A Gradient Crystal Plasticity Theory Based on an Extended Energy Balance

An overview of different methods for the derivation of extended continuum models is given. A gradient plasticity theory is established in the context of small deformations and single slip by considering the invariance of an extended energy balance with respect to Euclidean transformations, where the plastic slip is considered as an additional degree of freedom. Thermodynamically consistent flow rules at the grain boundary are derived. The theory is applied to a two- and a three-phase laminate

A Revision of Clausius Work on the Second Law. 1. On the Lack of Inner Consistency of Clausius Analysis Leading to the Law of Increasing Entropy

Abstract: This paper, the first in a series of four, will expose the lack of inner consistency of the analysis through which Clausius re-expressed the second law of thermodynamics: "Heat cannot, of itself, pass from a colder to a hotter body", as the law of increasing entropy: "The entropy of the universe tends to a maximum". In the two following papers the flaw in Clausius analysis producing the said lack of consistency will be located, corrected and some of its consequences, discussed. Among them the one stating that the identification of the two above written statements of the second law is valid only under certain circumstances. In the fourth and fina

Duhem's Balancing Act: Quasi-Static Reasoning in Physical Theory

The celebrated philosopher-physicist Pierre Duhem appears to maintain virtually contradictory views. On the one hand, he claims that science does not aim to explain natural phenomena, where he assumes that an “explanation” strives to reveal the natural world underpinnings hiding “behind the veil” of observable phenomena. Despite these strong disavowals, he also insists that successful scientific theories should converge on “natural classifications” which allegedly provide “hints concerning the true affinities of things.” But won’t such relationships also lie “behind the veil”? These warring inclinations have created significant exegetical confusion, leading his interpreters to classify him as an antirealist, a realist and everything else in between. Duhem is clearly trying to get across some important methodological lesson about science. But what is it? The trick is to align his philosophy more closely with the forms of physics he endorses. On this basis, I argue that Duhem’s disavowals of “explanation’’ actually represent arguments against a dynamic laws picture of science: the doctrine that science must seek laws that track material systems according to the basic patterns of D-N explanation. He argues that many of nature’s most important hidden quantities (e.g., entropy and potential energy) were not discovered in a dynamical manner but were instead uncovered by stringing together relationships in the “quasi-static” manner employed in thermodynamics. Indeed, it is the deep relationships of the latter subject of the latter subject that supply paradigms of the “natural classifications” that Duhem seeks. Once one follows through the details of his recommendations, employing concrete scientific examples, one realizes that Duhem’s reflections on the scientific method greatly enlarge our appreciation of what the many varieties of “good science” can look like. This challenges many dogmatic presumptions about the scientific methodology that still prevail in contemporary philosophy of science

The Physicist - Philosophers: The Legacy of James Clerk Maxwell and Herrmann von Helmholtz

One of the most effective, and most mysterious, tools of modern theoretical physics is a mathematical method including what is here called “field theory.” The success of this procedure in unraveling the “zoology” of fundamental particles and their behavior is a marvel. The philosophical context of this marvel is the source of endless academic controversy. The core of the method is a blend of mathematics and description created by “physicist-philosophers,” from Maxwell and Helmholtz to Einstein and Schrödinger. This book tries to unravel the mystery, or at least chronicle it.https://digitalcommons.bard.edu/facbooks/1000/thumbnail.jp

Making Ammonia

This Open Access book discusses the progress of science and the transfer of scientific knowledge to technological application. It also identifies the factors necessary to achieve this progress. Based on a case study of the physical chemist Fritz Haber's discovery of ammonia synthesis between 1903 and 1909, the book places Haber's work in historical and scientific (physicochemical) context. The scientific developments of the preceding century are framed in a way that emphasizes the confluence of knowledge needed for Haber's success. Against this background, Haber's work is presented in detail along with the indispensable contributions of his colleague, the physical chemist, Walter Nernst, and their assistants. The detailed accounts of scientific advancement remind us of the physical basis on which our scientific theories and ideas are built. Without this reminder we often forget how complex, and how beautiful achievements in science can be

New models of Jupiter in the context of Juno and Galileo

Observations of Jupiter's gravity field by Juno have revealed surprisingly small values for the high order gravitational moments, considering the abundances of heavy elements measured by Galileo 20 years ago. The derivation of recent equations of state for hydrogen and helium, much denser in the Mbar region, worsen the conflict between these two observations. In order to circumvent this puzzle, current Jupiter model studies either ignore the constraint from Galileo or invoke an ad hoc modification of the equations of state. In this paper, we derive Jupiter models which satisfy both Juno and Galileo constraints. We confirm that Jupiter's structure must encompass at least four different regions: an outer convective envelope, a region of compositional, thus entropy change, an inner convective envelope and an extended diluted core enriched in heavy elements, and potentially a central compact core. We show that, in order to reproduce Juno and Galileo observations, one needs a significant entropy increase between the outer and inner envelopes and a smaller density than for an isentropic profile, associated with some external differential rotation. The best way to fulfill this latter condition is an inward decreasing abundance of heavy elements in this region. We examine in details the three physical mechanisms able to yield such a change of entropy and composition: a first order molecular-metallic hydrogen transition, immiscibility between hydrogen and helium or a region of layered convection. Given our present knowledge of hydrogen pressure ionization, combination of the two latter mechanisms seems to be the most favoured solution

Doctor of Philosophy

dissertationTransport in disordered composite media is a problem that arises throughout the sciences and engineering and has attracted significant theoretical, computational, and experimental interest. One of the key features of these types of problems is the critical dependence of the effective transport properties on system parameters, such as volume fraction, component contrast ratio, applied field strength, etc. In recent years a broad range of mathematical techniques have been developed to study phase transitions exhibited by such composites, revealing features which are virtually ubiquitous in disordered systems. Here we construct a multifaceted mathematical framework describing phase transitions exhibited by two phase random media, using techniques from: statistical mechanics, percolation theory, random matrix theory, and a critical theory for Stieltjes functions of a complex variable involving the spectral measure of a self-adjoint random operator (or matrix). In particular, we present a general theory for critical behavior of transport in two phase random media. The theory holds for lattice and continuum percolation models in both the static case with real parameters and the frequency dependent quasi-static case with complex parameters. Through a direct, analytic correspondence between the magnetization of the Ising model and the effective parameter problem of two phase random media, we show that the critical exponents of the transport coefficients satisfy the standard scaling relations for phase transitions in statistical mechanics. Our work also shows that delta components form in the underlying spectral measures at the spectral endpoints precisely at the percolation threshold pc and 1 − pc. This is analogous to the Lee-Yang-Ruelle characterization of the Ising model phase transition, and identifies these transport transitions with the collapse of spectral gaps in these measures. Using random matrix theory, we also characterize these transport transitions via transitions in the eigenvalue statistics of the underlying random matrix. Finally, we construct a canonical ensemble statistical mechanics framework for general transport models of two phase random dielectric media, which parallels the Ising model. Our physically consistent model is formulated from first principles in physics, and is both physically transparent and mathematically tractable