Dissipative particle dynamics for interacting systems

We introduce a dissipative particle dynamics scheme for the dynamics of non-ideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective, density dependent forces reduces the local structure as compared to previously proposed models. This is an important feature in mesoscopic modeling, since it ensures a realistic length and time scale separation in coarse-grained models. We consider in detail the behavior of a van der Waals fluid and a binary mixture with a miscibility gap. We discuss the physical implications of having a single length scale characterizing the interaction range, in particular for the interfacial properties.Comment: 25 pages, 12 figure

Kazhdan-Lusztig tensoring and Harish-Chandra categories

We use the Kazhdan-Lusztig tensoring to define affine translation functors, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA, and to sketch a functorial approach to ``affine Harish-Chandra bimodules''.Comment: 22 pages late

Open String Field Theory around Universal Solutions

We study the physical spectrum of cubic open string field theory around universal solutions, which are constructed using the matter Virasoro operators and the ghost and anti-ghost fields. We find the cohomology of the new BRS charge around the solutions, which appear with a ghost number that differs from that of the original theory. Considering the gauge-unfixed string field theory, we conclude that open string excitations perturbatively disappear after the condensation of the string field to the solutions.Comment: 14 pages, LaTeX with ptptex.cls, typos correcte

Super-bicharacter construction of quantum vertex algebras

We extend the bicharacter construction of quantum vertex algebras first proposed by Borcherds to the case of super Hopf algebras. We give a bicharacter description of the charged free fermion super vertex algebra, which allows us to construct different quantizations of it in the sense of $H_D$-quantum vertex algebras, or specializations to Etingof-Kazhdan quantum vertex algebras. We give formulas for the analytic continuation of product of fields, the operator product expansion and the normal ordered product in terms of the super-bicharacters.Comment: submitted contribution to "Integrable systems and quantum symmetries 2007"; 14 pages enlarged versio

Vertex Lie algebras and cyclotomic coinvariants

Electronic version of an article published as Benoît Vicedo and Charles Young, Commun. Contemp. Math. 0, 1650015 (2016) [62 pages] DOI: http://dx.doi.org/10.1142/S0219199716500152 Vertex Lie algebras and cyclotomic coinvariants.Given a vertex Lie algebra $\mathscr L$ equipped with an action by automorphisms of a cyclic group $\Gamma$, we define spaces of cyclotomic coinvariants over the Riemann sphere. These are quotients of tensor products of smooth modules over `local' Lie algebras $\mathsf L(\mathscr L)_{z_i}$ assigned to marked points $z_i$, by the action of a `global' Lie algebra ${\mathsf L}^{\Gamma}_{\{z_i \}}(\mathscr L)$ of $\Gamma$-equivariant functions. On the other hand, the universal enveloping vertex algebra $\mathbb V (\mathscr L)$ of $\mathscr L$ is itself a vertex Lie algebra with an induced action of $\Gamma$. This gives `big' analogs of the Lie algebras above. From these we construct the space of `big' cyclotomic coinvariants, i.e. coinvariants with respect to ${\mathsf L}^{\Gamma}_{\{z_i \}}(\mathbb V(\mathscr L))$. We prove that these two definitions of cyclotomic coinvariants in fact coincide, provided the origin is included as a marked point. As a corollary we prove a result on the functoriality of cyclotomic coinvariants which we require for the solution of cyclotomic Gaudin models in arXiv:1409.6937. At the origin, which is fixed by $\Gamma$, one must assign a module over the stable subalgebra $\mathsf L(\mathscr L)^{\Gamma}$ of $\mathsf L(\mathscr L)$. This module becomes a $\mathbb V(\mathscr L)$-quasi-module in the sense of Li. As a bi-product we obtain an iterate formula for such quasi-modules.Peer reviewe

Jordanian Solutions of Simplex Equations

We construct for all $N$ a solution of the Frenkel--Moore $N$--simplex equation which generalizes the $R$--matrix for the Jordanian quantum group.Comment: 6 page

Constructing quantum vertex algebras

This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

Effect of sinusoidal modulated currents and acute hypoxia on corticosterone content and activity of certain dehydrogenases in tissues of different rat organs during hypokinesia

The state of hypokinesia in rats was reproduced by keeping them for 30 days in special box cages that restricted their mobility in all directions. Results show the resistance to acute hypoxic hypoxia is increased. This is linked to the considerable rise in the reduced level of corticosterone in different organs and the succinate dehydrogenase activity in the liver and brain. The letter indicated the primary oxidation of succinate, which has great importance in the adaptation of the oxidative metabolism to acute oxygen insufficiency. The use of sinusoidal modulated currents in the period of hypokinesia promotes normalization of the indices for resistance of the rats to acute hypoxia