Energetic Formulation of Large-Deformation Poroelasticity

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

Alignment of carbon nanotubes under the influences of nematic liquid crystals and electric fields — an analytical study

Carbon nanotubes (CNTs) have benefits in various fields, they are disadvantageous due to their tendency to form aggregates and poorly controlled alignment of the CNT molecules (characterized by order parameters). These deficiencies can be overcome by dispersing the CNTs in nematic liquid crystal (LC) and placing the mixture under the influence of an electric field. In this study, Doi and Landau–de Gennes free energy density equations are used to analytically confirm that an electric field increases the order parameters of CNTs and LCs in a dispersion mixture. The anchoring strength of the nematic LC is also found to affect the order parameters of the CNTs and LC. Further, increasing the length-to-diameter ratio of the CNTs increases their alignment without affecting the LC alignment. These findings indicate that CNT molecular alignment can be controlled by adjusting the CNT length-to-diameter ratio, anchoring the LCs, and adjusting the electric field strength.

Helical phase in two-dimensional magnets due to four-spin interactions

We demonstrate that in ferromagnets with the D3h point group of symmetry a possible origin of phase transition from a collinear ferromagnetic state to a non-collinear state can be the fourth order contributions to the free energy density that are allowed by this point group of symmetry. At the same time, Dzyaloshinskii-Moria interaction vanishes in such materials. Via symmetry analysis we derive seven possible fourth order contributions to the free energy density with respect to the unit vector of the local magnetization direction but only two of them can be considered as independent. Moreover, for two-dimensional systems only one survives. Considered symmetry class is essential because a large group of two-dimensional intrinsic ferromagnets belongs to it, for example a monolayer Fe3GeTe2. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves.

A Forth Law of Thermodynamics: Synergy Increases Free Energy While Decreasing Entropy

Synergy, emerges from synchronized reciprocal positive feedback loops between a network of diverse actors. For this process to proceed, compatible information from different sources synchronically coordinates the actions of the actors resulting in a nonlinear increase in the useful work or potential energy the system can manage. In contrast noise is produced when incompatible information is mixed. This synergy produced from the coordination of different agents achieves non-linear gains in free energy and in information (negentropy) that are greater than the sum of the parts. The final product of new synergies is an increase in individual autonomy of an organism that achieves increased emancipation from the environment with increases in productivity, efficiency, capacity for flexibility, self-regulation and self-control of behavior through a synchronized division of ever more specialized labor. Examples that provide quantitative data for this phenomenon are presented. Results show that increases in free energy density require decreases in entropy density. This is proposed as a law of thermodynamics.

Chemical Potential-Based Modeling of Shale Gas Transport

Shale gas plays an increasingly important role in the current energy industry. Modeling of gas flow in shale media has become a crucial and useful tool to estimate shale gas production accurately. The second law of thermodynamics provides a theoretical criterion to justify any promising model, but it has been never fully considered in the existing models of shale gas. In this paper, a new mathematical model of gas flow in shale formations is proposed, which uses gas density instead of pressure as the primary variable. A distinctive feature of the model is to employ chemical potential gradient rather than pressure gradient as the primary driving force. This allows to prove that the proposed model obeys an energy dissipation law, and thus, the second law of thermodynamics is satisfied. Moreover, on the basis of energy factorization approach for the Helmholtz free energy density, an efficient, linear, energy stable semi-implicit numerical scheme is proposed for the proposed model. Numerical experiments are also performed to validate the model and numerical method.

A Forth Law of Thermodynamics: Synergy Increases Free Energy While Decreasing Entropy

Synergy, emerges from synchronized reciprocal positive feedback loops between a network of diverse actors. For this process to proceed, compatible information from different sources synchronically coordinates the actions of the actors resulting in a nonlinear increase in the useful work or potential energy the system can manage. In contrast noise is produced when incompatible information is mixed. This synergy produced from the coordination of different agents achieves non-linear gains in free energy and in information (negentropy) that are greater than the sum of the parts. The final product of new synergies is an increase in individual autonomy of an organism that achieves increased emancipation from the environment with increases in productivity, efficiency, capacity for flexibility, self-regulation and self-control of behavior through a synchronized division of ever more specialized labor. Examples that provide quantitative data for this phenomenon are presented. Results show that increases in free energy density require decreases in entropy density. This is proposed as a law of thermodynamics.

Viscoelastic Effects on the Response of Electroelastic Materials

Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney–Rivlin equation for the stress–strain relationship of the elastomeric material. A modified Mooney–Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney–Rivlin equations.

Fishnet four-point integrals: integrable representations and thermodynamic limits

We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.

Nonlinear magnetoelectric effects in Al-substituted strontium hexaferrite

This report is on the observation and theory of electric field E induced non-linear magnetoelectric (NLME) effects in single crystal platelets of ferrimagnetic M-type strontium aluminum hexagonal ferrite. Using microwave measurement techniques, it was found that a DC electric field along the hexagonal c-axis results in significant changes in the saturation magnetization and uniaxial magneto-crystalline anisotropy field and these changes are proportional to the square of the applied static electric field. The NLME effects were present with or without an external bias magnetic field. The E-induced variation in magnetic order parameters is attributed to weakening of magnetic exchange and spin–orbit interactions since conduction electrons in the ferrite are effectively excluded from both interactions while being in transit from one Fe ion to another. We present a phenomenological theory which considers magneto-bielectric effects characterized by a quadratic term in electric field E in the free energy density. The coefficients for the NLME coupling terms have been calculated from experimental data and they do show variations with the Al substitution level and the largest rates of change of the saturation magnetization and anisotropy constant change with the applied power were observed for x = 0.4. It was also clear from the study that strength of the NLME effect does not depend on the amount Al substitution, but critically depends on the electrical conductivity of the sample with the highest NLME coefficients estimated for the sample with the highest conductivity. Results of this work are of importance for a new family of electric field tunable, miniature, high frequency ferrite devices.

A Thermodynamic-Consistent Model for the Thermo-Chemo-Mechanical Couplings in Amorphous Shape-Memory Polymers

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.