Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense and the self-consistent scheme must follow Baym’s Φ-derivable concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent equations of motio...

Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sh...

Synopsis : The transient network model of Green-Tobolsky [1946], Yamamoto [1956] and Tanaka-Edwards [1992] is formulated within the frame of thermodynamics of irreversible processes, using as a fundamental quantity the chemical potential associated to the connection of strands to the network and treating these connections as chemical-like reactions. All thermodynamic quantities are thus natural...

Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a connected reductive algebraic group over k and let g be the Lie algebra of G. Note that G acts on G and on g by the adjoint action and on g by the coadjoint action. (For any k-vector space V we denote by V ∗ the dual vector space.) Let GC be the reductive group over C of the same type as G. Let UG be the variety...

In this paper, we provide a theoretical basis using thermodynamic stability analysis for explaining the spontaneous nucleation and growth of a high density of 1-D structures of a variety of materials from low-melting metals such as Ga, In, or Sn. The thermodynamic stability analysis provides a theoretical estimate of the extent of supersaturation of solute species in molten metal solvent. Using...

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describ...

We recently introduced the dynamical cluster approximation ~DCA!, a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation ~exact result! is obtained b...

It is well known that thermodynamics raises conceptual difficulties. Far to be limited to students having to learn the subject, this impression is sometimes mentioned by specialists themselves who confess not being totally sure of the consistency of the thermodynamic theory, despite the fact that its practical usefulness is indisputable. The present paper deals with this interesting question an...

We assess the errors produced by considering temperature as a conservative tracer in fluviokarst studies. Heat transfer that occurs between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) is the reason why one should be careful in making this assumption without caution. We consider the karstic aquifer as an Open Thermodynamic System (OTS), which boundaries are permeable to thermal...

Comparative Molecular Field Analysis (CoMFA) has been used to develop three-dimensional quantitative structure-property relationship (3D-QSPR) models for the fusion enthalpy at the melting point (Delta(fus)H(m)(T(fus))) of a representative set of polychlorinated biphenyls (PCBs). Various alignment schemes, such as inertial, as is, atom fit, and field fit, were used in this study to evaluate the...