•A barrier condition may enforce non-reciprocal behavior of thermodynamic systems.•The Thermodynamic Extremal Principle is formulated for non-reciprocal systems.•The Thermodynamic Extremal Principle ...is extended to treat rate-independent processes.•A thermodynamic consistent derivation of non-associated plasticity is given.•This extension allows treating a large family of non-reciprocal physical processes.
Onsager’s Reciprocal Relations between thermodynamic forces and fluxes, for which Onsager was awarded the Nobel Prize, automatically follow from Thermodynamic Extremal Principles. Thus, the principles have been up to now non-applicable for the treatment of experimentally determined or theoretically modeled non-reciprocal systems as e.g. those involving magnetic fields. Recently, we were able to demonstrate that adding of a certain barrier constraint as bilinear form of thermodynamic forces and fluxes accounted by the Thermodynamic Extremal Principles leads to non-reciprocal relations between the thermodynamic forces and fluxes. In this work, we extend this formulation to rate-independent systems possessing non-differentiable dissipation functions. As an application, we show that the non-associated models of pressure dependent plasticity can be obtained in this fashion.
Continued development and validation of quantitative imaging and biochemical assessment techniques are critical research priorities to lead to improved diagnosis and treatment of PTOA. There is also ...a compelling need to advance understanding of how mechanical joint injuries lead to joint degeneration, and to define the roles of acute joint damage and post–joint injury incongruity and instability as etiologic factors leading to development of OA.22 As OA occurs more frequently in the military population and ACL tears are endemic to the military, it is essential that the military become more active in funding research and seeking novel research cohorts to help solve some of the most fundamental problems in PTOA. The military population, while deeply affected by PTOA, may also prove to be pivotal in determining improved diagnostic techniques and treatment interventions to help minimize the long-term effects of this disease.
We present the results of a 500ks long XMM-Newton observation and a 120ks long quasi-simultaneous Chandra observation of the Narrow-Line Seyfert 1 galaxy 1H0707-495 performed in 2010 September. ...Consistent with earlier results by Fabian et al. and Zoghbi et al., the spectrum is found to be dominated by relativistically broadened reflection features from an ionized accretion disc around a maximally rotating black hole. Even though the spectra changed between this observation and earlier XMM-Newton observations, the physical parameters of the black hole and accretion disc (i.e. spin and inclination) are consistent between both observations. We show that this reflection spectrum is slightly modified by absorption in a mildly relativistic, highly ionized outflow which changed velocity from around 0.11c to 0.18c between 2008 January and 2010 September. Alternative models, in which the spectral shape is dominated by absorption, lead to spectral fits of similar quality, however, the parameters inferred for the putative absorber are unphysical. PUBLICATION ABSTRACT
•A modeling study for diffusion of hydrogen with traps is presented.•Introduction of a new chemical diffusion coefficient.•Density of traps and average depth of traps can be determined.•Lattice ...diffusion and sub-surface concentration of atomic hydrogen can be determined.
An improved diffusion theory accounting for trapping effects is applied to evaluation of hydrogen permeation experiments performed for pure iron and pearlitic and martensitic steels. The trapping parameters as molar volume and depth of traps are determined by fitting experiments by simulations based on the theory. The concentration-dependent chemical diffusion coefficient of hydrogen is extracted indicating that the trapping effect on diffusion in pure iron and pearlitic steel is negligible. However, it is significant for martensitic steel, for which the chemical diffusion coefficient cannot be considered as concentration-independent as it is established in current standards.
Approximately a decade ago a new concept to describe the kinetics of one-phase solid state systems evolving by diffusion and activity of vacancies has been published by the authors. The concept is ...based on the Onsager-Ziegler Thermodynamic Extremal Principle (TEP). In course of the last decade several improvements and corrections have been performed, which justify an overworking of the concept. A short introduction of the TEP is followed by a detail investigation of the Gibbs energy and its rate as well as of dissipation and dissipation function due to multicomponent diffusion process coupled with vacancy activity provoking swelling/shrinkage and creep and thus internal stress state development. The application of TEP allows an exact derivation of driving forces for the coupled processes. The Manning theory of diffusion is applied and the derivation of evolution equations for all system parameters (site fractions, swelling/shrinkage and creep strain tensor) is provided.
Deposition of an interstitial atom in octahedral or tetrahedral sites in a bcc-crystal provokes one of three types of local tensorial eigenstrains. Interaction of the interstitial atoms with an ...external and/or defect-generated stress state and their diffusion cause different occupancies of individual types of sites. The diffusion paths are analyzed for atoms occupying octahedral or tetrahedral sites. The current original model quantifies the anisotropy of diffusion by factors being functions of occupancies of individual types of sites. Coupling of this new model with a very recent model of interstitial diffusion, already accounting for various types of interstitial sites, provides a rather sophisticated theoretical model for simulation of interstitial diffusion in stressed crystals.
Interactions of impurity interstitial atoms with dislocations may play an important role in strengthening of structural materials as well as in other phenomena like hydrogen embrittlement. Impurity ...interstitial atoms occupy octahedral (typical for carbon) or tetrahedral (typical for hydrogen) sites in bcc metals, both showing solely tetragonal symmetry of three types distinguished by orientation with respect to the main crystallographic (1, 2, 3) directions. Placing an atom at one of such sites one of the three types of local multiaxial eigenstrain states is provoked. This eigenstrain state interacts with the stress field of the dislocation, and the corresponding interaction term provides a mechanical part of the generalized chemical potential of the interstitial component. For a proper description of the distribution of the interstitial component in the stressed lattice three site fractions X1, X2 and X3, corresponding to the types of sites, are necessary. Interstitials like hydrogen and carbon are mobile even at room temperature and diffuse spontaneously to places with the lowest interaction energy. As the individual types of interstitial sites are interconnected by fast diffusion paths, one can assume local equilibrium among atoms occupying the three types of interstitial sites. This fact is expressed by a unique value of their generalized chemical potential. The gradient of this potential drives diffusion of interstitial atoms. At any time the atoms redistribute locally to the three types of sites according to the condition of local equilibrium. Thus, generally in the stressed bcc lattice the three site fractions X1, X2 and X3 have different values and provoke a multiaxial eigenstrain state resulting in an eigenstress state. Hence, the stress field of the dislocation is superposed by the eigenstress state. This may cause a significant relaxation (i.e. reduction) of the total stress state depending on the amount of the interstitial atoms in the system and their diffusion kinetics. Very recently, the individual diffusion paths of interstitial atoms occupying octahedral or tetrahedral positions in a stressed bcc lattice have been identified. The respective model predicts a significant anisotropy of diffusion caused by the differences in local values of X1, X2 and X3 in addition to the standard elastodiffusion due to deformation of the lattice. This leads to a significant modification of the standard diffusion equation, because the introduced “diffusion occupancy factors” are directly dependent on the values of X1, X2 and X3. Assuming a straight dislocation (with its dislocation line coinciding with the z-coordinate axis and the slip plane as the x-z-plane of the local coordinate system) and its interaction with the interstitial component, it is advantageous to evaluate the eigenstrain tensor in the local coordinate system (x, y, z) and solve the problem in that system. Then the space around the dislocation can be divided into cylindrical representative volume elements with axes parallel to z-axis and small cross-sections in x- and y- directions. In each of the representative volume elements spatially constant values of X1, X2 and X3 and of the eigenstrain tensor are assumed. As one can calculate the eigenstress state inside and outside of each cylindrical representative volume element, embedded in an eigenstrain-free infinite matrix, the total stress state is then given by linear superposition of the eigenstress states of all representative volume elements and the stress state induced by the dislocation. The goal of the proposed review paper is to comprise a collection of the knowledge of the last seven decades dealing with the following topics: • stress fields induced by edge and screw dislocation; a presentation of the most recent solution technique and discussion of previous solutions; • eigenstrains of carbon and hydrogen atoms placed in octahedral and tetrahedral sites; a selection of the values of reliable sources; • assembling of the interstitial atoms, acting as inclusions with a misfit eigenstrain state, in cylindrical representative volume elements; • eigenstrain states in cylindrical representative volume elements due to occupancy of interstitial atoms described by X1, X2 and X3; • eigenstress fields generated by eigenstrains in cylindrical representative volume elements; • formulation of the generalized chemical potential of interstitial atoms in the stressed bcc lattice; • anisotropic diffusion equations for interstitials in a stressed bcc lattice, accounting for elastodiffusion and the effect of occupancy of different types of interstitial sites. A collection of equations provides a basis for acquiring a complex model of kinetics of interactions of interstitial atoms with (especially prioritizing) dislocations in the bcc lattice. This represents the “research part” of the review paper. Thus the paper focuses on kinetics of interactions of interstitials occupying tetrahedral and octahedral positions with edge and screw dislocations. As results of simulations the kinetics of distribution of the site fractions X1, X2 and X3 around the dislocation as well as the relaxation (i.e. reduction) of the dislocation stress due to eigenstress are provided.
Within optimality theory, an animal's home range can be considered a fitness-driven attempt to obtain resources for survival and reproduction while minimizing costs. We assessed whether brown bears ...(Ursus arctos) in two island populations maximized resource patches within home ranges (Resource Dispersion Hypothesis RDH) or occupied only areas necessary to meet their biological requirements (Temporal Resource Variability Hypothesis TRVH) at annual and seasonal scales. We further examined how intrinsic factors (age, reproductive status) affected optimal choices. We found dynamic patterns of space use between populations, with support for RDH and TRVH at both scales. The RDH was likely supported seasonally as a result of bears maximizing space use to obtain a mix of nutritional resources for weight gain. Annually, support for RDH likely reflected changing abundances and distributions of foods within different timber stand classes. TRVH was supported at both scales, with bears minimizing space use when food resources were temporally concentrated. Range sizes and optimal strategies varied among sex and reproductive classes, with males occupying larger ranges, supporting mate seeking behavior and increased metabolic demands of larger body sizes. This work emphasizes the importance of scale when examining animal movement ecology, as optimal behavioral decisions are scale dependent.
The coarsening of precipitates in a matrix with a non-zero volume fraction is treated by assuming that the exchange of matter between the precipitates occurs by diffusion in the matrix within finite ...zones surrounding the precipitates. The thermodynamic extremal principle is used for the derivation of evolution equations for the precipitate radii. Accordingly, non-steady-state and steady-state distribution functions are deduced, depending on the system parameter characterizing the finite diffusion zones. The distribution functions tend exactly to the established Lifshitz–Slyozov–Wagner distribution for a zero volume fraction of the precipitates. The steady-state distribution functions are expressed by means of distinct volume-fraction-dependent parameters, which are presented by analytical expressions and in diagrams. To treat non-steady-state systems, ensembles of up to 106 precipitates can easily be handled by standard computational methods.
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