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DOE OSTI2016

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Design of a high-temperature cell for cobalt-60 irradiations of aqueous solutions with in situ UV–visible spectroscopy

To understand the speciation of solutes in aqueous solutions in high temperature radiation environments, we report the design and fabrication of a custom-built, high temperature (≤300 °C) titanium irradiation cell with in situ optical spectroscopy capabilities, as afforded by coupled fiber optic cables. The wetted surfaces of the 8-inch tall cylindrical cell with 3.5 in. diameter are entirely made of titanium, sapphire, and gold, which are chemically and radiolytically inert. The initial benchmarking results are reported, including the baseline spectrum of deionized water as a function of temperature, the stability of a spectrum over 4 h at 100 °C, and an irradiated Fricke dosimetry solution under ambient irradiator temperature conditions (27.0 ± 0.5 °C). Further, the average gamma radiation dose rate in the cell in its current configuration is 26.1 ± 1.3 Gy min -1 . This cell has application in studying several processes throughout the nuclear fuel cycle, including the reactor coolant behavior.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2014

Study of the nanobubble phase of aqueous NaCl solutions by dynamic light scattering

Aqueous NaCl solutions with different concentrations have been investigated by dynamic scattering of laser radiation. It is experimentally shown that these solutions contain scattering particles with a wide size distribution in a range of ∼10 – 100 nm. The experimental results indirectly confirm the existence of quasi-stable gas nanobubbles in the bulk of aqueous ionic solutions. (light scattering)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Study of the dielectric function of aqueous solutions of glucose and albumin by THz time-domain spectroscopy

We report a study of aqueous solutions of glucose and bovine serum albumin using THz time-domain spectroscopy. To describe the permittivity of the solutions of these substances, we use a simplified model being applicable in the frequency range of 0.05 – 2.7 THz. On the assumption that most of the water molecules become bound at high concentrations of glucose and protein in the solution, the changes in water characteristics are investigated. To improve the reliability of the results, the measurements are performed by two independent methods: the method of attenuated total internal reflection and the transmission method. Combination of the results obtained by these two methods allows expanding the spectral range towards lower frequencies. (laser biophotonics)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems

Lyapunov-type oscillation and wandering indicators are defined for solutions of systems of differential equations; these are the average frequency of zeros for the projection of a solution onto some line and the average angular velocity of rotation of a solution about the origin in some basis, respectively. An integral equality relating these indicators is obtained. The indicators introduced are shown to coincide if, prior to averaging, the oscillation indicators are minimized over all possible lines, and the wandering indicators over all possible bases. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Solutions to higher-order anisotropic parabolic equations in unbounded domains

The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder D=(0,∞)×Ω, where Ω⊂R{sup n}, n≥3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t→∞ is found. An upper estimate characterizing the decay of the solution is established, which is close to the lower estimate if the domain is sufficiently 'narrow'. The same authors have previously obtained results of this type for second order anisotropic parabolic equations. Bibliography: 29 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Smooth solutions of the Navier-Stokes equations

We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R{sup 3}. We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

CCD MEASUREMENTS OF DOUBLE AND MULTIPLE STARS AT NAO ROZHEN AND ASV IN 2011. FIVE LINEAR SOLUTIONS

Using the 2 m telescope of the Bulgarian National Astronomical Observatory at Rozhen, observations of 222 double or multiple stars were carried out during three nights in 2011. This is the sixth series of measurements of CCD frames of double and multiple stars obtained at Rozhen. Also in 2011, using the 0.6 m telescope of the Serbian Astronomical Station on the mountain of Vidojevica, observations of 208 double or multiple stars were carried out during six nights. This is the first series of measurements of CCD frames of double and multiple stars obtained at this station. In this paper, we present the results for the position angle and angular separation for 337 pairs and residuals for 72 pairs with published orbital elements or linear solutions. These observations have angular separations in the range from 1.''37 to 172.''81, with a median angular separation of 7.''66. We also present the recalculated linear solutions for four pairs and one linear solution that has been calculated for the first time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

STEADY GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC INFLOW/OUTFLOW SOLUTION ALONG LARGE-SCALE MAGNETIC FIELDS THAT THREAD A ROTATING BLACK HOLE

General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line. Here we present the first self-consistent, semi-analytical solution for a cold, Poynting flux–dominated (PFD) GRMHD flow, which passes all four critical (inner and outer, Alfvén, and fast magnetosonic) points along a parabolic streamline. By assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated, the outflow part of the solution can be constrained by the inflow part. The semi-analytical method can provide fiducial and complementary solutions for GRMHD simulations around the rotating black hole, given that the black hole spin, global streamline, and magnetizaion (i.e., a mass loading at the inflow/outflow separation) are prescribed. For reference, we demonstrate a self-consistent result with the work by McKinney in a quantitative level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES

This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

We consider the general scalar field Horndeski Lagrangian coupled to dark matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of dark matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problem since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Anisotropic cosmological solutions in massive vector theories

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

New torsion black hole solutions in Poincaré gauge theory

We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordström type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordström-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled to gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Self-interacting inelastic dark matter: a viable solution to the small scale structure problems

Self-interacting dark matter has been proposed as a solution to the small-scale structure problems, such as the observed flat cores in dwarf and low surface brightness galaxies. If scattering takes place through light mediators, the scattering cross section relevant to solve these problems may fall into the non-perturbative regime leading to a non-trivial velocity dependence, which allows compatibility with limits stemming from cluster-size objects. However, these models are strongly constrained by different observations, in particular from the requirements that the decay of the light mediator is sufficiently rapid (before Big Bang Nucleosynthesis) and from direct detection. A natural solution to reconcile both requirements are inelastic endothermic interactions, such that scatterings in direct detection experiments are suppressed or even kinematically forbidden if the mass splitting between the two-states is sufficiently large. Using an exact solution when numerically solving the Schrödinger equation, we study such scenarios and find regions in the parameter space of dark matter and mediator masses, and the mass splitting of the states, where the small scale structure problems can be solved, the dark matter has the correct relic abundance and direct detection limits can be evaded.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Nanoscale insights into the structure of solution-processed graphene by x-ray scattering

Abstract Chemical exfoliation is an attractive approach for the synthesis of graphene due to its low cost and simplicity. However, challenges still remain in the characterization of solution-processed graphene, in particular with atomic resolution. Through this work we demonstrate the x-ray pair distribution function as a novel approach to study solution-processed graphene or other 2D materials with atomic resolution, directly in solution, produced by liquid-phase and electrochemical exfoliations. The results show the disappearance of long-range atomic correlations, in both cases, confirming the production of single and few-layer graphene. In addition, a considerable ring distortion has been observed as compared to graphite, irrespective of the solvent used: the normal surface angle to the sheet of the powder sample should be less than 6°, compatible with ripples formation observed in suspended graphene. We attribute this effect to the interaction of solvent molecules with the graphene nanosheets.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗