Principle Of Minimum Energy Dissipation Research Articles

Energy evolution mechanism of structural surfaces in sandstones with different dips based on the energy principle.

A uniaxial compression test was conducted on sandstone specimens at various inclination angles to determine the energy evolution characteristics during deformation and damage. Based on the principle of minimum energy dissipation, an intrinsic model incorporating the damage threshold was developed to investigate the mechanical properties of sandstone at different inclination angles, and the energy damage evolution during deformation and damage. This study indicated that when the inclination angle of the structural surface remained below 40°, sandstone exhibited varying mechanical properties based on different inclination angles. The peak strain was positively correlated with the inclination angle, whereas the compressive strength and modulus of elasticity showed negative correlations. From an energy perspective, the deformation and damage of sandstone under external loading entail processes of energy input, accumulation, and dissipation. Moreover, higher inclination angles of the structural surface resulted in a smaller absorbed peak strain and a reduced proportion of dissipated energy relative to the energy input, thereby affecting the evolution of energy damage throughout the process. As the inclination angle of the structural surface increased, the absorbed total strain at the peak value decreased, whereas the proportion of the dissipated energy increased. Additionally, the damage threshold and critical value of the rock specimens increased with the inclination angle. The critical value, a composite index comprising the peak strain, compressive strength, and elastic modulus, also increased accordingly. These findings can offer a novel perspective for analyzing geological disasters triggered by fissure zones within underground rock formations.

Study on Failure Energy per Unit Area of Concrete Specimens Based on Minimum Energy Dissipation Theory.

In order to study the strength change of concrete specimens under different loading conditions, based on the principle of minimum energy dissipation, the damage energy per unit area of concrete was studied. By using finite element numerical simulation software for concrete specimens with different failure modes of tension, pressure, bending and torsion, a double-broken line damage constitutive model is adopted. The failure forms of concrete specimens under different loading conditions, as well as the failure area and failure energy of each specimen during loading, are simulated and analyzed. The failure energy per unit area under different failure modes was quantitively calculated, the relationship between the failure area and failure energy consumption under different failure modes was analyzed. The results show that, under different failure modes, the failure area of concrete specimens is different, the energy consumed during failure is different, and the strength is different. However, no matter how the failure mode changes during the failure process, the failure energy W per unit area remains constant and fluctuates in the range of 2.0~6.0 mJ/cm2, which is related to the physical properties of concrete itself.

Quantitative prediction of ultra-deep tight sandstone fractures based on the theory of minimum energy dissipation

Structural fractures are key factors that influence natural gas migration and accumulation within ultra-deep tight reservoirs. To obtain a quantitative forecast of the development and distribution of reservoir fractures in the Keshen gas reservoir, we analyzed the characteristics of the region's structural evolution and paleo-tectonic stress field settings. A reasonable geological model of the research area was built based on an interpretation of the geological structure, a test for rock mechanics, and an experiment on acoustic emission. Thereafter, a 3-D paleo-tectonic stress field during the mid-late Himalayan movement was simulated using the finite element method. By introducing the principle of minimum energy dissipation, which to our knowledge, was done for the first time in the field, mechanical constitutive models, rock failure criteria, and fracture parameter calculation models were derived and used to determine the quantitative development of fractures and predict zones prone to fracture development. The fracture distribution in the ultra-deep Keshen gas reservoir is mainly controlled by folds, buried depth, faults, and lithology. Interestingly, even in the strong tectonic compression movement, the stress field was not continuously transmitted forward but showed fluctuation or cyclicity, indicating that fractures might have occurred at each time stage. The predicted areas with developed fractures were consistent with wells having high fracture linear density (i.e., measured results) and in locations with high-producing gas wells. We believe that the novel method in this study can be of great significance to fracture research in other ultra-deep petroliferous basins.

Institutional transformation of society in the light of the sociosynergetic paradigm

The object of theoretical research presented in this article is society as an open non-equilibrium system capable of self-organization. The subject of the study are the factors and driving forces of the institutional transformation of the societal system. The relevance of the study is justified by the prolonged transformational period in the life of Russian society, as well as the increasingly widespread socio-structural crisis phenomena in the world. The scientific problem is determined based on such well-known facts as the low predictability and manageability of the processes of institutional transformation, on the one hand, and the need to reduce the risks associated with them, on the other. Accordingly, the question is raised about the mechanism of institutional transformation, which is proposed to be considered using the principles and provisions of sociosynergetics as a methodological basis. The main element of novelty in this article is the synthesis of neoinstitutional theory with the provisions of sociosynergetics. The study analyzes the process of institutional transformation from the standpoint of the sociosynergetic concept using such categories as energy dissipation, entropy, stationary and nonequilibrium state in their social expression. The characteristics of the evolutionary and crisis stages in the development of the institutional system are given. Attention is focused on the risks of the transformation period and the relationship of its results with the previous period of stability. As a result of the conducted research , the author formulates the following conclusions:1) Subjects of social relations act in accordance with the principle of minimum energy dissipation, as a result of which the foundations of any new order are laid in fluctuations of the previous structure.2) The course of the crisis (transformational) process is adversely affected by both excessive control actions aimed at preserving the previous order, and premature and ill-conceived reforms.3) The prolonged transformation threatens the complete degradation of the societal system due to the depletion of resources needed to reduce entropy.

Quantitative prediction of multistage fractures of ultra-deep tight sandstone based on the theory of minimum energy dissipation

Due to strong reservoir heterogeneity and low-resolution limit of geophysical data, it is difficult to predict fractures in ultra-deep reservoirs by conventional methods. In this research, we established a novel geomechanical model for prediction of fracture distribution in brittle reservoirs, especially for ultra-deep tight sandstone reservoirs. Methodologically, we intended to introduce the minimum energy dissipation principle considering time variable, combined with the generalized Hooke’s law containing damage variable, and obtained the energy dissipation rate expression corresponding to the energy dissipation process of brittle rocks. Combined with the three-shear energy yield criterion, the Lagrangian multiplier was introduced to deduce and construct the constitutive model and the failure criterion of rocks under the framework of the theory of minimum energy dissipation. Based on the law of conservation of energy, the stress-energy coupling characterization model of fracture density parameter was derived. Finally, all the improved geomechanical equations were incorporated into a finite element software to quantitatively simulate the distributions of tectonic stress filed and fractures based on paleo-structure restoration of Keshen anticline during the middle and late Himalayan periods. Its predictions agreed well with measured fracture density from reservoir cores and image logs.

A new HVAC ductwork steady-state flow analysis method: The Minimum Energy Dissipation Principle applied to flow networks including the effects of branched junctions

The fact that the popular head loss coefficient concept, may become negative in branched junctions, is a symptom that something is not correctly managed. The paper makes a review of recent works which have sought new models based on physical concepts, as a way to avoid speaking about “negative losses”. Herwing and Schmandt [1], showed that the origin of the negative sign was a diffusive shear work exchange between the two streams of a branched junction. Traditionally, the head losses at the branched junctions are neglected, but definitely it cannot be done in HVAC air-duct networks.Firstly, the paper illustrates how, by ignoring this “negative loss” contradiction, traditional duct network analysis may encounter unexpected numerical difficulties. Secondly, it shows that the Minimum Energy Dissipation Principle (MinEDP) can be successfully applied to analyze the steady-state of any flow network (not necessarily HVAC ductworks), with or without shear work at junctions. Moreover, the new method does not need to know the latter, beforehand, although the nature of the solution is very different in either case.Finally, the paper includes a practical example of an HVAC ductwork to illustrate the outcomes. The new method works smoothly and quickly and does not need any ad hoc modification to cope with an eventual “negative” head loss.

Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

Presented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat—nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

Bounding of Flow and Transport Analysis in Heterogeneous Saturated Porous Media: A Minimum Energy Dissipation Principle for the Bounding and Scale-Up

We apply minimum kinetic energy principles from classic mechanics to heterogeneous porous media flow equations to derive and evaluate rotational flow components to determine bounding homogenous representations. Kelvin characterized irrotational motions in terms of energy dissipation and showed that minimum dynamic energy dissipation occurs if the motion is irrotational; i.e., a homogeneous flow system. For porous media flow, reductions in rotational flow represent heterogeneity reductions. At the limit, a homogeneous system, flow is irrotational. Using these principles, we can find a homogenous system that bounds a more complex heterogeneous system. We present mathematics for using the minimum energy principle to describe flow in heterogeneous porous media along with reduced special cases with the necessary bounding and associated scale-up equations. The first, simple derivation involves no boundary differences and gives results based on direct Kelvin-type minimum energy principles. It provides bounding criteria, but yields only a single ultimate scale-up. We present an extended derivation that considers differing boundaries, which may occur between scale-up elements. This approach enables a piecewise less heterogeneous representation to bound the more heterogeneous system. It provides scale-up flexibility for individual model elements with differing sizes, and shapes and supports a more accurate representation of material properties. We include a case study to illustrate bounding with a single direct scale-up. The case study demonstrates rigorous bounding and provides insight on using bounding flow to help understand heterogeneous systems. This work provides a theoretical basis for developing bounding models of flow systems. This provides a means to justify bounding conditions and results.

Entropy Density Acceleration and Minimum Dissipation Principle: Correlation with Heat and Matter Transfer in Glucose Catabolism.

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine’s minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration for a single cell is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells.

On Sound Propagation in Dispersive Media

Sound propagation in monodisperse emulsions with arbitrary volume concentrations is studied theoretically using a cell model. It is assumed that emulsion cells are bounded by thin and imponderable rigid shells allowing realization of the minimum energy dissipation principle with viscous acoustic losses. Solutions covering many particular cases and wide parameter and variable ranges have been obtained. These solutions are suitable for studying acoustic properties of emulsions and suspensions, marine sediments, fogs, and smoke, as well as elastoviscous materials with solid or liquid inclusions, etc. Sound propagation and absorption in emulsions and suspensions are considered in more detail. The experimental data in the literature is compared.

The Presence of a Revolution Load and Its Rotational Speed of Half the Speed of the Journal Are Necessary Conditions for the Half-Frequency Whirl of Radial Bearings

<p class="1Body">In the radial sliding bearing lubrication theory, the half-frequency whirl phenomena are commonly introduced. However, the correlation of the half-frequency whirl theory with the measured resonance phenomenon is low. This paper studies the establishment of the half-frequency whirl theory, and finds that while researchers are aware of the half-frequency whirl, they disregard the necessary conditions of its occurrence. If there is no revolution load, then the half-frequency whirl does not comply with the principle of minimum potential energy. If it does not conform to the principle of minimum energy dissipation, then the half-frequency whirl does not exist. Only when the revolution load exists and its speed is half the speed of the journal will the half frequency whirl occur. Engineering oil whip results from the vibration of the rotating system. A precise radial sliding bearing lubrication theory should use cylindrical coordinates, consider the compressibility of the liquid, and consider the surface shear stress in the journal bearing capacity calculations.</p>

Consistent modeling of a single PEM fuel cell using Onsager's principle

In this paper a novel approach is proposed for a three-dimensional (3D) modeling of a High Temperature Exchange Membrane Fuel Cell (HTPEMFC). This new modeling is based on Onsager's principle of minimum energy dissipation that is applicable for near equilibrium and coupled irreversible systems. In particular, for low conductivity membranes, this leads to a one directional proton movement through the membrane. The resulting equations are numerically solved for a real single cell geometry, using a 3D finite volume discretization. Results are analyzed and validated against experimental data.

Analysis and Comparison on Typical Methods for Predicting Composite Roughness of River

Composite roughness is an important parameter in river hydraulic calculations. In this paper, various typical methods for predicting composite roughness of river were summarized, including Einstein Method, Lotter Method, JIANG Method and Weighted Average Method, their theoretical rigors were discussed from both perspectives of minimum energy dissipation principle and analytical analysis, and their calculation precisions were verified by a large number of flume test data. Research shows that Einstein Method complies with the principle of minimum energy dissipation, also is the necessary and sufficient condition of resistance equation having unique solution, and its calculation precision is higher, therefore, Einstein Method is more suitable for composite resistance calculation of river with single cross section.

Specific features in realization of the principle of minimum energy dissipation during individual development

Realization of the principle of minimum energy dissipation (Prigogine's theorem) during individual development has been analyzed. This analysis has suggested the following reformulation of this principle for living objects: when environmental conditions are constant, the living system evolves to a current steady state in such a way that the difference between entropy production and entropy flow (psi(u) function) is positive and constantly decreases near the steady state, approaching zero. In turn, the current steady state tends to a final steady state in such a way that the difference between the specific entropy productions in an organism and its environment tends to be minimal. In general, individual development completely agrees with the law of entropy increase (second law of thermodynamics).

A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

AbstractWe develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the On-sager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.

Linking principles of soil formation and flow regimes

Summary Preferential flow (PF) is a fundamentally important soil hydrologic process that controls a variety of soil physical, chemical, and biological functions. However, the lack of theory in this field and the existence of conceptual and technological bottlenecks continue to hinder the advancement of PF modeling and prediction. This paper explores three theoretical perspectives on the relationships between pedogenesis and flow regimes in field soils. First, we examine non-equilibrium thermodynamics as applied to open dissipative field soils with continuous energy inputs and mass exchanges with the surrounding environment. The dual-partitioning of pedogenesis (dissipating and organizing processes) is consistent with the theory of dissipative structure, which explains the genesis and evolution of soil architecture (structure + matrix) and organized heterogeneity found in various soils. Such organized heterogeneity leads to widespread potential for PF occurrence. Second, we investigate constructal theory to explain the tendency for dual-flow regimes in soils – one with high resistivity (Darcy flow) and the other with low resistivity (PF) – together, they form PF configuration that provides the least global flow resistance. This theory is applied to explain some general characteristics of weathering processes and related flow regime changes, which are supported by limited chronologic data from the literature on subsoil’s saturated hydraulic conductivity decrease after a soil reaches a certain age. Third, the theory of evolving networks sheds light on a variety of PF networks observed in field soils, which increase the effectiveness of energy and mass transfer in the subsurface. This is because networks are a part of the organization resulting from the minimum energy dissipation principle and far-from-equilibrium thermodynamics. All the three theories discussed support the notion that the potential for PF occurrence in field soils is likely universal. However, controversies and challenges associated with these theories require further efforts to rigorously test their applicability in natural soils and to formulate explicit quantitative relationships between PF occurrence and its controls. The principle of soil formation and evolution provides a useful guide to this endeavor.

Hydrodynamic boundary conditions: An emergent behavior of fluid–solid interactions

By using the Onsager principle of minimum energy dissipation, the hydrodynamic boundary conditions at the fluid–solid interface are shown to be the natural emergent behavior of microscopic interactions that lead to the interfacial tension and the tangential friction at the fluid–solid interface [T. Qian, C. Qiu, P. Sheng, J. Fluid Mech. 611 (2008) 333]. This is satisfying because the equations of motion, e.g., the Stokes equation, and the hydrodynamic boundary conditions can now be derived from a unified framework. The resulting continuum hydrodynamic formulation yields predictions for immiscible two-phase flows that are in quantitative agreement with molecular dynamic simulations. In particular, the classical problem of the moving contact line is resolved. We also show results on the moving contact line over chemically patterned surfaces which exhibit striking nanoscale characteristics as well as sub-quadratic dependence of the moving contact line dissipation on its average velocity.

Stick-Slip Motion of Moving Contact Line on Chemically Patterned Surfaces

Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation. PACS: 68.08.-p, 83.50.Rp, 83.10.Mj, 83.10.Ff

A scaling approach to the derivation of hydrodynamic boundary conditions

We show hydrodynamic boundary conditions to be the inherent consequence of the Onsager principle of minimum energy dissipation, provided the relevant effects of the wall potential appear within a thin fluid layer next to the solid wall, denoted the surface layer. The condition that the effect of the surface layer on the bulk hydrodynamics must be independent of its thicknesshis shown to imply a set of consistent ‘scaling relationships’ betweenhand the surface-layer variables/parameters. The use of the scaling relations, in conjunction with the surface-layer equations of motion derived from the Onsager principle, directly leads to the hydrodynamic boundary conditions. We demonstrate the surface-layer scaling process both physically and mathematically, and relate the parameters of the boundary conditions to those in the surface-layer equations of motion. In spatial regions outside the surface layer, equivalence between the use of surface-layer dynamics and boundary conditions is numerically demonstrated for Couette flows. As an application of the present approach, we derive the liquid-crystal hydrodynamic boundary conditions in which the rotational and translational dynamics are coupled.

Study On the Damage Evolution Equation of Rockburst

This paper introduces the principle of minimum energy dissipation and its general procedures to establish development equation of internal variable. With the accepted viewpoint that the damage is only mechanics of energy dissipation during the rockburst and utilizing the total strength criterion based on released strain energy, the general damage evolution equation is deduced. Compared with the traditional research method of damage evolution equation, this method has universal and objective characteristics.