Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .1. THEORETICAL DEVELOPMENT

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three-dimensional scattering integral equations satisfying constraints of relativistic unitarity and convariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three-dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and convariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations. (C) 1994 Academic Press, Inc.

An interplanetary mission to Neptune system: Gravitational capture and maneuvers around triton

The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Nonlocal asymmetric exclusion process on a ring and conformal invariance

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram, and consequently the values of the current, depend on u and the density of particles. In the special case of half-lling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-lling value.

Complex stochastic boolean systems: comparing bitstrings with the same hamming weight

[EN]A complex stochastic Boolean system (CSBS) is a complex system depending on an arbitrarily large number

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

Contours in Motion

My practice-led research explores and maps workflows for generating experimental creative work involving inertia based motion capture technology. Motion capture has often been used as a way to bridge animation and dance resulting in abstracted visuals outcomes. In early works this process was largely done by rotoscoping, reference footage and mechanical forms of motion capture. With the evolution of technology, optical and inertial forms of motion capture are now more accessible and able to accurately capture a larger range of complex movements. The creative work titled “Contours in Motion” was the first in a series of studies on captured motion data used to generating experimental visual forms that reverberate in space and time. With the source or ‘seed’ comes from using an Xsens MVN - Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. The aim of the creative work was to diverge way from a standard practice of using particle system and/or a simple re-targeting of the motion data to drive a 3d character as a means to produce abstracted visual forms. To facilitate this divergence a virtual dynamic object was tether to a selection of data points from a captured performance. The proprieties of the dynamic object were then adjusted to balance the influences from the human movement data with the influence of computer based randomization. The resulting outcome was a visual form that surpassed simple data visualization to project the intent of the performer’s movements into a visual shape itself. The reported outcomes from this investigation have contributed to a larger study on the use of motion capture in the generative arts, furthering the understanding of and generating theories on practice.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Jauheiden erottuminen

Partikkelisysteemien segregaatio eli erottuminen on ilmiö, jossa tasalaatuisen jauheseoksen komponenteilla on taipumus erota toisistaan. Jauheen erottumistaipumus riippuu partikkelien ominaisuuksista, ympäröivistä olosuhteista ja partikkelien välisistä vuorovaikutuksista. Segregaatiomekanismeja on esitetty kirjallisuudessa valtava määrä ja pienetkin erot partikkelien välisissä ominaisuuksissa ja vuorovaikutuksissa voivat johtaa täysin eri segregaatiomekanismeihin. Segregaatioilmiö on lääketeollisuuden näkökulmasta hyvin keskeinen, eikä sitä tunneta vielä riittävän hyvin, jotta siltä osattaisiin systemaattisesti välttyä. Nykyinen segregaatiotutkimus perustuu suurelta osin yrityksen ja erehdyksen kautta tapahtuvaan oppimiseen. Todellisen segregaatioilmiön ymmärtämiseen tarvittaisiin innovatiivisia tutkimusmenetelmiä. Kokeellisen osan tarkoituksena oli kehittää ja perustestata menetelmä, jolla voidaan tutkia erilaisten partikkelisysteemien erottumiskäyttäytymistä, ja käyttää tätä menetelmää farmaseuttisten rae- ja pellettiseosten segregaation tutkimiseen. Tavoitteena oli todistaa kehitetyn Babel-laitteen toimintaperiaatteen soveltuvuus partikkelisysteemien erottumiskäyttäytymisen tutkimiseen, mutta suoritetut kokeet olivat lähinnä menetelmän ja laitteen testausta. Ongelmiksi muodostuivat Babel-laitteen asettamat rajoitukset, partikkelien sähköistyminen ja partikkelien väliset vuorovaikutukset. Käytetyt suoraviivaiset lähestymistavat eivät riittäneet segregaation aiheuttamiseen Babel-laitteella. Vertikaalisen ravistelun seurauksena syntynyt konvektiopyörre esti segregaation syntymisen. Johtopäätöksenä voidaan sanoa, että Babel-laite mittaa hyvin ja toistettavasti sekä se kykenee erottamaan erikokoiset partikkelit ja erilaiset kokojakaumat toisistaan. Laitteen kehittämistavoitteena olisi saada segregaatio paremmin näkyviin jauheseoksissa ravistelun seurauksena. Tällöin voitaisiin tehdä päätelmiä jauheseoksen erottumistaipumuksesta ja systeemissä vallitsevista erottumismekanismeista. Laitteen ja menetelmän jatkokehittäminen voisi tuottaa hyödyllistä lisätietoa, mikä edesauttaisi segregaation ymmärtämistä ilmiönä entistä paremmin

Dependence of collision frequency on distance between two hard-sphere particles estimated by computer simulation

A Monte Carlo simulation is performed to study the dependence of collision frequency on interparticle distance for a system composed of two hard-sphere particles. The simulation quantitatively shows that the collision frequency drops down sharply as the distance between two particles increases. This characteristic provides a useful evidence for the collision-reaction dynamics of aggregation process for the two-particle system described in the other reference.

Neutron-neutron scattering parameters from the ^3He(d,t)2p and ^3H(d,^3He)2n reactions

The energy spectra of tritons and Helium-3 nuclei from the reactions ³He(d,t)2p, ³H(d,³He)2n, ³He(d,³He)pn, and ³H(d,t)pn were measured between 6° and 20° at a bombarding energy of 10.9 MeV. An upper limit of 5 μb/sr. was obtained for producing a bound di-neutron at 6° and 7.5°. The ³He(d,t)2p and ³H(d,³He)2n data, together with previous measurements at higher energies, have been used to investigate whether one can unambiguously extract information on the two-nucleon system from these three-body final state reactions. As an aid to these theoretical investigations, Born approximation calculations were made employing realistic nucleon-nucleon potentials and an antisymmetrized final state wave function for the five-particle system. These calculations reproduce many of the features observed in the experimental data and indicate that the role of exchange processes cannot be ignored. The results show that previous attempts to obtain information on the neutron-neutron scattering length from the ³H(d,³He)2n reaction may have seriously overestimated the precision that could be attained.