Theory of Structural Glasses and Supercooled Liquids

We review the Random First Order Transition Theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature $T_g$. These include: the viscosity catastrophe and heat capacity jump at $T_g$, and their connection; the non-exponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractral cooperative rearrangements; deviations from the Stokes-Einstein relation close to $T_g$; aging, and its correlation with fragility; the excess density of states at cryogenic temperatures due to two level tunneling systems and the Boson Peak.Comment: submitted to Ann. Rev. Phys. Che

Dynamics on the Way to Forming Glass: Bubbles in Space-time

We review a theoretical perspective of the dynamics of glass forming liquids and the glass transition. It is a perspective we have developed with our collaborators during this decade. It is based upon the structure of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered systems as they approach non-ergodic or jammed states. It is characterized in terms of dynamical heterogeneity, facilitation and excitation lines. These features are associated with a newly discovered class of non-equilibrium phase transitions. Equilibrium properties have little if anything to do with it. The broken symmetries of these transitions are obscure or absent in spatial structures, but they are vivid in space-time (i.e., trajectory space). In our view, the glass transition is an example of this class of transitions. The basic ideas and principles we review were originally developed through the analysis of idealized and abstract models. Nevertheless, the central ideas are easily illustrated with reference to molecular dynamics of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che

Theoretical and methodological approaches to the determination of the "capital of enterprise" economic essence

Розглянуто основні підходи до обґрунтування сутності поняття "капітал підприємства". Сформовано власне визначення категорії "капітал" підприємства як матеріальні, грошові та нематеріальні ресурси, що авансовано у формування активів підприємства, необхідних для здійснення його господарської діяльності в довгостроковій перспективі, з метою отримання доходу та прибутку. Визначено склад взаємопов'язаних і взаємообумовлених внутрішніх і зовнішніх факторів, що впливають на структуру капіталу підприємства та визначають можливості управління ним.The main approaches to substantiating the essence of the concept of "capital of an enterprise" are considered. The actual definition of the category of "capital" of the enterprise as material, monetary and intangible resources, which was advanced in forming the assets of an enterprise necessary for its economic activity in the long run, was formed for the purpose of obtaining income and profits. The composition of interconnected and mutually determined internal and external factors influencing the structure of the enterprise capital and determine the possibilities of management of it are determined. The internal factors determining the peculiarities of the formation and composition of the capital of enterprises are: the organizational and legal form of the enterprise's activity, the existing capital structure, the level of profitability of the operating acti vity, the size of the enterprise and the stage of its life cycle, the degree of financial stability, the priorities of owners and management in choosing a method of financial provision, etc. External factors are the following: the state of the legislative process, the level of administrative influence on the economy of enterprises, the stability of the commodity market, the financial market situation, the tax burden on the enterprise, the ratio of creditors and investors to a particular enterprise, the degree of credit risk and the level of potential of the banking system, tendencies of development of other branches of economy

Patterns of relative species abundance in rainforests and coral reefs

A formidable many-body problem in ecology is to understand the complex of factors controlling patterns of relative species abundance (RSA) in communities of interacting species. Unlike many problems in physics, the nature of the interactions in ecological communities is not completely known. Although most contemporary theories in ecology start with the basic premise that species interact, here we show that a theory in which all interspecific interactions are turned off leads to analytical results that are in agreement with RSA data from tropical forests and coral reefs. The assumption of non-interacting species leads to a sampling theory for the RSA that yields a simple approximation at large scales to the exact theory. Our results show that one can make significant theoretical progress in ecology by assuming that the effective interactions among species are weak in the stationary states in species-rich communities such as tropical forests and coral reefs

Discontinuous Galerkin finite element method applied to the coupled unsteady Stokes/Cahn-Hilliard equations

International audienceTwo-phase flows driven by the interfacial dynamics are studied by tracking implicitly interfaces in the framework of the Cahn-Hilliard theory. The fluid dynamics is described by the Stokes equations with an additional source term in the momentum equation taking into account the capillary forces. A discontinuous Galerkin finite element method is used to solve the coupled Stokes/Cahn-Hilliard equations. The Cahn-Hilliard equation is treated as a system of two coupled equations corresponding to the advection-diffusion equation for the phase field and a non-linear elliptic equation for the chemical potential. First, the variational formulation of the Cahn-Hilliard equation is presented. A numerical test is achieved showing the optimal-order in error bounds. Second, the variational formulation in discontinuous Galerkin finite element approach of the Stokes equations is recalled in which the same space of approximation is used for the velocity and the pressure with an adequate stabilization technique. The rates of convergence in space and time are evaluated leading to an optimal-order in error bounds in space and a second order in time with a backward differentiation formula at the second order. Numerical tests devoted to two-phase flows are provided on ellipsoidal droplet retraction, on the capillary rising of a liquid in a tube and on the wetting drop over a horizontal solid wall