Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model

In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible ways of circumventing this problem, including the use of a local version of the method of characteristics, non-polynomial FEM bases and Lie-group discretization methods.Comment: 12 pages, accepted Math. and Comp. Simul., May 200

The Introduction of Yoga Recovery on Physiological and Psychological Stress and Performance in NCAA Athletes

NCAA student athletes face unique physiological and psychological stressors daily, which may contribute to overtraining, burnout, and other physical and mental health issues. However, NCAA institutions often leave recovery up to the individual athlete due to time restriction and Countable Athletic Related Activities (CARA) hour limitations on team mandated activities. Attention to methods to promote recovery from these training loads is increasing in NCAA institutions. A mind-body activity such as yoga is proposed to have physiological and psychological benefits for student athletes. The goal of this review is to identify which aspects of yoga promote the most effective recovery in measures such as: performance, physical biomarkers of stress, muscle damage, heart rate variability, sleep quality, mood state, anxiety, and depression. A recovery yoga protocol is presented, based on the current literature on the topic, to suggest a time- and cost-effective mind-body recovery modality for NCAA student athletes. The recommendation of this review concludes that, among other approaches, NCAA athletes are ideal candidates to undertake the practice of a yoga-based relaxation technique. As such, initial incorporation of yoga is recommended for 20 minutes twice weekly, with a third 60- minute practice each week for a more integrated mind-body yoga experience. From the literature, there is a scientific rationale to understand and anticipate physiological effects such as decreased muscle soreness, heart rate variability, and oxidative stress and psychological effects of improved mood, decreased anxiety, and depression in terms of yoga efficacy. Based on this rationale, introduction of yoga-based recovery is likely to improve some aspects of academic and athletic performance, as well as overall greater wellbeing upon completion of the recommended intervention. However, well-founded conclusions are tentative because explicit mechanistic research is sparse. Accordingly, outcomes based research is needed to confirm the extent to which introduction of these recovery-based approaches will benefit yoga novices

Non-Orthogonal Multiple Access for FSO Backhauling

We consider a free space optical (FSO) backhauling system which consists of two base stations (BSs) and one central unit (CU). We propose to employ non-orthogonal multiple access (NOMA) for FSO backhauling where both BSs transmit at the same time and in the same frequency band to the same photodetector at the CU. We develop a dynamic NOMA scheme which determines the optimal decoding order as a function of the channel state information at the CU and the quality of service requirements of the BSs, such that the outage probabilities of both BSs are jointly minimized. Moreover, we analyze the performance of the proposed NOMA scheme in terms of the outage probability over Gamma-Gamma FSO turbulence channels. We further derive closed-form expressions for the outage probability for the high signal-to-noise ratio regime. Our simulation results confirm the analytical derivations and reveal that the proposed dynamic NOMA scheme significantly outperforms orthogonal transmission and existing NOMA schemes.Comment: This paper has been submitted to IEEE WCNC 201

Vibrational instability, two-level systems and Boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.Comment: 28 pages, 3 figure

Statistical Modeling of FSO Fronthaul Channel for Drone-based Networks

We consider a drone-based communication network, where several drones hover above an area and serve as mobile remote radio heads for a large number of mobile users. We assume that the drones employ free space optical (FSO) links for fronthauling of the users' data to a central unit. The main focus of this paper is to quantify the geometric loss of the FSO channel arising from random fluctuation of the position and orientation of the drones. In particular, we derive upper and lower bounds, corresponding approximate expressions, and a closed-form statistical model for the geometric loss. Simulation results validate our derivations and quantify the FSO channel quality as a function of the drone's instability, i.e., the variation of its position and orientation.Comment: This paper has been submitted to ICC 201

Field-induced structural aging in glasses at ultra low temperatures

In non-equilibrium experiments on the glasses Mylar and BK7, we measured the excess dielectric response after the temporary application of a strong electric bias field at mK--temperatures. A model recently developed describes the observed long time decays qualitatively for Mylar [PRL 90, 105501, S. Ludwig, P. Nalbach, D. Rosenberg, D. Osheroff], but fails for BK7. In contrast, our results on both samples can be described by including an additional mechanism to the mentioned model with temperature independent decay times of the excess dielectric response. As the origin of this novel process beyond the "tunneling model" we suggest bias field induced structural rearrangements of "tunneling states" that decay by quantum mechanical tunneling.Comment: 4 pages, 4 figures, accepted at PRL, corrected typos in version

Pressure dependence of diffusion in simple glasses and supercooled liquids

Using molecular dynamics simulation, we have calculated the pressure dependence of the diffusion constant in a binary Lennard-Jones Glass. We observe four temperature regimes. The apparent activation volume drops from high values in the hot liquid to a plateau value. Near the critical temperature of the mode coupling theory it rises steeply, but in the glassy state we find again small values, similar to the ones in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory

Diffusion and jump-length distribution in liquid and amorphous Cu33_{33}Zr67_{67}

Using molecular dynamics simulation, we calculate the distribution of atomic jum ps in Cu$_{33}$Zr$_{67}$ in the liquid and glassy states. In both states the distribution of jump lengths can be described by a temperature independent exponential of the length and an effective activation energy plus a contribution of elastic displacements at short distances. Upon cooling the contribution of shorter jumps dominates. No indication of an enhanced probability to jump over a nearest neighbor distance was found. We find a smooth transition from flow in the liquid to jumps in the g lass. The correlation factor of the diffusion constant decreases with decreasing temperature, causing a drop of diffusion below the Arrhenius value, despite an apparent Arrhenius law for the jump probability