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In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
We study the Darboux transformation method for one-dimensional stationary Dirac equation with linear potential. We obtain new exactly solvable potentials associated to new solutions of the first Hamiltonian and a series of new Hamiltonians are obtained. Finally, as a particular case, we introduce another form of the Darboux operator that is applicable to generating new potentials.
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕ{sub t} of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕ{sub t}. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕ{sub t}. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.
Highlights: • This model, reproduces conductivity and Hall angle of high-T{sub c} cuprates. • It exhibits metal-insulator transition under variation of magnetic field. • Obtained transport properties for a backreacted non-linear electrodynamics model. - Abstract: We consider arcsin electrodynamics in a holographic set up along with dilatonic and axionic scalar fields. Considering backreaction of the matter fields on the geometry we study direct conductivity of the dual theory and obtain the conductivity matrix. Since obtaining an exact solution is difficult in general, we have studied several limiting cases. In particular, at the strong momentum dissipation limit, we find for hyperscaling violating geometry as the background, the resistivity and Hall coefficient will behave as ∼T and ∼T{sup 2} respectively. Then we restrict to a simpler model, where we find that the variation of the magnetic field can lead to metal–insulator transition/crossover.
Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.
Although monoclinic bismuth vanadate (BiVO 4 ) is a promising photoanode for solar water splitting, its practical use is hindered by imperfect photocurrent generation/collection, low photovoltage compared to the bandgap, and corrosion side reactions that limit durability. Here, we introduce a controlled-annealing sol–gel process for BiVO 4 thin-film photoanodes along with an optimized linear-sweep-voltammetry photodeposition of CoFeO x H y cocatalysts. The resulting BiVO 4 films annealed at 550 °C exhibited a photocurrent density of 4.1 mA/cm 2 at 1.23 V RHE under 1 sun AM 1.5G solar simulation and a low onset potential of 0.26 V RHE due to high majority carrier conductivity, a crystalline bulk with reduced defects as evidenced by x-ray photoelectron spectroscopy and photoluminescence lifetime analysis, and thus enhanced photocarrier collection. However, significant degradation in performance was found due to interfacial photocorrosion. To protect the surface and speed the oxygen-evolution reaction CoFeO x H y cocatalyst layers were deposited. By varying the number of consecutive sweeps and adjusting the applied bias range, an ultra-thin (~15 nm) CoFeO x H y cocatalyst layer was uniformly grown deposited over 30 cycles on the BiVO 4 surface. The resulting BiVO 4 /CoFeO x H y yielded 4.03 mA/cm 2 at 1.23 V RHE and onset potential of 0.24 V RHE , with stable operation (~15 % loss in photocurrent at 1.23 V RHE relative to ~60 % loss in the uncatalyzed control sample). These conformal CoFeO x H y catalytic layers function simultaneously to selectively collect photoexcited holes from the BiVO 4 , catalyze the water-oxidation reaction, and protect the BiVO 4 from photodegradation.
Hempseed is a rich source of dietary fiber; however, there has been limited research on the variability of carbohydrate composition in hempseed cell walls. The primary aim of this study was to conduct a comprehensive chemical and structural analysis of the cell wall polysaccharides in ten hempseed cultivars. Water-soluble polysaccharides (WSP) and water-insoluble residues (WIR) were isolated and subsequently analyzed for their monosaccharide composition using HPAEC-PAD, glycosyl linkage analysis using GC–MS, and structural characterization via NMR spectroscopy. All hempseed cultivars contained a high proportion of insoluble fibers and smaller amounts of soluble polysaccharides. Glucose and xylose were the most abundant components of the WIR fractions, while the WSP fractions contained abundant amounts of galactose, galacturonic acid, arabinose, rhamnose, and mannose. The results of linkage and spectroscopic analysis were consistent with the compositional analysis, identifying cellulose and acetylated linear xylans as primary components of WIR, and arabinogalactans, rhamnogalacturonans, heteromannans, xyloglucans, and arabinan as predominant in WSP. Altogether, the study revealed a comparable cell wall structure among the analyzed hemp seed varieties. The high fiber content of whole hempseed-based ingredients presents significant potential for food manufacturers seeking to develop products with enhanced dietary fiber content, offering both functional and nutritional benefits for consumers.
Linear low-density polyethylene (LLDPE) waste is difficult to upcycle into more valuable carbon materials because it tends to completely decompose into small molecules during thermal processing. In this work, LLDPE is upcycled into a high quality turbostratic graphene using a pre-treatment step to oxidatively crosslink the polymer with the assistance of solid additives (KCl and K 2 CO 3 ) that improve crosslinking by increasing the effective surface area of the polymer melt during processing. After this pretreatment step, the crosslinked polymer could then be carbonized and catalytically graphenized between 400–950°C without decomposition of the polymer feedstock. The LLDPE derived graphene (LLDPE-G) obtained from this process has a Brunauer–Emmett–Teller (BET) specific surface area, up to 1800m 2 g -1 and average Raman I D /I G and I 2D /I G ratios of 0.85 and 0.57, respectively, indicating high quality graphene. When used as an electrode material in symmetric supercapacitors, LLDPE-G possesses a specific capacitance up to 175Fg -1 at a mass loading of 20mgcm -2 , which is two times the commercial requirement, yielding an areal capacitance of 3.5 Fcm -2 . Moreover, LLDPE-G exhibits exceptional cycling stability with a capacitance retention of 95.8 % after 100,000 cycles at a current density of 4.0 Ag -1 . Additionally, the KCl and K 2 CO 3 solids are recycled and reused over 3 complete reaction cycles to make new LLDPE-G with the material quality and electrocapacitive performance retained and verified after each cycle. Our approach creates new opportunities for upcycling waste LLDPE and other varieties of polyethylene into a higher value graphene used for electrochemical energy storage applications.
Demand response (DR) has become a key element in balancing the power grid as the contribution of time-varying renewable power generation increases. Chemical plants are appealing candidates for DR programs as they offer large, concentrated and flexible loads. DR participation calls for frequent production rate changes over time scales that overlap with the dominant dynamics of the plant. Production scheduling should therefore consider the process dynamics explicitly. Here we present a data-driven approach for modelling the scheduling-relevant dynamics based on historical closed-loop operating data using autoregressive with extra inputs (ARX) models. We introduce a new, linear scheduling problem formulation based on the ARX representation, and demonstrate its implementation on an industrial air separation unit.
A persistent challenge present in inverse or parameter estimation problems with interior data is how to deal with uncertainty in the boundary conditions employed in the forward or state model. In this work we focus on a linear plane stress inverse elasticity problem with measured displacement data where one component of the measured displacement field is known with considerably greater precision than the other. This situation is commonly encountered when the displacement field is measured using ultrasound or optical coherence tomography. We present a novel computational formulation in which no displacement or traction boundary conditions are assumed. The formulation results in coupling the state and adjoint equations, that are typically uncoupled when a well-posed state model is available. Two variants of residual-based stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.
Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.
Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.
We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.
Here, we present the Alternating Anderson–Richardson (AAR) method: an efficient and scalable alternative to preconditioned Krylov solvers for the solution of large, sparse linear systems on high performance computing platforms. Specifically, we generalize the recently proposed Alternating Anderson–Jacobi (AAJ) method (Pratapa et al., 2016) to include preconditioning, discuss efficient parallel implementation, and provide serial MATLAB and parallel C/C++ implementations. In serial applications to nonsymmetric systems, we find that AAR is comparably robust to GMRES, using the same preconditioning, while often outperforming it in time to solution; and find AAR to be more robust than Bi-CGSTAB for the problems considered. In parallel applications to the Helmholtz and Poisson equations, we find that AAR shows superior strong and weak scaling to GMRES, Bi-CGSTAB, and Conjugate Gradient (CG) methods, using the same preconditioning, with consistently shorter times to solution at larger processor counts. Finally, in massively parallel applications to the Poisson equation, on up to 110,592 processors, we find that AAR shows superior strong and weak scaling to CG, with shorter minimum time to solution. We thus find that AAR offers a robust and efficient alternative to current state-of-the-art solvers, with increasing advantages as the number of processors grows.
Commissioning of a large accelerator facility like FRIB needs support from an online beam dynamics model. Considering the new physics challenges of FRIB such as modeling of non-axisymmetric superconducting RF cavities and multi-charge state acceleration, there is no readily available online beam tuning code. The design code of FRIB super-conducting linac, IMPACT-Z, is not suitable for online tuning because of its code design and running speed. Therefore, the Fast Linear Accelerator Modeling Engine (FLAME), specifically designed to fulfill FRIB’s online modeling challenges, is proposed. The physics model of FLAME, especially its novel way of modeling non-axisymmetric superconducting RF cavities using a multipole expansion based thin-lens kick model, is discussed in detail, and the benchmark results against FRIB design code is presented, after which the software design strategy of FLAME and its execution speed is presented.
We implement the multi-species linearized model collision operator, based on the approach proposed by Kolesnikov, in the full-f continuum gyrokinetic code COGENT. We describe the operator and use it in several COGENT simulations of highly collisional plasmas. We analyze simulation results with the Braginskii fluid model to illustrate that COGENT recovers both friction and thermal forces. Finally, we simulate the neoclassical transport of heavy impurities with COGENT and illustrate agreement with previously published theoretical results.
Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.
Highlights: • NARX models are established in other environmental research, but are unused in temperature-related mortality research. • NARX models do not assume any particular shape to the temperature-mortality association. • NARX models are cross-validated and are easily modified to take on real-time, multi-step-ahead predictions and hindcasts. • Year-round, daily mortality in 41 different US cities was modeled using an ensemble of NARX models in each location. • Models show skill everywhere. Results vary spatially and seasonally, improving upon a persistence model by 17% points. • When compared with distributed lag non-linear models, the output time series are largely similar Temperature-mortality relationships are nonlinear, time-lagged, and can vary depending on the time of year and geographic location, all of which limits the applicability of simple regression models in describing these associations. This research demonstrates the utility of an alternative method for modeling such complex relationships that has gained recent traction in other environmental fields: nonlinear autoregressive models with exogenous input (NARX models). All-cause mortality data and multiple temperature-based data sets were gathered from 41 different US cities, for the period 1975–2010, and subjected to ensemble NARX modeling. Models generally performed better in larger cities and during the winter season. Across the US, median absolute percentage errors were 10% (ranging from 4% to 15% in various cities), the average improvement in the r-squared over that of a simple persistence model was 17% (6–24%), and the hit rate for modeling spike days in mortality (>80th percentile) was 54% (34–71%). Mortality responded acutely to hot summer days, peaking at 0–2 days of lag before dropping precipitously, and there was an extended mortality response to cold winter days, peaking at 2–4 days of lag and dropping slowly and continuing for multiple weeks. Spring and autumn showed both of the aforementioned temperature-mortality relationships, but generally to a lesser magnitude than what was seen in summer or winter. When compared to distributed lag nonlinear models, NARX model output was nearly identical. These results highlight the applicability of NARX models for use in modeling complex and time-dependent relationships for various applications in epidemiology and environmental sciences.