A study in the mathematical theory of the conduction of heat

This work represents a study in the application of the Laplace Trans format! on method to the Theory of Conduction of Heat; with a few exceptions indicated in footnotes, the derivation by this method of all the results is new. In Chapters II, VI, VIII, and X which contain collections of results, some of these are classical and given for completeness, and some are new* Almost all the results of Chapters I, III, IV, VII, and IX are believed to be new# None of this work has been submitted for any degree, and it is entirely my own with the exception of Chapters I and X, which have been written for publication in collaboration with Professor Carslaw. These are included here since they form an essential part of the whole scheme; the problems considered were solved independently and published jointly. The parts of this thesis which the referee may deem suitable will be published as soon as possible. Chapters I, VII, and X, and portion of Chapter I1/ have already been published, and Chapter III, and portions of Chapters VIII and IX are in the press# It is my pleasure to adknowledge my great indebtedness to Professor Carslaw who not only aroused my interest in the subject, but in the course of a frequent correspondence extending over several years has been most generous with advice and criticism# I am also indebted to Miss M. E. Clarke for her assistance with the computations of Chapter V and for the preparation of the typescript

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Post-injection normal closure of fractures as a mechanism for induced seismicity

Understanding the controlling mechanisms underlying injection-induced seismicity is important for optimizing reservoir productivity and addressing seismicity-related concerns related to hydraulic stimulation in Enhanced Geothermal Systems. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations, and the shear slip of pre-existing fractures. Previous experiments indicate that fracture deformation in the normal direction reverses as the pressure decreases, e.g., at the end of stimulation. We hypothesize that this normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for post-injection seismicity. To test this hypothesis, hydraulic stimulation is modeled by numerically coupling fracture deformation, pressure diffusion and stress alterations for a synthetic geothermal reservoir in which the flow and mechanics are strongly affected by a complex three-dimensional fracture network. The role of the normal closure of fractures is verified by comparing simulations conducted with and without the normal closure effect

Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

A Model for Force Fluctuations in Bead Packs

We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for force distribution function for this model, including exact results for certain contact angle probability distributions, with numerical simulations of force distributions in random sphere packings. This model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings

Histological, Immunohistological, and Clinical Features of Merkel Cell Carcinoma in Correlation to Merkel Cell Polyomavirus Status

Merkel cell carcinoma is a rare, but highly malignant tumor of the skin with high rates of metastasis and poor survival. Its incidence rate rises and is currently about 0.6/100000/year. Clinical differential diagnoses include basal cell carcinoma, cyst, amelanotic melanoma, lymphoma and atypical fibroxanthoma. In this review article clinical, histopathological and immunhistochemical features of Merkel cell carcinoma are reported. In addition, the role of Merkel cell polyomavirus is discussed

Unexpected cell type-dependent effects of autophagy on polyglutamine aggregation revealed by natural genetic variation in C. elegans.

BACKGROUND: Monogenic protein aggregation diseases, in addition to cell selectivity, exhibit clinical variation in the age of onset and progression, driven in part by inter-individual genetic variation. While natural genetic variants may pinpoint plastic networks amenable to intervention, the mechanisms by which they impact individual susceptibility to proteotoxicity are still largely unknown. RESULTS: We have previously shown that natural variation modifies polyglutamine (polyQ) aggregation phenotypes in C. elegans muscle cells. Here, we find that a genomic locus from C. elegans wild isolate DR1350 causes two genetically separable aggregation phenotypes, without changing the basal activity of muscle proteostasis pathways known to affect polyQ aggregation. We find that the increased aggregation phenotype was due to regulatory variants in the gene encoding a conserved autophagy protein ATG-5. The atg-5 gene itself conferred dosage-dependent enhancement of aggregation, with the DR1350-derived allele behaving as hypermorph. Surprisingly, increased aggregation in animals carrying the modifier locus was accompanied by enhanced autophagy activation in response to activating treatment. Because autophagy is expected to clear, not increase, protein aggregates, we activated autophagy in three different polyQ models and found a striking tissue-dependent effect: activation of autophagy decreased polyQ aggregation in neurons and intestine, but increased it in the muscle cells. CONCLUSIONS: Our data show that cryptic natural variants in genes encoding proteostasis components, although not causing detectable phenotypes in wild-type individuals, can have profound effects on aggregation-prone proteins. Clinical applications of autophagy activators for aggregation diseases may need to consider the unexpected divergent effects of autophagy in different cell types

Trauma histories among justice-involved youth: findings from the National Child Traumatic Stress Network.

BackgroundUp to 90% of justice-involved youth report exposure to some type of traumatic event. On average, 70% of youth meet criteria for a mental health disorder with approximately 30% of youth meeting criteria for post-traumatic stress disorder (PTSD). Justice-involved youth are also at risk for substance use and academic problems, and child welfare involvement. Yet, less is known about the details of their trauma histories, and associations among trauma details, mental health problems, and associated risk factors.ObjectiveThis study describes detailed trauma histories, mental health problems, and associated risk factors (i.e., academic problems, substance/alcohol use, and concurrent child welfare involvement) among adolescents with recent involvement in the juvenile justice system.MethodThe National Child Traumatic Stress Network Core Data Set (NCTSN-CDS) is used to address these aims, among which 658 adolescents report recent involvement in the juvenile justice system as indexed by being detained or under community supervision by the juvenile court.ResultsAge of onset of trauma exposure was within the first 5 years of life for 62% of youth and approximately one-third of youth report exposure to multiple or co-occurring trauma types each year into adolescence. Mental health problems are prevalent with 23.6% of youth meeting criteria for PTSD, 66.1% in the clinical range for externalizing problems, and 45.5% in the clinical range for internalizing problems. Early age of onset of trauma exposure was differentially associated with mental health problems and related risk factors among males and females.ConclusionsThe results indicate that justice-involved youth report high rates of trauma exposure and that this trauma typically begins early in life, is often in multiple contexts, and persists over time. Findings provide support for establishing trauma-informed juvenile justice systems that can respond to the needs of traumatized youth

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions