Spin Filtering via Resonant Reflection of Relativistic Surface States

A microscopic approach is developed to scattering of surface states from a non-magnetic linear defect at a surface with strong spin-orbit interaction. Spin-selective reflection resonances in scattering of Rashba-split surface states by an atomic stripe are theoretically discovered in a proof-of-principle calculation for a model crystal potential. Spin-filtering properties of such linear defects are analyzed within an envelope-function formalism for a perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model is found to be in full accord with the microscopic theory, which reveals the essential physics behind the scattering resonance. The spin-dependent reflection suggests a novel mechanism to manipulate spins on the nanoscale.Comment: 6 pages, 4 figures, 1 tabl

Opportunity costs and offsets acceptance in FI-REDD model

In previous studies, we have proposed financial instruments supporting REDD (FI-REDD). Within a microeconomic framework we modeled interactions between an electricity producer (EP), electricity consumer (EC), and forest owner (FO). FI-REDD allows for optional consumption of emission offsets by the EP (any amount up to the initially contracted volume is allowed), and includes a benefit-sharing mechanism between the EP and FO as it regards unused offsets. The modeling results indicated that FI-REDD might help avoid bankruptcy of CO2-intensive producers at high levels of CO2 prices. We demonstrated the impact of benefit-sharing and risk preferences on the contracted REDD offsets quantity. Here, we further develop the FI-REDD model by introducing two modifications. Firstly, we add opportunity cost of the forest owner, i.e. forest value alternative to REDD. This change leads to a realistic risk-adjusted supply curves for REDD, which are generated by the indifference (fair) pricing model and calculated for all possible benefit-sharing ratios. Secondly, we introduce an uncertainty associated with acceptance (fungibility) of REDD offsets in the second stage of the model. Modeling results demonstrate in a quantitative way the impact of fungibility uncertainty and positive effects of the benefit-sharing mechanism. An optimal value of the benefit-sharing ratio can be found that guarantees contracting the highest amounts of offsets at the low equilibrium price. This qualitative feature of the benefit-sharing mechanism is robust with respect to the uncertainty parameters in the model. We also undertake an in-depth analysis of decision making of the electricity producer using 3D visualization tools

Nonlinear dispersion of stationary waves in collisionless plasmas

A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $\Delta\omega$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $\Delta\omega\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation

REDD-based Offsets: Benefit Sharing and Risks

In this study we apply systems analysis methods to modeling financial instruments supporting the Reduced Emissions from Deforestation and Degradation (REDD) program. We consider a risk-aware forest owner and an electricity producer evaluating the REDD-based offsets with benefit-sharing mechanism under uncertain CO2 prices. For a range of CO2 prices and respective risks perceived by the forest owner (seller) and electricity producer (buyer), we apply a model of fair (indifference) pricing. The decision-making process under uncertainty is formalized in the spirit of Howard Raiffa’s “Decision analysis” (1968). Parties’ risk preferences are reflected by exponential utility functions. The potentially contracted amounts of REDD offsets are analyzed under various risk preferences and for different benefit sharing opportunities and price levels. Our results show that a risk-averse attitude considerably increases the contracted amounts of REDD offsets (compared to risk-neutral case) and, therefore, creates a higher potential for REDD implementation. We demonstrate a possibility of situations, when parties could agree on a certain range of REDD contracts, for example, smaller amounts of REDD offsets are traded for higher prices, and larger amounts for lower prices, but contracting a moderate amount at a moderate price is impossible. Higher benefit-sharing ratios can also increase contracted amounts even in the case of risk-taking electricity producer. Our modeling results highlight two ways to promote higher REDD participation: (i) increasing risk aversion of the energy producers, and (ii) implementing the mechanism of benefit/risk sharing between REDD consumer and supplier

Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Solution of Evolutionary Games via Hamilton-Jacobi-Bellman Equations

This poster is focused on construction of solutions for bimatrix evolutionary games based on methods of the theory of optimal control and generalized solutions of Hamilton-Jacobi-Bellman equations. It is assumed that the evolutionary dynamics describe interactions of agents in large population groups in biological and social models or interactions of investors in financial markets. Interactions of agents are subject to the dynamic process which provides the possibility to control flows between different types of behavior or investments. It is worth noting that the dynamics of interactions can be interpreted as the system of Kolmogorov’s type differential equations. Parameters of the dynamics are not fixed a priori and can be treated as controls constructed either as time programs or on the feedback principle. Payoff functionals in the evolutionary game of two coalitions are determined by the limit of average matrix gains on an infinite horizon. The notion of a dynamical Nash equilibrium is introduced in the class of control feedbacks within Krasovskii’s theory of differential games. Elements of a dynamical Nash equilibrium are based on guaranteed feedbacks constructed within the framework of the theory of generalized solutions of Hamilton-Jacobi-Bellman equations. The value functions for the series of differential games are constructed analytically and their stability properties are verified using the technique of conjugate derivatives. The equilibrium trajectories are generated on the basis of positive feedbacks originated by value functions. It is shown that the proposed approach provides new qualitative results for the equilibrium trajectories in evolutionary games and ensures better results for payoff functionals than replicator dynamics in evolutionary games or Nash values in static bimatrix games. The efficiency of the proposed approach is demonstrated by applications to construction of equilibrium dynamics for agents’ interactions in financial markets