Dual time scales in simulated annealing of a two-dimensional Ising spin glass

We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature $T=0$ of the two-dimensional Ising model with random $J= \pm 1$ couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, $\tau \sim L^z$, are $z=8.28 \pm 0.03$ for the relaxation of the order parameter and $z=10.31 \pm 0.04$ for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for $T \to 0$ simulated annealing are different from the temperature-dependent equilibrium dynamic exponent $z_{\rm eq}(T)$, for which previous studies have found a divergent behavior; $z_{\rm eq}(T\to 0) \to \infty$. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.Comment: 13 pages, 16 figure

Evolution of transport properties of BaFe2-xRuxAs2 in a wide range of isovalent Ru substitution

The effects of isovalent Ru substitution at the Fe sites of BaFe2-xRuxAs2 are investigated by measuring resistivity and Hall coefficient on high-quality single crystals in a wide range of doping (0 < x < 1.4). Ru substitution weakens the antiferromagnetic (AFM) order, inducing superconductivity for relatively high doping level of 0.4 < x < 0.9. Near the AFM phase boundary, the transport properties show non-Fermi-liquid-like behaviors with a linear-temperature dependence of resistivity and a strong temperature dependence of Hall coefficient with a sign change. Upon higher doping, however, both of them recover conventional Fermi-liquid behaviors. Strong doping dependence of Hall coefficient together with a small magnetoresistance suggest that the anomalous transport properties can be explained in terms of anisotropic charge carrier scattering due to interband AFM fluctuations rather than a conventional multi-band scenario.Comment: 7 pages, 6 figures, submitted to Phys. Rev.

Enhancement of plasticity in Ti-based metallic glass matrix composites by controlling characteristic and volume fraction of primary phase

In this study, Ti-based metallic glass matrix composites with high plasticity have been developed by controlling characteristic and volume fraction of primary phase embedded in the glass matrix. By careful alloy design procedure, the compositions of ß/glass phases, which are in metastable equilibrium have been properly selected, therefore the mechanical properties can be tailored by selecting the alloy compositions between the composition of ß and glass phases. The relation between the compressive yield strength and volume fraction of ß phase is well described using the rule of mixtures

Dynamic scaling in the 2D Ising spin glass with Gaussian couplings

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $\tau$ to the system length $L$; $\tau\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.Comment: 10 pages, 5 figure

Feedback noncausal model predictive control of wave energy converters

In this paper, a novel feedback noncausal model predictive control (MPC) strategy for sea wave energy converters (WECs) is proposed, where the wave prediction information can be explicitly incorporated into the MPC strategy to improve the WEC control performance. The main novelties of the MPC strategy proposed in this paper include: (i) the recursive feasibility and robust constraints satisfaction are guaranteed without a significant increase in the computational burden; (ii) the information of short-term wave prediction is incorporated into the feedback noncausal MPC method to maximise the potential energy output; (iii) the sea condition for the WEC to safely operate in can be explicitly calculated. The proposed feedback noncausal MPC algorithm can also be extended to a wide class of control design problems, especially to the energy maximisation problems with constraints to be satisfied and subject to persistent but predictable disturbances. Numerical simulations are provided to show the efficacy of the proposed feedback noncausal MPC

Quantifying the origin of metallic glass formation

The waiting time to form a crystal in a unit volume of homogeneous undercooled liquid exhibits a pronounced minimum τ_X* at a ‘nose temperature’ T* located between the glass transition temperature T_g, and the crystal melting temperature, T_L. Turnbull argued that τ_X* should increase rapidly with the dimensionless ratio t_(rg)=T_g/T_L. Angell introduced a dimensionless ‘fragility parameter’, m, to characterize the fall of atomic mobility with temperature above T_g. Both t_(rg) and m are widely thought to play a significant role in determining τ_X*. Here we survey and assess reported data for T_L, T_g, t_(rg), m and τ_X* for a broad range of metallic glasses with widely varying τ_X*. By analysing this database, we derive a simple empirical expression for τ_X*(t_(rg), m) that depends exponentially on t_(rg) and m, and two fitting parameters. A statistical analysis shows that knowledge of t_(rg) and m alone is therefore sufficient to predict τ_X* within estimated experimental errors. Surprisingly, the liquid/crystal interfacial free energy does not appear in this expression for τ_X*

The initial temporal evolution of a feedback dynamo for Mercury

Various possibilities are currently under discussion to explain the observed weakness of the intrinsic magnetic field of planet Mercury. One of the possible dynamo scenarios is a dynamo with feedback from the magnetosphere. Due to its weak magnetic field Mercury exhibits a small magnetosphere whose subsolar magnetopause distance is only about 1.7 Hermean radii. We consider the magnetic field due to magnetopause currents in the dynamo region. Since the external field of magnetospheric origin is antiparallel to the dipole component of the dynamo field, a negative feedback results. For an alpha-omega-dynamo two stationary solutions of such a feedback dynamo emerge, one with a weak and the other with a strong magnetic field. The question, however, is how these solutions can be realized. To address this problem, we discuss various scenarios for a simple dynamo model and the conditions under which a steady weak magnetic field can be reached. We find that the feedback mechanism quenches the overall field to a low value of about 100 to 150 nT if the dynamo is not driven too strongly

Is "not just right experience" (NJRE) in obsessive-compulsive disorder part of an autistic phenotype?

OBJECTIVE: Harm avoidance (HA) and "not just right experience" (NJRE) have been proposed to be 2 core motivational processes underlying obsessive-compulsive disorder (OCD). The objective of this study was to explore whether NJRE demarcates a neurodevelopmental OCD subgroup distinct from HA related to autistic traits and/or to a broader phenotype of cognitive rigidity and sensory processing difficulties associated with an earlier age of OCD onset. METHODS: A correlational design investigated whether NJRE and HA are distinct entities in OCD and explored their relationship to autism spectrum disorder (ASD) traits measured by the Autism Quotient (AQ), sensory processing, set-shifting, and age of OCD onset in an OCD sample (N=25). RESULTS: NJRE was only moderately (r=.34) correlated to HA and not significant in this study. Consistent with predictions, NJRE was associated with sensory processing difficulties and an earlier age of OCD onset. No significant relationships were found between NJRE and ASD traits as measured by the AQ or set-shifting difficulties. CONCLUSIONS: These preliminary findings suggest a lack of evidence demonstrating NJRE as a manifestation of core autistic traits as measured by the AQ. However, NJRE was associated with sensory abnormalities and an earlier age of OCD onset. The role of NJRE as a developmental, and possibly neurodevelopmental, risk factor for OCD possibly warrants further investigation

Seiberg-Witten prepotential for E-string theory and random partitions

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.Comment: 14 page