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DOE OSTI2014

Short-time asymptotics of a rigorous path integral for N = 1 supersymmetric quantum mechanics on a Riemannian manifold

Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Integrated two-cylinder liquid piston Stirling engine

Heat engines utilizing the Stirling cycle may run on low temperature differentials with the capacity to function at high efficiency due to their near-reversible operation. However, current approaches to building Stirling engines are laborious and costly. Typically the components are assembled by hand and additional components require a corresponding increase in manufacturing complexity, akin to electronics before the integrated circuit. We present a simple and integrated approach to fabricating Stirling engines with precisely designed cylinders. We utilize computer aided design and one-step, planar machining to form all components of the engine. The engine utilizes liquid pistons and displacers to harness useful work from heat absorption and rejection. As a proof of principle of the integrated design, a two-cylinder engine is produced and characterized and liquid pumping is demonstrated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Transmission integral analysis of Mössbauer spectra displaying hyperfine parameter distributions with arbitrary profile

Accurate quantitative analysis of Mössbauer spectra displaying thickness effects requires the consideration of the so-called transmission integral when modeling the spectral shape. Whereas this is straightforward when the correct model for the decomposition of the absorber's nuclear resonance absorption cross-section into individual components is a priori known, in the absence of such knowledge and notably in the presence of hyperfine parameter distributions with an unknown profile, the so-called model-independent evaluation methods could be used to fit the spectra. However, the methods available for this purpose were developed for the analysis of spectra for which the thin absorber approximation is valid, and thus they do not take the sample thickness and related effects into account. Consequently, in order to use them for spectra displaying thickness effects, their usage needs to be generalized by combining them with transmission integral fitting. A new algorithm realizing such a generalized version of the Hesse-Rübartsch model-independent evaluation method was developed recently as an integral part of the MossWinn program. In the present work, the working principle of the newly developed algorithm is described in details along with examples illustrating the capabilities of the method for the case of {sup 57}Fe Mössbauer spectroscopy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Direct path integral estimators for isotope fractionation ratios

Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Calculation of the molecular integrals with the range-separated correlation factor

Explicitly correlated quantum chemical calculations require calculations of five types of two-electron integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called “range-separated” correlation factor is used. This correlation factor combines the well-known short range behaviour resulting from the electronic cusp condition, with the exact long-range asymptotics derived for the helium atom [Lesiuk, Jeziorski, and Moszynski, J. Chem. Phys. 139, 134102 (2013)]. Almost all steps of the presented procedure are formulated recursively, so that an efficient implementation and control of the precision are possible. Additionally, the present formulation is very flexible and general, and it allows for use of an arbitrary correlation factor in the electronic structure calculations with minor or no changes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Quantum stopping times stochastic integral in the interacting Fock space

Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Development of highly accurate approximate scheme for computing the charge transfer integral

The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Path integral molecular dynamics within the grand canonical-like adaptive resolution technique: Simulation of liquid water

Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Photonic integration for UV to IR applications

Photonic integration opens the potential to reduce size, power, and cost of applications normally relegated to table- and rack-sized systems. Today, a wide range of precision, high-end, ultra-sensitive, communication and computation, and measurement and scientific applications, including atomic clocks, quantum communications, processing, and high resolution spectroscopy, are ready to make the leap from the lab to the chip. However, many of these applications operate at wavelengths not accessible to the silicon on insulator-based silicon photonics integration platform due to absorption, power handling, unwanted nonlinearities, and other factors. Next generation photonic integration will require ultra-wideband photonic circuit platforms that scale from the ultraviolet to the infrared and that offer a rich set of linear and nonlinear circuit functions as well as low loss and high power handling capabilities. This article provides an assessment of the field in ultra-wideband photonic waveguides to bring power efficient, ultra-high performance systems to the chip-scale and enable compact transformative precision measurement, signal processing, computation, and communication techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

42 ENGINEERING↗
DOE OSTI2014

Method of adiabatic modes in research of smoothly irregular integrated optical waveguides: zero approximation

We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides. (integral optical waveguides)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Double integrated laser-thyristor

Comparative experiments are performed on a semiconductor laser with different numbers (one or two) of emitting sections monolithically integrated with an electronic switch (thyristor). It is shown that the functional integration of a laser with a thyristor in one heterostructure makes it possible to achieve efficient operation of the laser in a pulsed regime (up to 50 W), while the use of vertical integration of two laser sections in this device additionally increases the optical output power to 90 W with all other conditions being the same. (lasers)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Topological classification of the Goryachev integrable case in rigid body dynamics

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Review and Modeling of Integrated Energy Systems with Nuclear Reactor Coupled Desalination and District Heating

Detailed reviews of a past advanced nuclear reactor based integrated energy system, as well as other nuclear reactor and fossil fuel based integrated energy systems have been performed for this work. Review of the utilization of heat from nuclear reactors for various applications and cogeneration has been done. The heat can be utilized by extraction of the steam from the turbine while the steam is still at a desired temperature. While use of nuclear process heat for district heating in countries like Finland, France, China, Poland, and elsewhere is discussed, more focus of the review has been given on nuclear desalination processes. Integrated energy systems (IES) where distinct types of reactors like PWR, BWR, sodium cooled fast reactor, heavy water reactor and other advanced reactors are coupled with various nuclear desalination processes like multi-effect distillation (MED), multi-stage flashing (MSF) and reverse osmosis (RO) methods have been discussed. The nuclear desalination plant at Aktau has been discussed in more detail due to its decades of successful operation. The IES of the Aktau plant coupled with 5-effect MED desalination plant has been taken as a reference for modeling the Open Modelica (OM) based IES of this work. Here, the OM IES model shows good agreement with the MED plant output of Aktau and can be extended for future applications of IES.

42 ENGINEERING↗
DOE OSTI2025

Drying of strawberries with airborne ultrasound and other integrated dehydration mechanisms

This article presents a comprehensive investigation into the drying of strawberries using multiple dehydration methods with an emphasis on energy efficiency and sustainability. Initially, an airborne ultrasonic transducer with a frequency of 21 kHz was employed in batch operations to examine the effects of controlling parameters, including applied power, distance from the transducer plate, sample thickness, and sample holder type. The Energy Ratio, defined as the ratio of thermal energy required to evaporate moisture to ultrasonic energy, was observed to reach up to 2.2, particularly during the initial stages of drying. Subsequently, the Smart Dryer integrated airborne ultrasound (US) dehydration, slot jet reattachment (SJR) nozzle convective drying, infrared (IR) drying, and their combinations, enabling a systematic exploration of various drying conditions on the drying time and quality of strawberries. The integration of airborne US with SJR nozzles and IR drying demonstrates a promising approach for optimizing drying processes. This method not only preserves the quality of dried strawberries but also improves the energy factor to 0.88, reducing drying time by 89% compared with other conditions. Key quality attributes of the dried strawberries, such as color and water activity, were evaluated to understand the influence of each drying method. The findings highlight the potential of these integrated drying techniques as sustainable solutions for efficient and high-quality strawberry dehydration.

42 ENGINEERING↗