Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Non-thermal transitions in a model inspired by moral decisions

This work introduces a model in which agents of a network act upon one another according to three different kinds of moral decisions. These decisions are based on an increasing level of sophistication in the empathy capacity of the agent, a hierarchy which we name Piaget's ladder. The decision strategy of the agents is non-rational, in the sense they are arbitrarily fixed, and the model presents quenched disorder given by the distribution of its defining parameters. An analytical solution for this model is obtained in the large system limit as well as a leading order correction for finite-size systems which shows that typical realisations of the model develop a phase structure with both continuous and discontinuous non-thermal transitions.

Climate change and plankton phenology in freshwater: current trends and future commitments

A solid body of empirical, experimental and theoretical evidence accumulated over recent years indicated that freshwater plankton experienced advance in phenology in response to climate change. Despite rapidly growing evidence for phenological changes, we still lack a comprehensive understanding of how climate change alters plankton phenology in freshwater. To overcome current limitations, we need to shed some light on trends and constraints in current research. The goal of this study is to identify current trends and gaps based on analysis of selected papers, by the help of which we can facilitate further advance in the field. We searched the literature for plankton phenology and confined our search to studies where climate change has been proposed to alter plankton phenology and rates of changes were quantified. We did not restrict our search for empirical ontributions; experimental and theoretical studies were considered as well. In the following we discuss the spatio-temporal setting of selected studies, contributions of different taxonomic groups, emerging methodological constraints, measures of phenological trends; and finally give a list of recommendations on how to improve our understanding in the field. The majority of studies were confined to deep lakes with a skewed geographical distribution toward Central Europe, where scientists have long been engaged in limnology. Despite these findings, recent studies suggest that plankton in running waters may experience change in phenology with similar magnitude. Average rate of advancement in phenology of freshwater plankton exceeded those of the marine plankton and the global average. Increasing study duration was not coupled either with increasing contribution of discontinuous data or with increasing rates of phenological changes. Future studies may benefit from i) delivering longterm data across scientific and political boundaries; ii) extending study sites to broader geographical areas with a more explicit consideration of running waters; iii) applying plankton functional groups; iv) increasing the application of satellite data to quantify phytoplankton bloom phenology; v) extending analyses of time series beyond the spring period; vi) using various metrics to quantify variation in phenology; vii) combining empirical, experimental and theoretical approaches; and last but not least viii) paying more attention to emergence dynamics, nonresponding species and trophic mismatch.

Psychic Punishment Costs and Deterrence

In this paper we analyze criminal deterrence in the presence of specific psychic costs of punishments. We consider a dynamic model with three players, analyzing the choices of a representative lawmaker, potential criminal and judge. In our setting the lawmaker decides whether to introduce a fixed punishment enhancement above a chosen threshold of crime level, depending on its popularity among the voters. In reaction, the judge, who is influenced by her own preferences as well as the opinion of her peer group, might change the probability of punishment, through affecting the standard of reasonable doubt. Our results suggest that large discontinuous and mandatory increases in punishment can have unintended effects that are contrary to the stated goal of such punishment enhancements. In equilibrium, when either the judge or her peer group is "anti-punishment" enough, the level of criminal activity might increase in response to the punishment enhancement. This perverse effect is less likely to occur if there is a higher number of peer groups within the "elite", so that a greater extent of self-selection by judges can occur. Our results have relevance for a number of areas outside the traditional criminal justice system as well, such as special courts (such as ecclesiastical or military courts), or the strictness and enforcement of regulations.

Microvariation at the human D1S80 locus

Microvariant allelic polymorphisms have been known since 1966 when Harris, Hubby and Lewontin described the huge store of genetic variation detectable at the polypeptide level. Later Jeffreys used MVR (minisatellite variant repeat) analysis to describe the variation hidden within minisatellite VNTRs and to propose a mutational mechanism.^ The questions I have asked follow these traditions: (1) How much microvariant polymorphism exists at the discrete allele minisatellite D1S80 locus? (2) Do alleles or groups of alleles associate randomly with the flanking markers to form haplotypes? (3) What mechanisms might explain mutations at this locus? What are the phylogenetic relationships among the alleles?^ The minisatellite locus D1S80 (1p35-36), GenBank sequence (Accession # D28507), is a highly polymorphic Variable Number of Tandem Repeat (VNTR) based on a 16 base core. D1S80 alleles are electrophoretically separable into discontinuous sets of equivalent length alleles. Sequence variation or minor length variation within these classes was expected: I have sought to determine the nature of this microvariant heterogeneity by sequencing nominal and variant alleles.^ Alleles were analyzed by Single-Strand Conformation Polymorphism (SSCP) analysis. Sequences were determined to ascertain whether sequence variation or size variation is the major cause of altered electrophoretic migration of microvariant D1S80 alleles. Twenty three alleles from 14 previously typed individuals were sequenced. The individuals were from African American, Caucasian, or Hispanic databases.^ A Tsp509 I restriction site, previously reported as a Hinf I flanking polymorphism, and a 3$\sp\prime$ flanking region BsoF I restriction site polymorphism were identified. There appears to be a strong association of the 5$\sp\prime$ flanking region Hinf I(+) and Tsp509 I(-) site and the 3$\sp\prime$ flanking region BsoF I(-) site with the 18 allele, while the 24 tends to be associated with the Hinf I(-), Tsp509 I(+) and BsoF I(+) sites.^ The general conclusion for this locus is clearly the closer you look, the more you find. D1S80 allelic polymorphisms are primarily due to variation in the number of repeat units and to sequence variation among repeats. The sequenced based gene tree depicts two major classes of alleles which conform to the two most common alleles, reflecting either equivalent age or population size bottlenecks. ^

Repetitive DNA fragments as taxonomic markers for {\it Penaeus\/} sibling taxa (Decapoda: Dendrobranchiata: Penaeidae) from the southern terminus of the Florida peninsula, U.S.A.

Sympatric populations of P. brasiliensis and P. duorarum from Biscayne Bay, Florida, revealed species-specific satellite DNA organizational patterns with the restriction endonuclease EcoRI. The species-specific satellite DNA patterns can be explained as resulting from differential amplification/deletion events having altered monomer arrays after the divergence of these two species. Two discontinuous populations of P. duorarum (Biscayne Bay and Dry Tortugas) were found to exhibit distinct EcoRI satellite fragment patterns; BamHI repetitive fragments specific to the Dry Tortugas P. duorarum population were also detected. In addition, the evolutionary conservation of the Penaeus (Farfantepenaeus) satellites was investigated. The putative conservation of sequences related to one cloned P. duorarum satellite monomer unit suggests that the FTR satellite DNA family may not only be of use as a genome tag to distinguish between sibling and cryptic Penaeus species but may also serve as a probe to better understand decapod crustacean genome organization and evolution. ^

Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

Ammonite biostratigraphy, lithofacies variations, and paleoceanographic implications for Barremian-Aptian sequences of northeastern Mexico

Two Barremian-Aptian sequences studied in Durango and Nuevo Leon States, northeastern Mexico include three lithic units which have been described as the Cupido Formation of Barremian-early Early Aptian age, its lateral equivalent, the Lower Tamaulipas Formation, and the La Peña Formation extending through the early Albian. ^ The present work improves the existing ammonite Aptian biozonation by considering constraints associated with a discontinuous spatial and temporal record of the different taxa within the La Peña Formation. ^ Four ammonite biozones are established: (1) The Dufrenoyia justinae Zone for the late Early Aptian, (2) The Burckhardtites nazasensis/Rhytidoplites robertsi Zone for the middle Aptian, (3) The Cheloniceras inconstans Zone for the early Late Aptian, and (4) The Hypacanthoplites cf. leanzae Zone for the late late Aptian. ^ Also, a detailed sedimentological analysis of the sections shed further light on the possible causes that controlled intermittent occurrences of the ammonites in relation to the prevailing paleoceanographic and paleoecologic conditions in northeastern Mexico during the late Barremian-Aptian. ^ Microfacies analyses show that the upper part of the Cupido facies are represented by biocalcirudite with rudists, biocalcarenites with oolites and algae, and rich benthonic foraminifera assemblages with ostracods. These facies are related to paleoceanographic conditions of sedimentation within a shallow-marine carbonate platform. Its lateral equivalent, deep-water facies extended to the southeast and it is represented by the Lower Tamaulipas Formation, which includes planktonic foraminifera, ostracods, and mollusk and echinoid fragments. The beginning of deposition of the La Peña Formation in the late Early Aptian is characterized by an increase in terrigenous materials and significant decrease in the abundance of benthic fauna. The La Peña Formation is recognized by an alternation of marls and shale limestones containing ammonites, planktonic foraminifera, ostracods, and radiolaria toward the top. Accumulation of the La Peña continued throughout the end of the Aptian and records changes in conditions of sedimentation and productivity in the water column, which abruptly terminated the carbonate deposition in the Cupido Platform. ^ Results of carbon/carbonate content analyses show that changes from the Cupido to the La Peña facies are also characterized by an increase of organic carbon, which indicate the onset of enhanced dysoxic/anoxic conditions in the lower water column. ^

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Development of effective approaches to the large-scale aerodynamic testing of low-rise buildings

Low-rise buildings are often subjected to high wind loads during hurricanes that lead to severe damage and cause water intrusion. It is therefore important to estimate accurate wind pressures for design purposes to reduce losses. Wind loads on low-rise buildings can differ significantly depending upon the laboratory in which they were measured. The differences are due in large part to inadequate simulations of the low-frequency content of atmospheric velocity fluctuations in the laboratory and to the small scale of the models used for the measurements. A new partial turbulence simulation methodology was developed for simulating the effect of low-frequency flow fluctuations on low-rise buildings more effectively from the point of view of testing accuracy and repeatability than is currently the case. The methodology was validated by comparing aerodynamic pressure data for building models obtained in the open-jet 12-Fan Wall of Wind (WOW) facility against their counterparts in a boundary-layer wind tunnel. Field measurements of pressures on Texas Tech University building and Silsoe building were also used for validation purposes. The tests in partial simulation are freed of integral length scale constraints, meaning that model length scales in such testing are only limited by blockage considerations. Thus the partial simulation methodology can be used to produce aerodynamic data for low-rise buildings by using large-scale models in wind tunnels and WOW-like facilities. This is a major advantage, because large-scale models allow for accurate modeling of architectural details, testing at higher Reynolds number, using greater spatial resolution of the pressure taps in high pressure zones, and assessing the performance of aerodynamic devices to reduce wind effects. The technique eliminates a major cause of discrepancies among measurements conducted in different laboratories and can help to standardize flow simulations for testing residential homes as well as significantly improving testing accuracy and repeatability. Partial turbulence simulation was used in the WOW to determine the performance of discontinuous perforated parapets in mitigating roof pressures. The comparisons of pressures with and without parapets showed significant reductions in pressure coefficients in the zones with high suctions. This demonstrated the potential of such aerodynamic add-on devices to reduce uplift forces.

Ammonite biostratigraphy, lithofacies variations, and paleoceanographic implications for barremian-aptian sequences of northeastern Mexico

Two Barremian-Aptian sequences studied in Durango and Nuevo Leon States, northeastern Mexico include three lithic units which have been described as the Cupido Formation of Barremian-early Early Aptian age, its lateral equivalent, the Lower Tamaulipas Formation, and the La Pena Formation extending through the early Albian. The present work improves the existing ammonite Aptian biozonation by considering constraints associated with a discontinuous spatial and temporal record of the different taxa within the La Pena Formation. Four ammonite biozones are established: 1) The Dufrenoyia justinae Zone for the late Early Aptian, 2) The Burckhardtites nazasensis/Rhytidoplites robertsi Zone for the middle Aptian, 3) The Cheloniceras inconstans Zone for the early Late Aptian, and 4) The Hypacanthoplites cf. leanzae Zone for the late late Aptian. Also, a detailed sedimentological analysis of the sections shed further light on the possible causes that controlled intermittent occurrences of the ammonites in relation to the prevailing paleoceanographic and paleoecologic conditions in northeastern Mexico during the late Barremian-Aptian. Microfacies analyses show that the upper part of the Cupido facies are represented by biocalcirudite with rudists, biocalcarenites with oolites and algae, and rich benthonic foraminifera assemblages with ostracods. These facies are related to paleoceanographic conditions of sedimentation within a shallow-marine carbonate platform. Its lateral equivalent, deep-water facies extended to the southeast and it is represented by the Lower Tamaulipas Formation, which includes planktonic foraminifera, ostracods, and mollusk and echinoid fragments. The beginning of deposition of the La Pena Formation in the late Early Aptian is characterized by an increase in terrigenous materials and significant decrease in the abundance of benthic fauna. The La Pena Formation is recognized by an alternation of marls and shale limestones containing ammonites, planktonic foraminifera, ostracods, and radiolaria toward the top. Accumulation of the La Pena continued throughout the end of the Aptian and records changes in conditions of sedimentation and productivity in the water column, which abruptly terminated the carbonate deposition in the Cupido Platform. Results of carbon/carbonate content analyses show that changes from the Cupido to the La Pena facies are also characterized by an increase of organic carbon, which indicate the onset of enhanced dysoxic/anoxic conditions in the lower water column.