Критический ток в длинном джозефсоновском контакте во внешнем магнитном поле при слабом пиннинге

The analysis of possible current distributions when passing current through a periodically modulated long Josephson contact located in an external magnetic field is carried out. An approach based on the analysis of continuous configuration modification proceeding in the direction of Gibbs potential reduction is used for the calculation. The case when the pinning parameter is less than the critical value is considered. It is shown that at any value of the external magnetic field, there is a critical value of the transport current, when exceeded, the situation ceases to be stationary, as a result of which energy passes into radiation and heat, i.e. currents cease to be persistent. The value of the critical current is determined by the value of the magnetic field at which the vortices begin to fill the entire length of the contact. With an increase in the external magnetic field, the critical value of the current decreases.

A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials

In this article, we develop a new implicit constitutive relation, which is based on a thermodynamic foundation that relates the Hencky strain to the Cauchy stress, by assuming a structure for the Gibbs potential based on the Cauchy stress. We study the tension/compression of a cylinder, biaxial stretching of a thin plate and simple shear within the context of our constitutive relation. We then compare the predictions of the constitutive relation that we develop and that of Ogden’s constitutive relation with the experiments of Treloar concerning tension/compression of a cylinder, and we show that the predictions of our constitutive relation provide a better description than Ogden’s model, with fewer material moduli.

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle still linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv=mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@=mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink, the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, that Carnot identified as reversible temperature-dependent but unequal exchanges in caloric. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’ exclusively to negative Gibbs energy (-G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.

PHYSIOLOGICAL FUNCTIONAL STATES OF MITOCHONDRIA IN THE THERMODYNAMIC AND ELECTROCHEMICAL CYCLE

Aim.This study was performed to identify the possible physiological and pathogenetic processes taking place in the mitochondrial matrix which create the conditions for lithogenesis of insoluble calcium phosphate salts (calcium carbonate...). Whereas, they can later be deposited in various tissues, taking into account the fact that the formation of calcium phosphate (calcium carbonate ...) in the human body occurs under normal physiological conditions (bone tissue, otolith...). It raises the urgency of the question of understanding the physiological and pathogenetic mechanisms of lithogenesis.Materials and methods. There was carried out a meta-analysis of the functional states of mitochondria, to which we 125 Kubanskij nauchnyj medicinskij vestnik 2018; 25 (5) applied a mathematical model based on the changing direction and velocity of the conjugated thermodynamic and electrochemical parameters (pressure, volume, temperature, Gibbs potential, exergy…). Considering the schemes of the oxidative phosphorylation proposed by R.Mitchell and R.Williams, we created a model of the thermodynamic and electrochemical cycle of mitochondria which gives a deeper understanding of the principles of the mechanisms of the ongoing processes in the system mitochondrial matrix-internal membrane-intermembrane space.Results.Based on the fundamental principle of functional interaction, there were proposed four functional states of mitochondria (M) in thermodynamic and electrochemical (TD-EC) cycle, to which was created a mathematical model that allows to systematize the processes accompanied by the accumulation of the electrochemical potential, in other words, the charge separation (ionization) in the paramembrane space. At the same time, on the one side of the inner membrane (mitochondrial intermembrane space) the positive charge predominates, and on the other side (the mitochondrial matrix) – the negative. These processes, in view of the repulsion of like charges, lead to the increase in pressure both in the mitochondrial matrix and in the intermembrane space. In this sense, the direction of the electrochemical processes, taking place in the intramembrane and intermembrane environment from the position of physical thermodynamics, is similar to the direction of the processes occurring in the compressible ionized gas (plasma).The states of mitochondria are considered when the velocity of electrons along the respiratory chain, which is associated with a change in the thermal potential, changes in the thickness of its internal membrane. For the medium inside the matrix, which is an ultra-microheterogeneous dispersive mass, and also using the thermodynamic analogy with the ionized gas, by the thermal potential (Ǫ) we mean the product of pressure (P) per volume (V): Ǫ= PV. Based on the mathematical model of the thermodynamic behavior of the mitochondria and on the limitations imposed by the laws of physical and chemical thermodynamics, it is established that the greatest degree of thermodynamic perfection in the process of mitochondrial respiration corresponds to the state of "respiratory control" which, among the set of Functional States, is acceptable to consider the fundamental (basic, the first), in other words, F-I.The hierarchy of the homeostatic system of mitochondria is built according to the degree and speed of energy consumption which constantly switches (fluctuates ...) because life is the consequence of a stable nonequilibrium state of the special molecules, since living systems are never in equilibrium and, due to their free Gibbs energy (G), perform a constant work against the equilibrium.There is a physiological "balance" between the various functional states competing for the mitochondrial energy resources: 1) involuntary (Gibbs potential G>0) endergonic phosphorylation process which triggers ATP synthase and is accompanied by the cooling; and 2) spontaneous (Gibbs potential G<0) exergonic process that increases the temperature of the external medium. The pathophysiological "unbalance" of these mechanisms, in which the conditions for the formation of the watersoluble salt of calcium phosphate dihydrate-Ca (H2 PO4 )2 interchange with the poorly soluble calcium hydrogenphosphateСаHPO4 , can be a pathogenetic cause of the occurrence of common diseases (nephrolithiasis, osteochondrosis, atherosclerosis ...).Conclusion.In the thermodynamic and electrochemical cycle of the mitochondrial system matrix-internal membraneintermembrane space, the direction and speed of physiological functional variables, which determine the presence and magnitude of the primary physiological needs, are important. In the multidimensional space of the physiological functional variables there is a gap of functionality. This is the range of parameters variations, the limits of which are distributed according to Gauss and are optimal for the habitat mode in the external environment, which is the cytoplasm in regards to the mitochondria. Going beyond the limits of the gap of functionality promotes the thermodynamic and electrochemical adaptation changes in the mitochondrial system itself which tends to return to the state of the thermodynamic "rest", while the mitochondria performs a cyclic process.Relying on the fact that the fundamental principle of the functional expediency establishes the primacy of the maximum residence time of any living system in the defined ("normative", "permissible" ...) limits of the functionality gap, the fluctuations of which are conditioned by the changing external conditions and internal needs, we express confidence that, taking into account the limitations imposed by the laws of physical and chemical thermodynamics, the greatest degree of thermodynamic perfection of the mitochondrial breathing process in the dynamical electrochemical cycle is performed in the state of the respiratory control (F-I), which corresponds to the maximum entropy (S) and the minimum Gibbs energy (G). In the thermodynamic and electrochemical cycle may arise the conditions that include the adaptive biochemical changes that favor the accumulation of Ca2+ in the mitochondrial matrix, and thereby confirm the direct dependence of the calcium retention capacity on the speed of the respiration of mitochondria. At the same time, a significant amount of Ca2+ accumulates in the mitochondrial matrix, which, combined with the hydrophosphate, is transformed into the calcium diphosphate − Ca3 (PO4 )2 , which has an extremely low solubility in water. This may be a primordial mechanism of lithogenesis with the subsequent deposition of calcium phosphate salts in various tissues, causing the diseases at the organ level, in the pathogenesis of which the violation of energy metabolism is common!