Topological characteristics of oil and gas reservoirs and their applications

We demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.Comment: 12 page

Constant Rank Bimatrix Games are PPAD-hard

The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for constant rank games, and asked if there exists a polynomial time algorithm to compute an exact NE. Adsul et al. (2011) answered this question affirmatively for rank-$1$ games, leaving rank-2 and beyond unresolved. In this paper we show that NE computation in games with rank $\ge 3$, is PPAD-hard, settling a decade long open problem. Interestingly, this is the first instance that a problem with an FPTAS turns out to be PPAD-hard. Our reduction bypasses graphical games and game gadgets, and provides a simpler proof of PPAD-hardness for NE computation in bimatrix games. In addition, we get: * An equivalence between 2D-Linear-FIXP and PPAD, improving a result by Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD. * NE computation in a bimatrix game with convex set of Nash equilibria is as hard as solving a simple stochastic game. * Computing a symmetric NE of a symmetric bimatrix game with rank $\ge 6$ is PPAD-hard. * Computing a (1/poly(n))-approximate fixed-point of a (Linear-FIXP) piecewise-linear function is PPAD-hard. The status of rank-$2$ games remains unresolved

Yang-Baxter maps and multi-field integrable lattice equations

A variety of Yang-Baxter maps are obtained from integrable multi-field equations on quad-graphs. A systematic framework for investigating this connection relies on the symmetry groups of the equations. The method is applied to lattice equations introduced by Adler and Yamilov and which are related to the nonlinear superposition formulae for the B\"acklund transformations of the nonlinear Schr\"odinger system and specific ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio

Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent \gamma= 2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power-laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution figures is available at http://www.pks.mpg.de/~edugal

Spatial structures and dynamics of kinetically constrained models for glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density, $v$, the spacing, $\Xi$, between mobile elements diverges exponentially or faster in $1/v$. Within the mobile elements, the dynamics is intrinsically cooperative and the characteristic time scale diverges faster than any power of $1/v$ (although slower than $\Xi$). The tagged-particle diffusion coefficient vanishes roughly as $\Xi^{-d}$.Comment: 4 pages. Accepted for pub. in Phys. Rev. Let

Deterministic models of quantum fields

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman and von Neumann is used to study the classical evolution of an ensemble of such systems. Its Liouville operator is decomposed into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a constraint on physical states, which is invariant under the Hamiltonian flow. Thus, choosing suitable variables, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. -- We briefly mention an U(1) gauge theory with ``varying alpha'' or dilaton coupling where a corresponding quantized theory emerges in the phase space approach. It is energy-parity symmetric and, therefore, a prototype of a model in which the cosmological constant is protected by a symmetry.Comment: 6 pages; synopsis of hep-th/0510267, hep-th/0503069, hep-th/0411176 . Talk at Constrained Dynamics and Quantum Gravity - QG05, Cala Gonone (Sardinia, Italy), September 12-16, 2005. To appear in the proceeding

Origin of the anomalies: the modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe

The non-Abelian dual Meissner effect as color-alignment in SU(2) lattice gauge theory

A new gauge (m-gauge) condition is proposed by means of a generalization of the Maximal Abelian gauge (MAG). The new gauge admits a space time dependent embedding of the residual U(1) into the SU(2) gauge group. This embedding is characterized by a color vector $\vec{m}(x)$. It turns out that this vector only depends of gauge invariant parts of the link configurations. Our numerical results show color ferromagnetic correlations of the $\vec{m}(x)$ field in space-time. The correlation length scales towards the continuum limit. For comparison with the MAG, we introduce a class of gauges which smoothly interpolates between the MAG and the m-gauge. For a wide range of the gauge parameter, the vacuum decomposes into regions of aligned vectors $\vec{m}$. The ''neutral particle problem'' of MAG is addressed in the context of the new gauge class.Comment: 15 pages, 6 figures, LaTeX using eps

Direct effects of warming increase woody plant abundance in a subarctic wetland

Both the direct effects of warming on a species’ vital rates and indirect effects of warming caused by interactions with neighboring species can influence plant populations. Furthermore, herbivory mediates the effects of warming on plant community composition in many systems. Thus, determining the importance of direct and indirect effects of warming, while considering the role of herbivory, can help predict long-term plant community dynamics. We conducted a field experiment in the coastal wetlands of western Alaska to investigate how warming and herbivory influence the interactions and abundances of two common plant species, a sedge, Carex ramenskii, and a dwarf shrub, Salix ovalifolia. We used results from the experiment to model the equilibrium abundances of the species under different warming and grazing scenarios and to determine the contribution of direct and indirect effects to predict population changes. Consistent with the current composition of the landscape, model predictions suggest that Carex is more abundant than Salix under ambient temperatures with grazing (53% and 27% cover, respectively). However, with warming and grazing, Salix becomes more abundant than Carex (57% and 41% cover, respectively), reflecting both a negative response of Carexand a positive response of Salix to warming. While grazing reduced the cover of both species, herbivory did not prevent a shift in dominance from sedges to the dwarf shrub. Direct effects of climate change explained about 97% of the total predicted change in species cover, whereas indirect effects explained only 3% of the predicted change. Thus, indirect effects, mediated by interactions between Carex and Salix, were negligible, likely due to use of different niches and weak interspecific interactions. Results suggest that a 2°C increase could cause a shift in dominance from sedges to woody plants on the coast of western Alaska over decadal timescales, and this shift was largely a result of the direct effects of warming. Models predict this shift with or without goose herbivory. Our results are consistent with other studies showing an increase in woody plant abundance in the Arctic and suggest that shifts in plant–plant interactions are not driving this change

Strangeness and heavy flavor at RHIC: Recent results from PHENIX

We report recent results of strangeness and heavy flavor measurements from PHENIX. The topics are: Elliptic flow of strangeness and heavy flavor electron production comparing to the other hadrons, $\phi$ meson production, and an exotic particle search.Comment: 8 pages, 6 figures, 1 table. Submitted to J. Phys. G (Proceedings of the 8th International Conference on Strangeness in Quark Matter, Cape Town, South Africa, September 15-20, 2004