps de vie moyen des neutrons et le coefficient d'échange thermique peuvent se déduire à partir des densités spectrales.

It is shown how the Lanczos algorithm (LA) can be applied to classical systems, leading naturally to a continued fraction representation equivalent to that obtained by Mori for the correlation functions. The relation of the LA to the method of moments suggests its utility for study of the theoretical structure, while the computational efficiency of the LA suggests its use for computer calculation of correlation functions. (AIP)