Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Potts fully frustrated model: Thermodynamics, percolation and dynamics in two dimensions

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore, this transition can be mapped onto a percolation transition. We numerically study the phase diagram in two dimensions (2D) for this model with frustration and without disorder and we compare it to the phase diagram of (i) the model with frustration and disorder and (ii) the ferromagnetic model. Introducing a parameter that connects the three models, we generalize the exact expression of the ferromagnetic Potts transition temperature in 2D to the other cases. Finally, we estimate the dynamic critical exponents related to the Potts order parameter and to the energy.

Disordered backgammon model

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale e*, is proposed. For such a solution, modes with energy ee* are equilibrated at the bath temperature, modes with ee* remain out of equilibrium, and relaxation occurs in the neighborhood of the threshold e~e*. The model is presented as a toy example to investigate the conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector is probed by the corresponding observable.

Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

Glutamatergic and GABAergic energy metabolism measured in the rat brain by (13) C NMR spectroscopy at 14.1 T.

Energy metabolism supports both inhibitory and excitatory neurotransmission processes. This study investigated the specific contribution of astrocytic metabolism to γ-aminobutyric acid (GABA) synthesis and inhibitory GABAergic neurotransmission that remained to be ilucidated in vivo. Therefore, we measured (13) C incorporation into brain metabolites by dynamic (13) C nuclear magnetic resonance spectroscopy at 14.1 T in rats under α-chloralose anaesthesia during infusion of [1,6-(13) C]glucose. The enhanced sensitivity at 14.1 T allowed to quantify incorporation of (13) C into the three aliphatic carbons of GABA non-invasively. Metabolic fluxes were determined with a mathematical model of brain metabolism comprising glial, glutamatergic and GABAergic compartments. GABA synthesis rate was 0.11 ± 0.01 μmol/g/min. GABA-glutamine cycle was 0.053 ± 0.003 μmol/g/min and accounted for 22 ± 1% of total neurotransmitter cycling between neurons and glia. Cerebral glucose oxidation was 0.47 ± 0.02 μmol/g/min, of which 35 ± 1% and 7 ± 1% was diverted to the glutamatergic and GABAergic tricarboxylic acid cycles, respectively. The remaining fraction of glucose oxidation was in glia, where 12 ± 1% of the TCA cycle flux was dedicated to oxidation of GABA. 16 ± 2% of glutamine synthesis was provided to GABAergic neurons. We conclude that substantial metabolic activity occurs in GABAergic neurons and that glial metabolism supports both glutamatergic and GABAergic neurons in the living rat brain. We performed (13) C NMR spectroscopy in vivo at high magnetic field (14.1 T) upon administration of [1,6-(13) C]glucose. This allowed to measure (13) C incorporation into the three aliphatic carbons of GABA in the rat brain, in addition to those of glutamate, glutamine and aspartate. These data were then modelled to determine fluxes of energy metabolism in GABAergic and glutamatergic neurons and glial cells.

Chemisorption of atomic aluminum on Si(111): Evidence for an adsorbate-induced relaxation based on ab initio cluster-model calculations

Interaction models of atomic Al with Si4H9, Si4H7, and Si6H9 clusters have been studied to simulate Al chemisorption on the Si(111) surface in the atop, fourfold atop, and open sites. Calculations were carried out using nonempirical pseudopotentials in the framework of the ab initio Hartree-Fock procedure. Equilibrium bond distances, binding energies for adsorption, and vibrational frequencies of the adatoms are calculated. Several basis sets were used in order to show the importance of polarization effects, especially in the binding energies. Final results show the importance of considering adatom-induced relaxation effects to specify the order of energy stabilities for the three different sites, the fourfold atop site being the preferred one, in agreement with experimental findings.

Evidence for oxygen-island formation on Al(111): Cluster-model theory and x-ray photoelectron spectroscopy

The O 1s x-ray photoelectron spectroscopy spectrum for Al(111)/O at 300 K shows two components whose behavior as a function of time and variation of detection angle are consistent with either (a) a surface species represented by the higher binding-energy (BE) component and a subsurface species represented by the lower BE component, or (b) small close-packed oxygen islands with the interior atoms represented by the lower BE component and the perimeter atoms by the higher BE component. We have modeled both situations using ab initio Hartree-Fock wave functions for clusters of Al and O atoms. For an O atom in a threefold site, it was found that a below-surface position gave a higher O 1s BE than an above-surface position, incompatible with interpretation (a). This change in the O 1s BE could arise because the bond for O to Al may have a more covalent character when the O is below the surface than when it is above the surface. We present evidence consistent with this view. An O adatom island with all the O atoms in threefold sites gives calculated O 1s BE's which are significantly higher for the perimeter O atoms. Further, the results for an isolated O island without the Al substrate present also give higher BE¿s for the perimeter atoms. Both these results are consistent with interpretation (b). Published scanning-tunneling-microscopy data supports the suggestion that the chemisorbed state consists of small, close-packed islands, whereas the presence of two vibrational modes in high-resolution electron-energy-loss spectroscopy data has been interpreted as representing surface and subsurface oxygen atoms. In light of the present results, we suggest that a vibrational interpretation in terms of interior and perimeter adatoms should be considered.

Performance of correlation functionals in ab initio chemisorption cluster-model calculations: Alkali metals on Si(111)

The performance of different correlation functionals has been tested for alkali metals, Li to Cs, interacting with cluster models simulating different active sites of the Si(111) surface. In all cases, the ab initio Hartree-Fock density has been obtained and used as a starting point. The electronic correlation energy is then introduced as an a posteriori correction to the Hartree-Fock energy using different correlation functionals. By making use of the ionic nature of the interaction and of different dissociation limits we have been able to prove that all functionals tested introduce the right correlation energy, although to a different extent. Hence, correlation functionals appear as an effective and easy way to introduce electronic correlation in the ab initio Hartree-Fock description of the chemisorption bond in complex systems where conventional configuration interaction techniques cannot be used. However, the calculated energies may differ by some tens of eV. Therefore, these methods can be employed to get a qualitative idea of how important correlation effects are, but they have some limitations if accurate binding energies are to be obtained.

Surface structure and stability of PdZn and PtZn alloys: Density-functional slab model studies

Geometric parameters of binary (1:1) PdZn and PtZn alloys with CuAu-L10 structure were calculated with a density functional method. Based on the total energies, the alloys are predicted to feature equal formation energies. Calculated surface energies of PdZn and PtZn alloys show that (111) and (100) surfaces exposing stoichiometric layers are more stable than (001) and (110) surfaces comprising alternating Pd (Pt) and Zn layers. The surface energy values of alloys lie between the surface energies of the individual components, but they differ from their composition weighted averages. Compared with the pure metals, the valence d-band widths and the Pd or Pt partial densities of states at the Fermi level are dramatically reduced in PdZn and PtZn alloys. The local valence d-band density of states of Pd and Pt in the alloys resemble that of metallic Cu, suggesting that a similar catalytic performance of these systems can be related to this similarity in the local electronic structures.

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

Prediction of resting energy expenditure from fat-free mass and fat mass.

On the basis of literature values, the relationship between fat-free mass (FFM), fat mass (FM), and resting energy expenditure [REE (kJ/24 h)] was determined for 213 adults (86 males, 127 females). The objectives were to develop a mathematical model to predict REE based on body composition and to evaluate the contribution of FFM and FM to REE. The following regression equations were derived: 1) REE = 1265 + (93.3 x FFM) (r2 = 0.727, P < 0.001); 2) REE = 1114 + (90.4 x FFM) + (13.2 x FM) (R2 = 0.743, P < 0.001); and 3) REE = (108 x FFM) + (16.9 x FM) (R2 = 0.986, P < 0.001). FM explained only a small part of the variation remaining after FFM was accounted for. The models that include both FFM and FM are useful in examination of the changes in REE that occur with a change in both the FFM and FM. To account for more of the variability in REE, FFM will have to be divided into organ mass and skeletal muscle mass in future analyses.

Electric dipole polarizability in 208Pb: insights from the droplet model

We study the electric dipole polarizability α D in 208 Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean-field models. We adopt the droplet model as a guide to better understand the correlations between α D and other isovector observables. Insights from the droplet model suggest that the product of α D and the nuclear symmetry energy at saturation density J is much better correlated with the neutron skin thickness r np of 208 Pb than the polarizability alone. Correlations of α D J with r np and with the symmetry energy slope parameter L suggest that α D J is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of the nuclear energy density functional by comparing our theoretical predictions against measurements of both α D and the parity-violating asymmetry in 208 Pb. We find that the recent experimental determination of α D in 208 Pb in combination with the range for the symmetry energy at saturation density J = [31 ± (2) est] MeV suggests r np (208 Pb) = 0 . 165 ± (0 . 009) expt ± (0 . 013) theor ± (0.021) est fm and L = 43 ± (6) expt ± (8) theor ± (12) est MeV

Inclusion of soil erosion impacts in life cycle assessment on a global scale: application to energy crops in Spain

Purpose: Despite the fundamental role of ecosystem goods and services in sustaining human activities, there is no harmonized and internationally agreed method for including them in life cycle assessment (LCA). The main goal of this study was to develop a globally applicable and spatially resolved method for assessing land-use impacts on the erosion regulation ecosystem service.Methods: Soil erosion depends much on location. Thus, unlike conventional LCA, the endpoint method was regionalized at the grid-cell level (5 arc-minutes, approximately 10×10 km2) to reflect the spatial conditions of the site. Spatially explicit characterization factors were not further aggregated at broader spatial scales. Results and discussion: Life cycle inventory data of topsoil and topsoil organic carbon (SOC) losses were interpreted at the endpoint level in terms of the ultimate damage to soil resources and ecosystem quality. Human health damages were excluded from the assessment. The method was tested on a case study of five three-year agricultural rotations, two of them with energy crops, grown in several locations in Spain. A large variation in soil and SOC losses was recorded in the inventory step, depending on climatic and edaphic conditions. The importance of using a spatially explicit model and characterization factors is shown in the case study.Conclusions and outlook: The regionalized assessment takes into account the differences in soil erosion-related environmental impacts caused by the great variability of soils. Taking this regionalized framework as the starting point, further research should focus on testing the applicability of the method trough the complete life cycle of a product and on determining an appropriate spatial scale at which to aggregate characterization factors, in order to deal with data gaps on location of processes, especially in the background system. Additional research should also focus on improving reliability of the method by quantifying and, insofar as it is possible, reducing uncertainty.

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.