Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Density-functional description of superconducting and magnetic proximity effects across a tunneling barrier

A density-functional formalism for superconductivity and magnetism is presented. The resulting relations unify previously derived Kohn-Sham equations for superconductors and for noncollinear magnetism. The formalism, which discriminates Cooper-pair singlets from triplets, is applied to two quantum liquids coupled by tunneling through a barrier. An exact expression is derived, relating the eigenstates and eigenvalues of the Kohn-Sham equations, unperturbed by tunneling, on one side of the barrier to the proximity-induced ordering potential on the other.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

Ric-8A, a G alpha protein guanine nucleotide exchange factor potentiates taste receptor signaling

Taste receptors for sweet, bitter and umami tastants are G-protein-coupled receptors (GPCRs). While much effort has been devoted to understanding G-protein-receptor interactions and identifying the components of the signalling cascade downstream of these receptors, at the level of the G-protein the modulation of receptor signal transduction remains relatively unexplored. In this regard a taste-specific regulator of G-protein signaling (RGS), RGS21, has recently been identified. To study whether guanine nucleotide exchange factors (GEFs) are involved in the transduction of the signal downstream of the taste GPCRs we investigated the expression of Ric-8A and Ric-8B in mouse taste cells and their interaction with G-protein subunits found in taste buds. Mammalian Ric-8 proteins were initially identified as potent GEFs for a range of G alpha subunits and Ric-8B has recently been shown to amplify olfactory signal transduction. We find that both Ric-8A and Ric-8B are expressed in a large portion of taste bud cells and that most of these cells contain IP3R-3 a marker for sweet, umami and bitter taste receptor cells. Ric-8A interacts with G alpha-gustducin and G alpha i2 through which it amplifies the signal transduction of hTas2R16, a receptor for bitter compounds. Overall, these findings are consistent with a role for Ric-8 in mammalian taste signal transduction.

Clarification of a wheat straw-derived medium with ion-exchange resins for xylitol crystallization

BACKGROUND: Xylitol bioproduction from lignocellulosic residues comprises hydrolysis of the hemicellulose, detoxification of the hydrolysate, bioconversion of the xylose, and recovery of xylitol from the fermented hydrolysate. There are relatively few reports on xylitol recovery from fermented media. In the present study, ion-exchange resins were used to clarify a fermented wheat straw hemicellulosic hydrolysate, which was then vacuum-concentrated and submitted to cooling in the presence of ethanol for xylitol crystallization. RESULTS: Sequential adsorption into two anion-exchange resins (A-860S and A-500PS) promoted considerable reductions in the content of soluble by-products (up to 97.5%) and in medium coloration (99.5%). Vacuum concentration led to a dark-colored viscous solution that inhibited xylitol crystallization. This inhibition could be overcome by mixing the concentrated medium with a commercial xylitol solution. Such a strategy led to xylitol crystals with up to 95.9% purity. The crystallization yield (43.5%) was close to that observed when using commercial xylitol solution (51.4%). CONCLUSION: The experimental data demonstrate the feasibility of using ion-exchange resins followed by cooling in the presence of ethanol as a strategy to promote the fast recovery and purification of xylitol from hemicellulose-derived fermentation media. (c) 2008 Society of Chemical Industry.

Use of activated charcoal and ion-exchange resin to cleaN up and concentrate enzymes in extracts from biodegraded wood.

Use of activated charcoal and ion-exchange resin to cleaN up and concentrate enzymes in extracts from biodegraded wood. Ceriporiopsis subvermispora was used for the biodegradation of Eucalyptus grandis chips in the presence or absence of co-substrates (glucose and corn steep liquor) during 7, 14 and 28 days. Afterwards, the biodegraded chips were extracted with 50 mM sodium acetate buffer (pH 5.5) supplemented with 0.01% Tween 60. High activities of manganese peroxidases (MnPs) were observed in all the extracts, both in the absence (430, 765 and 896 UI kg(-1) respectively) and in the presence of co-substrates (1,013; 2,066 and 2,323 UI kg(-1) respectively). The extracts presented a high ratio between absorbances at 280 and 405 nm, indicating a strong abundance of aromatic compounds derived from lignin over heme-peroxidases. Adsorption into activated charcoal showed to be an adequate strategy to reduce the absorbance at 280 urn in all the extracts. Moreover, it allowed to maximize the capacity of an anion exchange resin bed (DEAE-Sepharose) used to concentrate the MnPs present in the extracts. It was concluded that the use of activated charcoal followed by adsorption into DEAE Sepharose is a strategy that can be used to concentrate MnPs in extracts obtained during the biodegradation of E. grandis by C. subvermispora.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.