Short-range Model Research Articles

Exact solution of a classical short-range spin model with a phase transition in one dimension: The Potts model with invisible states

We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the q states of the ordinary Potts model, this possesses r additional states which contribute to the entropy, but not to the interaction energy. We determine the partition function, using the transfer-matrix method, in the general case of two ordering fields: h1 acting on a visible state and h2 on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h1=0. When Imh2=0 and r≥0, these zeros accumulate along a line that intersects the real temperature axis at the origin. This corresponds to the usual “phase transition” in a 1D system. However, for Imh2≠0 or r<0, the line of zeros intersects the positive part of the real temperature axis, which signals the existence of a phase transition at non-zero temperature.

ANALISIS FAKTOR-FAKTOR YANG MEMPENGARUHI IMPOR BERAS INDONESIA

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Simulating the effect of muscle stiffness and co-contraction on postural stability

Posture perturbation experiments can be used to assess the biomechanical factors underlying postural stability. However, experiments are limited by participant safety, inability to measure important factors such as muscle forces and the large number of conditions to be tested. We employed forward dynamics computer simulations to mimic posture perturbation experiments to assess the effect of short-range muscle stiffness and muscle co-contraction on the postural stability of a musculoskeletal model. Two novel simulation techniques were developed: a static-optimisation formulation that uses target joint stiffness to elicit muscle co-contraction and a realisation of a short-range stiffness muscle model as a passive, pre-stressed spring that can be used in forward dynamics simulations. Our simulation results demonstrated that the realistic short-range stiffness has a large impact on postural stability as compared to traditional Hill-type muscle models that underestimate intrinsic stiffness. We also found that muscle co-contraction contributed to postural stability, but to a lesser extent than the realistic intrinsic stiffness alone. Although the present study does not consider active responses, our simulations have revealed important factors that contribute to the body’s intrinsic stability and that may be helpful, in part, for compensating for diminished or delayed postural responses to maintain balance.

Exact solution of corner-modified banded block-Toeplitz eigensystems

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.

Long-time predictability in disordered spin systems following a deep quench.

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

Decimation of the Dyson–Ising ferromagnet

We study the decimation to a sublattice of half the sites of the one-dimensional Dyson–Ising ferromagnet with slowly decaying long-range pair potentials of the form 1|i−j|α, deep in the phase transition region (1<α≤2 and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials (α>2) and provides an example of a “standard” non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.

Enhanced magnetocaloric properties and critical behavior of (Fe0.72Cr0.28)3Al alloys for near room temperature cooling

Magnetic cooling is an environmentally friendly, energy efficient, thermal management technology relying on high performance magnetocaloric materials (MCM). Current research has focused on low cost, corrosion resistant, rare earth (RE) free MCMs. We report the structural and magnetocaloric properties of novel, low cost, RE free, iron based (Fe0.72Cr0.28)3Al alloys. The arc melted buttons and melt spun ribbons possessed the L21 crystal structure and B2 crystal structure, respectively. A notable enhancement of 33% in isothermal entropy change (−ΔSm) and 25% increase in relative cooling power (RCP) for the ribbons compared to the buttons can be attributed to higher structural disorder in the Fe–Cr and Fe–Al sub-lattices of the B2 structure. The critical behavior was investigated using modified Arrott plots, the Kouvel–Fisher plot and the critical isotherm technique; the critical exponents were found to correspond to the short-range order 3D Heisenberg model. The field and temperature dependent magnetization curves of (Fe0.72Cr0.28)3Al alloys revealed their soft magnetic nature with negligible hysteresis. Thus, these alloys possess promising performance attributes for near room temperature magnetic cooling applications.

Traveling solitons in long-range oscillator chains

We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi–Pasta–Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent . We obtain an analytic perturbative expression of traveling envelope solitons by introducing a non linear Schrödinger equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations for the value which was chosen as a case study.

The properties and structure of Ge[sbnd]Se[sbnd]Te glasses and thin films

Ge30Se70−xTex bulk glasses and thin films for x=0, 10 and 20 were prepared. The properties and structure were characterized by differential scanning calorimetry (DSC), Raman spectroscopy and also by 77Se and 125Te MAS NMR spectroscopy. The optical properties were also measured. The absence of crystalline phases was verified by XRD, while DSC indicated that the glasses were not phase separated. Although the glass transition temperature of both Ge30Se70 glass and thin film is the same, different ΔCp reveal a higher disorder of the thin film. Both the glass transition temperature and ΔCp of Te glasses as well as crystallization temperatures decrease when Te increases due to increasing GeTe2/2 instead of GeSe4/2 structural units thereby reducing 3D interconnection of the glassy network. Based on the 77Se MAS NMR results, the short-range order model was determined as a suitable structural model for Ge30Se70 glass. 77Se and 125Te MAS NMR confirmed that Ge in alloys with Te only reaches oxidation state +II in agreement with GeTe phase diagram and therefore no GeTe4/2 tetrahedra can be present in these glasses and/or films. Raman spectroscopy confirmed that the short-range order of glasses and films is basically the same. The refractive index of thin films increases with tellurium content. The optical band gap of the thin films strongly decreases from 2.02eV to 1.36eV with increasing Te content and simultaneously the increasing structural disorder and width of the band tails increase. Reduction of the oxidation state of germanium to GeII caused by a reaction with tellurium ultimately leads to a reduction in 3D connectivity of the non-crystalline matrix and the loss of the glass-forming ability of the GeSeTe system.

Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing interacting classical spin systems in the thermodynamic limit, including the occurrence of a phase transition, using topological arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is that, in the context of the classical models studied, the Euler characteristic embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the models, such quantities are those that do not violate the laws of thermodynamics (with the proviso that van der Waals loop states are mean field (MF) artifacts). We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of per site, and that using the Boltzmann microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the one-dimensional short-range XY models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range () and the short-range (Tc = 0) XY models. Further studies are very desirable in order to clarify the extension of the validity of our proposal.

Energy Harvesting-Based D2D Communications in the Presence of Interference and Ambient RF Sources

This paper considers a device-to-device (D2D) network with time-splitting protocol, where a D2D transmitter ( $ \text {T}_{\text {x}}$ ) first harvests energy from a multiple-antenna power beacon (PB) and ambient radio frequency sources, and then uses that harvested energy to transmit data to the D2D receiver ( $ \text {R}_{\text {x}}$ ). To improve the energy transfer efficiency, the PB is equipped with multiple antennas for energy transfer, and $ \text {T}_{\text {x}}$ is equipped with multiple antennas for energy harvesting. Two beamforming techniques, called best antenna-based beamforming and optimal beamforming vector, are proposed to use at the PB. We derive novel analytical expressions for the average harvested energy, power outage probability, and the outage probability of the information transfer link, considering the effect of co-channel interference from homogeneous Poison distributed interferes and the short-range propagation model for the path loss. We show that by deploying multiple harvesting energy antennas at $ \text {T}_{\text {x}}$ and by implementing optimal beamforming vector scheme at the PB, the system performance improves substantially. Furthermore, Monte-Carlo simulations are provided and verify the accuracy of our analytical results.

Solar Irradiance Nowcasting Case Studies near Sacramento

AbstractThe Sun4Cast solar power forecasting system, designed to predict solar irradiance and power generation at solar farms, is composed of several component models operating on both the nowcasting (0–6 h) and day-ahead forecast horizons. The different nowcasting models include a statistical forecasting model (StatCast), two satellite-based forecasting models [the Cooperative Institute for Research in the Atmosphere Nowcast (CIRACast) and the Multisensor Advection-Diffusion Nowcast (MADCast)], and a numerical weather prediction model (WRF-Solar). It is important to better understand and assess the strengths and weaknesses of these short-range models to facilitate further improvements. To that end, each of these models, including four WRF-Solar configurations, was evaluated for four case days in April 2014. For each model, the 15-min average predicted global horizontal irradiance (GHI) was compared with GHI observations from a network of seven pyranometers operated by the Sacramento Municipal Utility District (SMUD) in California. Each case day represents a canonical sky-cover regime for the SMUD region and thus represents different modeling challenges. The analysis found that each of the nowcasting models perform better or worse for particular lead times and weather situations. StatCast performs best in clear skies and for 0–1-h forecasts; CIRACast and MADCast perform reasonably well when cloud fields are not rapidly growing or dissipating; and WRF-Solar, when configured with a high-spatial-resolution aerosol climatology and a shallow cumulus parameterization, generally performs well in all situations. Further research is needed to develop an optimal dynamic blending technique that provides a single best forecast to energy utility operators.

Nonsequential double ionization of Ne subject to few-cycle femtosecond laser pulses

We investigate experimentally and theoretically the evolution of Ne2+ ion momentum distributions from Nonsequential Double Ionization (NSDI) in few-cycle laser pulses with respect to the Carrier Envelope Phase (CEP). The distributions depend strongly on the CEP and exhibit an asymmetric double-hump structure at some CEPs. A semiclassical calculation can reproduce the experimental observations qualitatively, where the rescattering scenario is identified as the main mechanism of double ionization. Analysis based on this semiclassical model reveals that double ionization happens a little later than the collision. Depending on the time difference between the ionization moment and the collision moment, we can distinguish two ionization pathways involved, i.e., Recollision Impact Ionization (RII) (with time difference below 0.1 optical cycle) and Recollision-Excitation and Subsequent Ionization (RESI) (with time difference above 0.1 optical cycle) pathways. The asymmetric pattern results from both RII and RESI: RII leads to the asymmetric double-hump structure, while RESI contributes to the low momentum part and makes the dip of the double-hump structure shallower. Furthermore, Ne2+ ion momentum distributions from RII depend strongly on the CEP and the distributions from RESI seem to be not very sensitive to the CEP. To shed more light on physical mechanism of the asymmetric momentum distribution, the momentum distributions from two ionized electrons are presented at the collision moment, the ionization moment and the moment right after laser field ends for each pathway, respectively. The comparison unravels that the asymmetry comes from the asymmetric acceleration from the laser electric field after the double ionization moments. To demonstrate the significant role of long range Coulomb potential in NSDI process, we replace the Coulomb potential with a short-range model potential in the calculation and the results show appreciable distinctions from the case of Coulomb potential. It is clarified that the Coulomb potential raises the yields of RESI process, which, in turn, makes the dip shallower.

Effect of long- and short-range interactions on the thermodynamics of dipolar spin ice

The thermodynamic properties of dipolar spin ice on square, honeycomb and shakti lattices in the long-range and short-range dipole interaction models are studied. Exact solutions for the density of states, temperature dependencies of heat capacity, and entropy are obtained for these lattices with a finite number of point dipoles by means of complete enumeration. The magnetic susceptibility and average size of the largest low-energy cluster are calculated for square spin ice by means of Wang–Landau and Metropolis methods. We show that the long-range interaction leads to a blurring of the energy spectrum for all considered lattices. The inclusion of the long-range interaction leads to a significant change in the thermodynamic behaviour. An additional peak of heat capacity appears in the case of the honeycomb lattice. The critical temperature shifts in the direction of low or high temperatures; the direction depends on the lattice geometry. The critical temperature of the phase transition of square spin ice in the long-range model with frustrated ground states is obtained with the Wang–Landau and Metropolis methods independently.

Phase behaviour of short range triangle well fluids: A comparison with lysozyme suspensions

The phase coexistence of colloidal suspensions is studied by Monte Carlo Replica Exchange (REMC) simulations using an attractive triangle potential model of short range (1.15σ ≤ λ ≤ 1.4) in a wide temperature range. Typical liquid-vapor coexistences are found at temperatures close to the critical one, while for lower temperatures the liquid-vapor metastability is broken in favor of the vapor-solid coexistence. Structural properties are accessed through the radial distribution function and the global order parameter. The formation of a solid phase with structure belonging to the close-packed family is shown. The coexistence curves are plotted in reduced coordinates and compared with those experimentally obtained for protein suspensions (lysozyme aqueous suspensions with additives). A good qualitative agreement between experimental data and simulation results is found.

Equivalent-neighbor Potts models in two dimensions.

We investigate the two-dimensional q=3 and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number z of equivalent neighbors. For not-too-large z, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges, the transitions become discontinuous. For q=3 we locate a tricritical point separating the continuous and discontinuous transitions near z=80, and a critical fixed point between z=8 and 12. For q=4 the transition becomes discontinuous for z>16. The scaling behavior of the q=4 model with z=16 approximates that of the q=4 merged critical-tricritical fixed point predicted by the renormalization scenario.

Critical properties of dissipative quantum spin systems in finite dimensions

We study the critical properties of finite-dimensional dissipative quantum spin systems with uniform ferromagnetic interactions. Starting from the transverse field Ising model coupled to a bath of harmonic oscillators with Ohmic spectral density, we generalize its classical representation to classical spin systems with O(n) symmetry and then take the large-n limit to reduce the system to a spherical model. The exact solution to the resulting spherical model with long-range interactions along the imaginary time axis shows a phase transition with static critical exponents coinciding with those of the conventional short-range spherical model in dimensions, where d is the spatial dimensionality of the original quantum system. This implies that the dynamical exponent is z = 2. These conclusions are consistent with the results of Monte Carlo simulations and renormalization group calculations for dissipative transverse field Ising and O(n) models in one and two dimensions. The present approach therefore serves as a useful tool for analytically investigating the properties of quantum phase transitions of the dissipative transverse field Ising and other related models. Our method may also offer a platform to study more complex phase transitions in dissipative finite-dimensional quantum spin systems, which have recently received renewed interest in the context of quantum annealing in a noisy environment.

Impact of single-point GPS integrated water vapor estimates on short-range WRF model forecasts over southern India

Specifying physically consistent and accurate initial conditions is one of the major challenges of numerical weather prediction (NWP) models. In this study, ground-based global positioning system (GPS) integrated water vapor (IWV) measurements available from the International Global Navigation Satellite Systems (GNSS) Service (IGS) station in Bangalore, India, are used to assess the impact of GPS data on NWP model forecasts over southern India. Two experiments are performed with and without assimilation of GPS-retrieved IWV observations during the Indian winter monsoon period (November–December, 2012) using a four-dimensional variational (4D-Var) data assimilation method. Assimilation of GPS data improved the model IWV analysis as well as the subsequent forecasts. There is a positive impact of ∼10 % over Bangalore and nearby regions. The Weather Research and Forecasting (WRF) model-predicted 24-h surface temperature forecasts have also improved when compared with observations. Small but significant improvements were found in the rainfall forecasts compared to control experiments.

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent α. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action SD, found in the short-range Ising universality class, and an “anomalous” CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for α>2, while for α<2 it dominates and determines the breakdown of the CS. Out of criticality SAN breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite α. As α increases such ELI breakdown becomes less and less pronounced and in the short-range limit α→∞ the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for α<1. Finally we show that at every finite α the critical exponents, defined as for the short-range (α→∞) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of α where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (SD) is present for 1<α<2 (for α>2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken.

A retrospective streamflow ensemble forecast for an extreme hydrologic event: a case study of Hurricane Irene and on the Hudson River basin

Abstract. This paper investigates the uncertainties in hourly streamflow ensemble forecasts for an extreme hydrological event using a hydrological model forced with short-range ensemble weather prediction models. A state-of-the art, automated, short-term hydrologic prediction framework was implemented using GIS and a regional scale hydrological model (HEC-HMS). The hydrologic framework was applied to the Hudson River basin ( ∼ 36 000 km2) in the United States using gridded precipitation data from the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR) and was validated against streamflow observations from the United States Geologic Survey (USGS). Finally, 21 precipitation ensemble members of the latest Global Ensemble Forecast System (GEFS/R) were forced into HEC-HMS to generate a retrospective streamflow ensemble forecast for an extreme hydrological event, Hurricane Irene. The work shows that ensemble stream discharge forecasts provide improved predictions and useful information about associated uncertainties, thus improving the assessment of risks when compared with deterministic forecasts. The uncertainties in weather inputs may result in false warnings and missed river flooding events, reducing the potential to effectively mitigate flood damage. The findings demonstrate how errors in the ensemble median streamflow forecast and time of peak, as well as the ensemble spread (uncertainty) are reduced 48 h pre-event by utilizing the ensemble framework. The methodology and implications of this work benefit efforts of short-term streamflow forecasts at regional scales, notably regarding the peak timing of an extreme hydrologic event when combined with a flood threshold exceedance diagram. Although the modeling framework was implemented on the Hudson River basin, it is flexible and applicable in other parts of the world where atmospheric reanalysis products and streamflow data are available.