Modern solvers for Helmholtz problems

CERN Document Server

Tang, Jok; Vuik, Kees

2017-01-01

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...

Nonlinearity, Viscosity and Air-Compressibility Effects on the Helmholtz Resonant Wave Motion Generated by an Oscillating Twin Body in a Free Surface

Science.gov (United States)

Ananthakrishnan, Palaniswamy

2012-11-01

The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.

Extraordinary acoustic transmission mediated by Helmholtz resonators

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Vijay Koju

2014-07-01

Full Text Available We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.

Multiscale modeling for ferroelectric materials: identification of the phase-field model’s free energy for PZT from atomistic simulations

International Nuclear Information System (INIS)

Völker, Benjamin; Landis, Chad M; Kamlah, Marc

2012-01-01

Within a knowledge-based multiscale simulation approach for ferroelectric materials, the atomic level can be linked to the mesoscale by transferring results from first-principles calculations into a phase-field model. A recently presented routine (Völker et al 2011 Contin. Mech. Thermodyn. 23 435–51) for adjusting the Helmholtz free energy coefficients to intrinsic and extrinsic ferroelectric material properties obtained by DFT calculations and atomistic simulations was subject to certain limitations: caused by too small available degrees of freedom, an independent adjustment of the spontaneous strains and piezoelectric coefficients was not possible, and the elastic properties could only be considered in cubic instead of tetragonal symmetry. In this work we overcome such restrictions by expanding the formulation of the free energy function, i.e. by motivating and introducing new higher-order terms that have not appeared in the literature before. Subsequently we present an improved version of the adjustment procedure for the free energy coefficients that is solely based on input parameters from first-principles calculations performed by Marton and Elsässer, as documented in Völker et al (2011 Contin. Mech. Thermodyn. 23 435–51). Full sets of adjusted free energy coefficients for PbTiO 3 and tetragonal Pb(Zr,Ti)O 3 are presented, and the benefits of the newly introduced higher-order free energy terms are discussed. (paper)

An efficient Helmholtz solver for acoustic transversely isotropic media

KAUST Repository

Wu, Zedong

2017-11-11

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on less medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we propose to separate the quasi-P wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the non-elliptic-anisotropic components, which form a pseudo-differential operator. We, then, develop a separable approximation of the dispersion relation of non-elliptic-anisotropic components, specifically for transversely isotropic (TI) media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the non-elliptical terms represented in the Fourier domain. A frequency domain Helmholtz formulation of the approach renders the iterative implementation efficient as the cost is dominated by the Lower-Upper (LU) decomposition of the impedance matrix for the simpler elliptical anisotropic model. Also, the resulting wavefield is free of S-wave artifacts and has balanced amplitude. Numerical examples show that the method is reasonably accurate and efficient.

An efficient Helmholtz solver for acoustic transversely isotropic media

KAUST Repository

Wu, Zedong; Alkhalifah, Tariq Ali

2017-01-01

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on less medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we propose to separate the quasi-P wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the non-elliptic-anisotropic components, which form a pseudo-differential operator. We, then, develop a separable approximation of the dispersion relation of non-elliptic-anisotropic components, specifically for transversely isotropic (TI) media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the non-elliptical terms represented in the Fourier domain. A frequency domain Helmholtz formulation of the approach renders the iterative implementation efficient as the cost is dominated by the Lower-Upper (LU) decomposition of the impedance matrix for the simpler elliptical anisotropic model. Also, the resulting wavefield is free of S-wave artifacts and has balanced amplitude. Numerical examples show that the method is reasonably accurate and efficient.

Helmholtz and the psychophysiology of time.

Science.gov (United States)

Debru, C

2001-09-01

After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background.

Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

Directory of Open Access Journals (Sweden)

Yang-Yang Chen

2016-01-01

Full Text Available The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons.

Magnetohydrodynamic Kelvin-Helmholtz instability; Magnetohydrodynamische Kelvin-Helmholtz-Instabilitaet

Energy Technology Data Exchange (ETDEWEB)

Brett, Walter

2014-07-21

In the presented work the Kelvin-Helmholtz-Instability in magnetohydrodynamic flows is analyzed with the methods of Multiple Scales. The concerned fluids are incompressible or have a varying density perpendicular to the vortex sheet, which is taken into account using a Boussinesq-Approximation and constant Brunt-Vaeisaelae-Frequencies. The Multiple Scale Analysis leads to nonlinear evolution equations for the amplitude of the perturbations. Special solutions to these equations are presented and the effects of the magnetic fields are discussed.

Helmholtz bright and boundary solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2007-01-01

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

Experimental realization of extraordinary acoustic transmission using Helmholtz resonators

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Brian C. Crow

2015-02-01

Full Text Available The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.

Mechanism of active transport: free energy dissipation and free energy transduction.

OpenAIRE

Tanford, C

1982-01-01

The thermodynamic pathway for "chemiosmotic" free energy transduction in active transport is discussed with an ATP-driven Ca2+ pump as an illustrative example. Two innovations are made in the analysis. (i) Free energy dissipated as heat is rigorously excluded from overall free energy bookkeeping by focusing on the dynamic equilibrium state of the chemiosmotic process. (ii) Separate chemical potential terms for free energy donor and transported ions are used to keep track of the thermodynamic ...

Helmholtz bright and boundary solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2007-02-16

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.

Nuclear safety research in HGF 2012; Fortschrittsbericht 2012. Programm 'Nukleare Sicherheitsforschung' Helmholtz-Gemeinschaft

Energy Technology Data Exchange (ETDEWEB)

Anon.

2013-06-15

After the events at the Japanese nuclear power plant of Fukushima Daiichi, the German Federal government decided that Germany will give up electricity generation from nuclear power within a decade. The last reactor will be disconnected from the power grid in 2022. Helping to make this opt-out safe is one of the duties of the Helmholtz Association with its Nuclear Safety Research Program within the Energy Research Area. Also the demolition of nuclear power plants and the repository problem will keep society, and thus also research, busy for a number of decades to come. Giving up electricity production from nuclear power thus must not mean giving up the required nuclear technology competences. In the fields of reactor safety, demolition, final storage, radiation protection, and crisis management, in critical support of international developments, and for competent evaluation of nuclear facilities around Germany, these competences will be in demand far beyond the German opt-out. This is the reason why the final report by the Ethics Committee on 'Safe Energy Supply' emphasizes the importance of nuclear technology research. Close cooperation on national, European and international levels is indispensable in this effort. Also nuclear safety research in the Helmholtz Association is aligned with the challenges posed by the opt-out of the use of nuclear power. It is important that the high competences in the areas of plant safety and demolition, handling of radioactive waste, and safe final storage as well as radiation protection be preserved. The Nuclear Safety Research Program within the Energy Research Area of the Helmholtz Association therefore will continue studying scientific and technical aspects of the safety of nuclear reactors and the safety of nuclear waste management. These research activities are provident research conducted for society and must be preserved for a long period of time. The work is closely harmonized with the activities of the partners

Progress toward Kelvin-Helmholtz instabilities in a High-Energy-Density Plasma on the Nike laser

Science.gov (United States)

Harding, E. C.; Drake, R. P.; Gillespie, R. S.; Grosskopf, M. J.; Huntington, C. M.; Aglitskiy, Y.; Weaver, J. L.; Velikovich, A. L.; Plewa, T.; Dwarkadas, V. V.

2008-04-01

In the realm of high-energy-density (HED) plasmas, there exist three primary hydrodynamic instabilities of concern: Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH). Although the RT and the RM instabilities have been readily observed and diagnosed in the laboratory, the KH instability remains relatively unexplored in HED plasmas. Unlike the RT and RM instabilities, the KH instability is driven by a lifting force generated by a strong velocity gradient in a stratified fluid. Understanding the KH instability mechanism in HED plasmas will provide essential insight into oblique shock systems, jets, mass stripping, and detailed RT-spike development. In addition, our KH experiment will help provide the groundwork for future transition to turbulence experiments. We present 2D FLASH simulations and experimental data from our initial attempts to create a pure KH system using the Nike laser at the Naval Research Laboratory.

HNF - Helmholtz Nano Facility

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Wolfgang Albrecht

2017-05-01

Full Text Available The Helmholtz Nano Facility (HNF is a state-of-the-art cleanroom facility. The cleanroom has ~1100 m2 with cleanroom classes of DIN ISO 1-3. HNF operates according to VDI DIN 2083, Good Manufacturing Practice (GMP and aquivalent to Semiconductor Industry Association (SIA standards. HNF is a user facility of Forschungszentrum Jülich and comprises a network of facilities, processes and systems for research, production and characterization of micro- and nanostructures. HNF meets the basic supply of micro- and nanostructures for nanoelectronics, fluidics. micromechanics, biology, neutron and energy science, etc.. The task of HNF is rapid progress in nanostructures and their technology, offering efficient access to infrastructure and equipment. HNF gives access to expertise and provides resources in production, synthesis, characterization and integration of structures, devices and circuits. HNF covers the range from basic research to application oriented research facilitating a broad variety of different materials and different sample sizes.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei

2012-07-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

Helmholtz resonance in a piezoelectric–hydraulic pump-based hybrid actuator

International Nuclear Information System (INIS)

Kim, Gi-Woo; Wang, K W

2011-01-01

This paper demonstrates that a hydraulically acting Helmholtz resonator can exist in a piezoelectric–hydraulic pump (PHP) based hybrid actuator, which in turn affects the volumetric efficiency of the PHP. The simulation and experimental results illustrate the effect of Helmholtz resonance on the flow rate performance of the PHP. The study also shows how to shift the Helmholtz resonant frequency to a higher value through changing parameters such as the cylinder diameter and the effective bulk modulus of the working fluid, which will improve the volumetric efficiency and broaden the operating frequency range of the PHP actuator

Simulation of Helmholtz Resonance Effects in Aircraft ECS

OpenAIRE

Pollok, Alexander; Schröffer, Andreas

2017-01-01

Helmholtz resonators are closed volumes that are connected to pipes. They exhibit a pronounced resonance frequency, where small boundary pressure excitations in the volume or the environment lead to large mass flow excitations in the pipe. Aircraft have a topology similar to Helmholtz resonators, the closed volume is represented by the cabin, while the pipe is represented by the Environmental Control System. Some discrepancies appear due to the non-zero mass-flow or friction effects in...

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

Energy Technology Data Exchange (ETDEWEB)

Okamoto, Kazuhisa [Nagoya University, Department of Physics, Nagoya (Japan); Nonaka, Chiho [Nagoya University, Department of Physics, Nagoya (Japan); Nagoya University, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya (Japan); Duke University, Department of Physics, Durham, NC (United States)

2017-06-15

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions. (orig.)

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

Science.gov (United States)

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-01

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

Kelvin-Helmholtz instability as a possible cause of edge localized modes

International Nuclear Information System (INIS)

Strauss, H.R.

1992-01-01

Edge localized modes may be a Kelvin-Helmholtz instability caused by the sheared rotation of H-mode plasmas. The Kelvin-Helmholtz instability is stabilized by coupling to Alfven waves. There is a critical velocity gradient, of the order of the Alfven velocity divided by the magnetic shear length. This is verified in a numerical simulation. The critical velocity shear is consistent with experiment. A non-linear simulation shows how the Kelvin-Helmholtz mode can cause oscillations of the velocity profile. (author). Letter-to-the-editor. 13 refs, 6 figs

Noise reduction efficiency of Helmholtz resonator in simulated channel of HVAC system

Directory of Open Access Journals (Sweden)

Hossein Ali Yousefi Rizi

2014-01-01

Conclusions: This research showed that the designed Helmholtz resonators at a certain frequency of low-frequency sound demonstrated the soundest decrease. The increase in the Helmholtz resonators′ chamber volume and their neck′s pass area are negatively associated with the rate of sound resonance. As a result, of determining the effective frequency range of the Helmholtz resonator, the designed resonator could be applied as an effective and efficient instrument of removing or decreasing noise.

Helmholtz solitons in power-law optical materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

2007-01-01

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified

Bistable Helmholtz solitons in cubic-quintic materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

2007-01-01

We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations

On Helmholtz Problem for Plane Periodical Structures

International Nuclear Information System (INIS)

Akishin, P.G.; Vinitskij, S.I.

1994-01-01

The plane Helmholtz problem of the periodical disc structures with the phase shifts conditions of the solutions along the basis lattice vectors and the Dirichlet conditions on the basic boundaries is considered. The Green function satisfying the quasi periodical conditions on the lattice is constructed. The Helmholtz problem is reduced to the boundary integral equations for the simple layer potentials of this Green function. The methods of the discretization of the arising integral equations are proposed. The procedures of calculation of the matrix elements are discussed. The reality of the spectral parameter of the nonlinear continuous and discretized problems is shown. 8 refs., 2 figs

Free energy of mixing of acetone and methanol: a computer simulation investigation.

Science.gov (United States)

Idrissi, Abdenacer; Polok, Kamil; Barj, Mohammed; Marekha, Bogdan; Kiselev, Mikhail; Jedlovszky, Pál

2013-12-19

The change of the Helmholtz free energy, internal energy, and entropy accompanying the mixing of acetone and methanol is calculated in the entire composition range by the method of thermodynamic integration using three different potential model combinations of the two compounds. In the first system, both molecules are described by the OPLS, and in the second system, both molecules are described by the original TraPPE force field, whereas in the third system a modified version of the TraPPE potential is used for acetone in combination with the original TraPPE model of methanol. The results reveal that, in contrast with the acetone-water system, all of these three model combinations are able to reproduce the full miscibility of acetone and methanol, although the thermodynamic driving force of this mixing is very small. It is also seen, in accordance with the finding of former structural analyses, that the mixing of the two components is driven by the entropy term corresponding to the ideal mixing, which is large enough to overcompensate the effect of the energy increase and entropy loss due to the interaction of the unlike components in the mixtures. Among the three model combinations, the use of the original TraPPE model of methanol and modified TraPPE model of acetone turns out to be clearly the best in this respect, as it is able to reproduce the experimental free energy, internal energy, and entropy of mixing values within 0.15 kJ/mol, 0.2 kJ/mol, and 1 J/(mol K), respectively, in the entire composition range. The success of this model combination originates from the fact that the use of the modified TraPPE model of acetone instead of the original one in these mixtures improves the reproduction of the entropy of mixing, while it retains the ability of the original model of excellently reproducing the internal energy of mixing.

Bistable dark solitons of a cubic-quintic Helmholtz equation

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

2010-01-01

We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

Helmholtz and Zoellner: nineteenth-century empiricism, spiritism, and the theory of space perception.

Science.gov (United States)

Stromberg, W H

1989-10-01

J. K. F. Zoellner began writing on "experimental proofs" of a fourth spatial dimension, and of the existence of spirits, in 1878. His arguments caused strong controversy, with rebuttal essays by Wilhelm Wundt and others. The author argues that Zoellner's case that these matters are experimental questions rested on arguments which Hermann von Helmholtz, inveighing against rationalist views of space and space perception, had recently published. Zoellner's use of Helmholtz's arguments to advance and defend his spiritist views occasioned strong criticism of Helmholtz, affected careers and reputations of scholars in Berlin and Leipzig, and caused enduring controversy over the credibility of Helmholtz's empiricist theory of space perception.

Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator

International Nuclear Information System (INIS)

Cao Hongjun; Seoane, Jesus M.; Sanjuan, Miguel A.F.

2007-01-01

The symmetry breaking phenomenon for a general Helmholtz-Duffing oscillator as a function of a symmetric parameter in the nonlinear force is investigated. Different values of this parameter convert the general oscillator into either the Helmholtz or the Duffing oscillator. Due to the variation of the symmetric parameter, the phase space patterns of the unperturbed Helmholtz-Duffing oscillator will cause a huge difference between the left-hand homoclinic orbit and the right-hand one. In particular, the area of the left-hand homoclinic orbits is a strictly monotonously decreasing function, while the area of the right-hand homoclinic orbit varies only in a very small range. There exist distinct local supercritical and subcritical saddle-node bifurcations at two different centers. The left-hand and the right-hand existing regions of the harmonic solutions of the Helmholtz-Duffing oscillator created by the left-hand and the right-hand saddle-node bifurcation curves will lead to different transition in the amplitude-frequency plane. There exists also a critical frequency which has the effect that the left-hand homoclinic bifurcation value is equal to the right-hand homoclinic bifurcation value. And, if the amplitude coefficient of the Helmholtz-Duffing oscillator is used as the control parameter, and it is larger than the same left-hand and right-hand homoclinic bifurcation, then the global stability of the system will be destroyed at a lowest cost. Besides this critical frequency, the left-hand and the right-hand homoclinic bifurcations are not only unequal, but also their effects for the system's stability are different. Among them, the effect resulting from the small homoclinic bifurcation for the system's stability is local and negligible, while the effect from the large homoclinic bifurcation is global but this is accomplished at a quite larger cost

The Determinate World Kant and Helmholtz on the Physical Meaning of Geometry

CERN Document Server

Hyder, David

2009-01-01

This study examines the place of Hermann von Helmholtz´s seminal papers on geometry in his philosophy of science. The arguments of these papers are traced back to his prior work on the theory of magnitudes, as well as to Helmholtz´s early, Kantian position. The author claims that Helmholtz should be understood not as opposing Kant, but as modifying the latter´s theory of magnitudes so as to remove obstacles to their common project of constructing a complete system of natural science.

Helmholtz algebraic solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2010-02-26

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

Helmholtz algebraic solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2010-01-01

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

Solving the Helmholtz equation in conformal mapped ARROWstructures using homotopy perturbation method

DEFF Research Database (Denmark)

Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole

2011-01-01

. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...

Transmission problems for the Helmholtz equation for a rectilinear-circular lune

Directory of Open Access Journals (Sweden)

Volodymyr Denysenko

2007-01-01

Full Text Available The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.

Acoustic superlens using Helmholtz-resonator-based metamaterials

International Nuclear Information System (INIS)

Yang, Xishan; Yin, Jing; Yu, Gaokun; Peng, Linhui; Wang, Ning

2015-01-01

Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between the neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range

The Helmholtz legacy in physiological acoustics

CERN Document Server

Hiebert, Erwin

2014-01-01

This book explores the interactions between science and music in the late nineteenth- and early twentieth century. It examines and evaluates the work of Hermann von Helmholtz, Max Planck, Shohe Tanaka, and Adriaan Fokker, leading physicists and physiologists who were committed to understanding crucial aesthetic components of the art of music, including the standardization of pitch and the implementation of various types of intonations. With a mixture of physics, physiology, and aesthetics, author Erwin Hiebert addresses throughout the book how just intonation came to intersect with the history of keyboard instruments and exert an influence on the development of Western music. He begins with the work of Hermann von Helmholtz, a leading nineteenth-century physicist and physiologist who not only made important contributions in vision, optics, electrodynamics and thermodynamics, but also helped advanced the field of music theory as well. The author traces the Helmholtzian trends of thought that become inherently ...

Computation of free energy

NARCIS (Netherlands)

van Gunsteren, WF; Daura, [No Value; Mark, AE

2002-01-01

Many quantities that are standardly used to characterize a chemical system are related to free-energy differences between particular states of the system. By statistical mechanics, free-energy differences may be expressed in terms of averages over ensembles of atomic configurations for the molecular

The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter

OpenAIRE

Tassev, Svetlin

2010-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys...

Thin-Layer Solutions of the Helmholtz and Related Equations

KAUST Repository

Ockendon, J. R.

2012-01-01

This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.

Accurate calculation of conformational free energy differences in explicit water: the confinement-solvation free energy approach.

Science.gov (United States)

Esque, Jeremy; Cecchini, Marco

2015-04-23

The calculation of the free energy of conformation is key to understanding the function of biomolecules and has attracted significant interest in recent years. Here, we present an improvement of the confinement method that was designed for use in the context of explicit solvent MD simulations. The development involves an additional step in which the solvation free energy of the harmonically restrained conformers is accurately determined by multistage free energy perturbation simulations. As a test-case application, the newly introduced confinement/solvation free energy (CSF) approach was used to compute differences in free energy between conformers of the alanine dipeptide in explicit water. The results are in excellent agreement with reference calculations based on both converged molecular dynamics and umbrella sampling. To illustrate the general applicability of the method, conformational equilibria of met-enkephalin (5 aa) and deca-alanine (10 aa) in solution were also analyzed. In both cases, smoothly converged free-energy results were obtained in agreement with equilibrium sampling or literature calculations. These results demonstrate that the CSF method may provide conformational free-energy differences of biomolecules with small statistical errors (below 0.5 kcal/mol) and at a moderate computational cost even with a full representation of the solvent.

Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level.

Science.gov (United States)

Olsson, Martin A; Söderhjelm, Pär; Ryde, Ulf

2016-06-30

In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

From Helmholtz to Schlick: The evolution of the sign-theory of perception.

Science.gov (United States)

Oberdan, Thomas

2015-08-01

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zurȕck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his 'method of coincidences', similar to the 'point-coincidences' featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism. Copyright © 2015 Elsevier Ltd. All rights reserved.

Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

Science.gov (United States)

Bernard, Julien

2018-02-01

I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

SOCIAL EQUIVALENT OF FREE ENERGY

Directory of Open Access Journals (Sweden)

Josip Stepanic

2004-06-01

Full Text Available Characterisation of unbounded resources of a social system within the sociological interpretation has resulted in a large number of different notions, which are relevant in different situations. From the view point of statistical mechanics, these notions resemble free energy. In this paper the concept of social free energy is introduced and first steps toward its development presented. The social free energy is a function equal to physical free energy appropriately determined for the social system, with intrinsically sociological interpretation as a measure of social action obtainable in a given social system without changes in its structure. Its construction is a consequence of response of a social system to recognised parts of environment dynamics. It is argued that development of a social system response resembles exciting the normal modes of a general, physical system.

The Helmholtz Hierarchy: phase space statistics of cold dark matter

International Nuclear Information System (INIS)

Tassev, Svetlin V.

2011-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ''Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories

Helmholtz and Goethe -- controversies at the birth of modern neuroscience.

Science.gov (United States)

Kesselring, Jürg

2013-01-01

Hermann von Helmholtz (1821-1894), a great German scientist and philosopher, made his mark during the exciting twilight period from the Enlightenment and Romanticism to the beginnings of modern neuroscience and offered new perspectives through his work. His early inclination was for physics, which he found more attractive than purely geometric and algebraic studies, but his father was not able to make it possible for him to study physics, and so he studied medicine in order to earn a living. His lecture before the Physical Society in Berlin on July 23, 1847, 'about the conservation of the force' marked an epochal turn, even though his intention had been to deliver 'merely, some critical investigations and arrangement of facts in favor of the physiologists' as well as good arguments for the refusal of the theory of 'vitality'. Even though these new concepts were at first dismissed as fantastic speculation by some of the authorities in physics and philosophy of the day, they were enthusiastically welcomed by younger students of philosophy and the older men soon had to allow themselves to be persuaded that the effectiveness of vitality, though great and beautiful, is actually always dependent on some source of energy. Helmholtz critically assessed Goethe as a physical scientist but he did not dispute his great importance as a poet. Copyright © 2012 S. Karger AG, Basel.

Exploring the ab initio/classical free energy perturbation method: The hydration free energy of water

International Nuclear Information System (INIS)

Sakane, Shinichi; Yezdimer, Eric M.; Liu, Wenbin; Barriocanal, Jose A.; Doren, Douglas J.; Wood, Robert H.

2000-01-01

The ab initio/classical free energy perturbation (ABC-FEP) method proposed previously by Wood et al. [J. Chem. Phys. 110, 1329 (1999)] uses classical simulations to calculate solvation free energies within an empirical potential model, then applies free energy perturbation theory to determine the effect of changing the empirical solute-solvent interactions to corresponding interactions calculated from ab initio methods. This approach allows accurate calculation of solvation free energies using an atomistic description of the solvent and solute, with interactions calculated from first principles. Results can be obtained at a feasible computational cost without making use of approximations such as a continuum solvent or an empirical cavity formation energy. As such, the method can be used far from ambient conditions, where the empirical parameters needed for approximate theories of solvation may not be available. The sources of error in the ABC-FEP method are the approximations in the ab initio method, the finite sample of configurations, and the classical solvent model. This article explores the accuracy of various approximations used in the ABC-FEP method by comparing to the experimentally well-known free energy of hydration of water at two state points (ambient conditions, and 973.15 K and 600 kg/m3). The TIP4P-FQ model [J. Chem. Phys. 101, 6141 (1994)] is found to be a reliable solvent model for use with this method, even at supercritical conditions. Results depend strongly on the ab initio method used: a gradient-corrected density functional theory is not adequate, but a localized MP2 method yields excellent agreement with experiment. Computational costs are reduced by using a cluster approximation, in which ab initio pair interaction energies are calculated between the solute and up to 60 solvent molecules, while multi-body interactions are calculated with only a small cluster (5 to 12 solvent molecules). Sampling errors for the ab initio contribution to

Multimode Coupling Theory for Kelvin–Helmholtz Instability in Incompressible Fluid

International Nuclear Information System (INIS)

Li-Feng, Wang; Ying-Jun, Li; Wen-Hua, Ye; Zheng-Feng, Fan

2009-01-01

A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not

Diabat Interpolation for Polymorph Free-Energy Differences.

Science.gov (United States)

Kamat, Kartik; Peters, Baron

2017-02-02

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

Free energy analysis of cell spreading.

Science.gov (United States)

McEvoy, Eóin; Deshpande, Vikram S; McGarry, Patrick

2017-10-01

In this study we present a steady-state adaptation of the thermodynamically motivated stress fiber (SF) model of Vigliotti et al. (2015). We implement this steady-state formulation in a non-local finite element setting where we also consider global conservation of the total number of cytoskeletal proteins within the cell, global conservation of the number of binding integrins on the cell membrane, and adhesion limiting ligand density on the substrate surface. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell in order to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experiments of Engler et al. (2003). We also simulate the experiments of Théry et al. (2006), whereby initially circular cells deform and adhere to "V-shaped" and "Y-shaped" ligand patches. Analysis of a number of different spread states reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations, i.e. a high concentration of highly aligned SFs occurs along free edges, with lower SF concentrations in the interior of the cell. In summary, the results of this study suggest that cell spreading is driven by free energy minimization based on a competition between decreasing

The free energy principle, negative energy modes, and stability

International Nuclear Information System (INIS)

Morrison, P.J.; Kotschenreuther, M.

1990-01-01

This paper is concerned with instability of equilibria of Hamiltonian, fluid and plasma dynamical systems. Usually the dynamical equilibrium of interest is not the state of thermodynamic equilibrium, and does not correspond to a free energy minimum. The relaxation of this type of equilibrium is conventionally considered to be initiated by linear instability. However, there are many cases where linear instability is not present, but the equilibrium is nonlinearly unstable to arbitrarily small perturbations. This paper is about general free energy expressions for determining the presence of linear or nonlinear instabilities. These expressions are simple and practical, and can be obtained for all equilibria of all ideal fluid and plasma models. By free energy, we mean the energy change upon perturbations of the equilibrium that respect dynamical phase space constraints. This quantity is measured by a self-adjoint quadratic form, called δ 2 F. The free energy can result in instability when δ 2 F is indefinite; i.e. there exist accessible perturbations that lower the free energy of the system. A primary purpose of this paper is to tie together three manifestations of what we will refer to as negative energy modes. The first is the conventional plasma physics notion of negative energy mode that is based on the definition of the energy in a homogeneous dielectric medium. A negative energy mode is a normal mode of the medium (plasma) that possesses negative dielectric energy. The second manifestation occurs in finite degree-of-freedom Hamiltonian normal form theory. The quadratic part of a Hamiltonian in the vicinity of an equilibrium point, which possesses only distinct oscillatory eigenvalues, has an invariant signature. Thus in cases where the quadratic form is indefinite, it is natural to refer to the modes corresponding to the negative signature as negative energy modes

Reconstruction of extended sources for the Helmholtz equation

KAUST Repository

Kress, Rainer; Rundell, William

2013-01-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our

Calculation of molecular free energies in classical potentials

International Nuclear Information System (INIS)

Farhi, Asaf; Singh, Bipin

2016-01-01

Free energies of molecules can be calculated by quantum chemistry computations or by normal mode classical calculations. However, the first can be computationally impractical for large molecules and the second is based on the assumption of harmonic dynamics. We present a novel, accurate and complete calculation of molecular free energies in standard classical potentials. In this method we transform the molecule by relaxing potential terms which depend on the coordinates of a group of atoms in that molecule and calculate the free energy difference associated with the transformation. Then, since the transformed molecule can be treated as non-interacting systems, the free energy associated with these atoms is analytically or numerically calculated. This two-step calculation can be applied to calculate free energies of molecules or free energy difference between (possibly large) molecules in a general environment. We demonstrate the method in free energy calculations for methanethiol and butane molecules in vacuum and solvent. We suggest the potential application of free energy calculation of chemical reactions in classical molecular simulations. (paper)

Thermodynamic Justification for the Parabolic Model for Reactivity Indicators with Respect to Electron Number and a Rigorous Definition for the Electrophilicity: The Essential Role Played by the Electronic Entropy.

Science.gov (United States)

Franco-Pérez, Marco; Gázquez, José L; Ayers, Paul W; Vela, Alberto

2018-02-13

The temperature-dependence of the Helmholtz free energy with respect to the number of electrons is analyzed within the framework of the Grand Canonical Ensemble. At the zero-temperature limit, the Helmholtz free energy behaves as a Heaviside function of the number of electrons; however, as the temperature increases, the profile smoothens and exhibits a minimum value at noninteger positive values of the fractional electronic charge. We show that the exact average electronic energy as a function of the number of electrons does not display this feature at any temperature, since this behavior is solely due to the electronic entropy. Our mathematical analysis thus indicates that the widely used parabolic interpolation model should not be viewed as an approximation for the average electronic energy, but for the dependence of the Helmholtz free energy upon the number of electrons, and this analysis is corroborated by numerical results. Finally, an electrophilicity index is defined for the Helmholtz free energy showing that, for a given chemical species, there exists a temperature value for which this quantity is equivalent to the electrophilicity index defined within the parabolic interpolation of the electronic energy as a function of the number of electrons. Our formulation suggests that the convexity property of the energy versus the number of electrons together with the entropic contribution does not allow for an analogous nucleophilicity index to be defined.

Free energy of hydration of niobium oxide

International Nuclear Information System (INIS)

Plodinec, M.J.

1996-01-01

Some of the glasses being formulated by SRTC researchers contain niobium oxide. In this report, the free energy of hydration of the oxide is calculated from the free energies of formation of the oxide, the hydroxide, and water. This value can be used in calculations of the free energy of hydration of glasses containing niobium

An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale.

Science.gov (United States)

McCarty, J; Clark, A J; Copperman, J; Guenza, M G

2014-05-28

Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k → 0 limit, c0. A numerical solution to the PRISM integral equations is used to determine c0, by adjusting the value of the effective hard sphere diameter, dHS, to agree with the predicted equation of state. This single quantity parameterizes the coarse-grained potential, which is used to perform mesoscale simulations that are directly compared with atomistic-level simulations of the same system. We test our coarse-graining formalism by comparing structural correlations, isothermal compressibility, equation of state, Helmholtz and Gibbs free energies, and potential energy and entropy using both united atom and coarse-grained descriptions. We find quantitative agreement between the analytical formalism for the thermodynamic properties, and the results of Molecular Dynamics simulations, independent of the chosen level of representation. In the mesoscale description, the potential energy of the soft-particle interaction becomes a free energy in the coarse-grained coordinates which preserves the excess free energy from an ideal gas across all levels of description. The structural consistency between the united-atom and mesoscale descriptions means the relative entropy between descriptions has been minimized without any variational optimization parameters. The approach is general and applicable to any polymeric system in different thermodynamic conditions.

The research reactor BER II at the Helmholtz-Center Berlin

Energy Technology Data Exchange (ETDEWEB)

Krohn, Herbert [Helmholtz-Zentrum Berlin (HZB), Berlin (Germany)

2012-10-15

For basic and application-oriented research assignments the Helmholtz-Center Berlin (Helmholtz Zentrum Berlin - HZB) runs a research reactor that operates as a source of neutron beams for a wide range of scientific investigations. At the end of the 1980{sup th} the BER II was completed renewed and fitted with new experimental facilities. The BER II is a light water cooled and moderated swimming pool type reactor to be operated at 10 MW thermal power. Six neutron guides deliver cold neutrons from the cold moderator cell to a neutron guide hall adjacent to the experiment hall. With its 24 experimental stations, experimenters at HZB have practically all neutron scattering or neutron radiography techniques at their disposal. (orig.)

The research reactor BER II at the Helmholtz-Center Berlin

International Nuclear Information System (INIS)

Krohn, Herbert

2012-01-01

For basic and application-oriented research assignments the Helmholtz-Center Berlin (Helmholtz Zentrum Berlin - HZB) runs a research reactor that operates as a source of neutron beams for a wide range of scientific investigations. At the end of the 1980 th the BER II was completed renewed and fitted with new experimental facilities. The BER II is a light water cooled and moderated swimming pool type reactor to be operated at 10 MW thermal power. Six neutron guides deliver cold neutrons from the cold moderator cell to a neutron guide hall adjacent to the experiment hall. With its 24 experimental stations, experimenters at HZB have practically all neutron scattering or neutron radiography techniques at their disposal. (orig.)

The free energy of the metastable supersaturated vapor via restricted ensemble simulations. III. An extension to the Corti and Debenedetti subcell constraint algorithm

International Nuclear Information System (INIS)

Nie, Chu; Geng, Jun; Marlow, William H.

2016-01-01

In order to improve the sampling of restricted microstates in our previous work [C. Nie, J. Geng, and W. H. Marlow, J. Chem. Phys. 127, 154505 (2007); 128, 234310 (2008)] and quantitatively predict thermal properties of supersaturated vapors, an extension is made to the Corti and Debenedetti subcell constraint algorithm [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)], which restricts the maximum allowed local density at any point in a simulation box. The maximum allowed local density at a point in a simulation box is defined by the maximum number of particles N m allowed to appear inside a sphere of radius R, with this point as the center of the sphere. Both N m and R serve as extra thermodynamic variables for maintaining a certain degree of spatial homogeneity in a supersaturated system. In a restricted canonical ensemble, at a given temperature and an overall density, series of local minima on the Helmholtz free energy surface F(N m , R) are found subject to different (N m , R) pairs. The true equilibrium metastable state is identified through the analysis of the formation free energies of Stillinger clusters of various sizes obtained from these restricted states. The simulation results of a supersaturated Lennard-Jones vapor at reduced temperature 0.7 including the vapor pressure isotherm, formation free energies of critical nuclei, and chemical potential differences are presented and analyzed. In addition, with slight modifications, the current algorithm can be applied to computing thermal properties of superheated liquids.

The Limit of Free Magnetic Energy in Active Regions

Science.gov (United States)

Moore, Ron; Falconer, David; Sterling, Alphonse

2012-01-01

By measuring from active-region magnetograms a proxy of the free energy in the active region fs magnetic field, it has been found previously that (1) there is an abrupt upper limit to the free energy the field can hold that increases with the amount of magnetic field in the active region, the active region fs magnetic flux content, and (2) the free energy is usually near its limit when the field explodes in a CME/flare eruption. That is, explosive active regions are concentrated in a main-sequence path bordering the free-energy ]limit line in (flux content, free-energy proxy) phase space. Here, from measurement of Marshall Space Flight Center vector magnetograms, we find the magnetic condition that underlies the free ]energy limit and the accompanying main sequence of explosive active regions. Using a suitable free ]energy proxy measured from vector magnetograms of 44 active regions, we find that (1) in active regions at and near their free ]energy limit, the ratio of magnetic-shear free energy to the non ]free magnetic energy the potential field would have is approximately 1 in the core field, the field rooted along the neutral line, and (2) this ratio is progressively less in active regions progressively farther below their free ]energy limit. This shows that most active regions in which this core-field energy ratio is much less than 1 cannot be triggered to explode; as this ratio approaches 1, most active regions become capable of exploding; and when this ratio is 1 or greater, most active regions are compelled to explode. From these results we surmise the magnetic condition that determines the free ]energy limit is the ratio of the free magnetic energy to the non-free energy the active region fs field would have were it completely relaxed to its potential ]field configuration, and that this ratio is approximately 1 at the free-energy limit and in the main sequence of explosive active regions.

Good Practices in Free-energy Calculations

Science.gov (United States)

Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher

2013-01-01

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.

Rayleigh-Taylor and Kelvin-Helmholtz instabilities in targets accelerated by laser ablation

International Nuclear Information System (INIS)

Emery, M.H.; Gardner, J.H.; Boris, J.P.

1982-01-01

With use of the fast2d laser-shell model, the acceleration of a 20-μm-thick plastic foil up to 160 km/s has been simulated. It is possible to follow the Rayleigh-Taylor bubble-and-spike development far into the nonlinear regime and beyond the point of foil fragmentation. Strong shear flow develops which evolves into the Kelvin-Helmholtz instability. The Kelvin-Helmholtz instability causes the tips of the spikes to widen and as a result reduce their rate of ''fall.''

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.

Science.gov (United States)

Deng, Nanjie; Zhang, Bin W; Levy, Ronald M

2015-06-09

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

Fourier-Based Fast Multipole Method for the Helmholtz Equation

KAUST Repository

Cecka, Cris

2013-01-01

The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.

Microscopically derived free energy of dislocations

NARCIS (Netherlands)

Kooiman, M.; Hütter, M.; Geers, M.G.D.

2015-01-01

The dynamics of large amounts of dislocations is the governing mechanism in metal plasticity. The free energy of a continuous dislocation density profile plays a crucial role in the description of the dynamics of dislocations, as free energy derivatives act as the driving forces of dislocation

Uncertainty Quantification in Alchemical Free Energy Methods.

Science.gov (United States)

Bhati, Agastya P; Wan, Shunzhou; Hu, Yuan; Sherborne, Brad; Coveney, Peter V

2018-05-02

Alchemical free energy methods have gained much importance recently from several reports of improved ligand-protein binding affinity predictions based on their implementation using molecular dynamics simulations. A large number of variants of such methods implementing different accelerated sampling techniques and free energy estimators are available, each claimed to be better than the others in its own way. However, the key features of reproducibility and quantification of associated uncertainties in such methods have barely been discussed. Here, we apply a systematic protocol for uncertainty quantification to a number of popular alchemical free energy methods, covering both absolute and relative free energy predictions. We show that a reliable measure of error estimation is provided by ensemble simulation-an ensemble of independent MD simulations-which applies irrespective of the free energy method. The need to use ensemble methods is fundamental and holds regardless of the duration of time of the molecular dynamics simulations performed.

Free energy profiles from single-molecule pulling experiments.

Science.gov (United States)

Hummer, Gerhard; Szabo, Attila

2010-12-14

Nonequilibrium pulling experiments provide detailed information about the thermodynamic and kinetic properties of molecules. We show that unperturbed free energy profiles as a function of molecular extension can be obtained rigorously from such experiments without using work-weighted position histograms. An inverse Weierstrass transform is used to relate the system free energy obtained from the Jarzynski equality directly to the underlying molecular free energy surface. An accurate approximation for the free energy surface is obtained by using the method of steepest descent to evaluate the inverse transform. The formalism is applied to simulated data obtained from a kinetic model of RNA folding, in which the dynamics consists of jumping between linker-dominated folded and unfolded free energy surfaces.

Optimization of field homogeneity of Helmholtz-like coils for measuring the balance of planar gradiometers

International Nuclear Information System (INIS)

Nordahn, M.A.; Holst, T.; Shen, Y.Q.

1999-01-01

Measuring the balance of planar SQUID gradiometers using a relatively small Helmholtz-like coil system requires a careful design of the coils in order to have a high degree of field uniformity along the radial direction. The level to which planar gradiometers can be balanced will be affected by any misalignment of the gradiometer relative to the ideal central position. Therefore, the maximum degree of balancing possible is calculated numerically for the Helmholtz geometry under various perturbations, including misalignment of the gradiometer along the cylindrical and the radial axis, and angular tilting relative to the normal plane. Furthermore, if the ratio between the coil separation and coil radius is chosen to be less than unity, calculations show that the expected radial uniformity of the field can be improved considerably compared to the traditional Helmholtz geometry. The optimized coil geometry is compared to the Helmholtz geometry and is found to yield up to an order of magnitude improvement of the worst case error signal within a volume spanned by the uncertainty in the alignment. (author)

Learning free energy landscapes using artificial neural networks.

Science.gov (United States)

Sidky, Hythem; Whitmer, Jonathan K

2018-03-14

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.

Learning free energy landscapes using artificial neural networks

Science.gov (United States)

Sidky, Hythem; Whitmer, Jonathan K.

2018-03-01

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.

Generalized formulation of free energy and application to photosynthesis

Science.gov (United States)

Zhang, Hwe Ik; Choi, M. Y.

2018-03-01

The origin of free energy on the earth is solar radiation. However, the amount of free energy it contains has seldom been investigated, because the free energy concept was believed to be inappropriate for a system of photons. Instead, the origin of free energy has been sought in the process of photosynthesis, imposing a limit of conversion given by the Carnot efficiency. Here we present a general formulation, capable of not only assessing accurately the available amount of free energy in the photon gas but also explaining the primary photosynthetic process more succinctly. In this formulation, the problem of "photosynthetic conversion of the internal energy of photons into the free energy of chlorophyll" is replaced by simple "free energy transduction" between the photons and chlorophyll. An analytic expression for the photosynthetic efficiency is derived and shown to deviate from the Carnot efficiency. Some predictions verifiable possibly by observation are also suggested.

Square Helmholtz coil with homogeneous field for magnetic measurement of longer HTS tapes

Energy Technology Data Exchange (ETDEWEB)

Alamgir, A.K.M. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China)]. E-mail: alam643@hotmail.com; Fang, J. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China); Gu, C. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China); Han, Z. [Applied Superconductivity Research Center, Department of Physics, Building Li Zhai, Room 209, Tsinghua University, Beijing 100084 (China)

2005-08-01

Magnetic ac loss measurement of HTS tapes and films at various magnetic field orientations becomes a crucial issue from the view point of measurement precision. In principle, due to tiny loss component and anisotropic properties, longer HTS sample subjected to very good homogeneous field could facilitate the accuracy of this kind of measurement. We investigated field profile of Helmholtz coils with square winding as a magnetizer for HTS tape and films. It is found that square winding exhibits better field-homogeneity than that of conventional circular winding with the similar coil dimensions for ideal condition. Being apart from ideal condition, we investigated field profile of square Helmholtz coil with various combinations of coil parameters and made a conclusion for the best combination based on the field homogeneity and field intensity. The design also provides noise reduction facilities by allowing compact and identical pick up-compensation coil arrangement. In addition, we optimized the final design of Helmholtz coil to compensate the influence of difficulties in square winding on the field distribution. Finally, as small as 0.5% field variation was estimated for 50 mm long sample to be magnetized under a proper combination of fabrication parameters. Investigation of field homogeneity, noise effect and a practical design of square Helmholtz coil as a pick-up coil based magnetizer will be reported.

Square Helmholtz coil with homogeneous field for magnetic measurement of longer HTS tapes

International Nuclear Information System (INIS)

Alamgir, A.K.M.; Fang, J.; Gu, C.; Han, Z.

2005-01-01

Magnetic ac loss measurement of HTS tapes and films at various magnetic field orientations becomes a crucial issue from the view point of measurement precision. In principle, due to tiny loss component and anisotropic properties, longer HTS sample subjected to very good homogeneous field could facilitate the accuracy of this kind of measurement. We investigated field profile of Helmholtz coils with square winding as a magnetizer for HTS tape and films. It is found that square winding exhibits better field-homogeneity than that of conventional circular winding with the similar coil dimensions for ideal condition. Being apart from ideal condition, we investigated field profile of square Helmholtz coil with various combinations of coil parameters and made a conclusion for the best combination based on the field homogeneity and field intensity. The design also provides noise reduction facilities by allowing compact and identical pick up-compensation coil arrangement. In addition, we optimized the final design of Helmholtz coil to compensate the influence of difficulties in square winding on the field distribution. Finally, as small as 0.5% field variation was estimated for 50 mm long sample to be magnetized under a proper combination of fabrication parameters. Investigation of field homogeneity, noise effect and a practical design of square Helmholtz coil as a pick-up coil based magnetizer will be reported

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom) ; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom) ; Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2006-12-15

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schroedinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz-Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations.

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2006-01-01

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schroedinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz-Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations

Kelvin-Helmholtz Instability: Lessons Learned and Ways Forward

Science.gov (United States)

Masson, A.; Nykyri, K.

2018-06-01

The Kelvin-Helmholtz instability (KHI) is a ubiquitous phenomenon across the Universe, observed from 500 m deep in the oceans on Earth to the Orion molecular cloud. Over the past two decades, several space missions have enabled a leap forward in our understanding of this phenomenon at the Earth's magnetopause. Key results obtained by these missions are first presented, with a special emphasis on Cluster and THEMIS. In particular, as an ideal instability, the KHI was not expected to produce mass transport. Simulations, later confirmed by spacecraft observations, indicate that plasma transport in Kelvin-Helmholtz (KH) vortices can arise during non-linear stage of its development via secondary process. In addition to plasma transport, spacecraft observations have revealed that KHI can also lead to significant ion heating due to enhanced ion-scale wave activity driven by the KHI. Finally, we describe what are the upcoming observational opportunities in 2018-2020, thanks to a unique constellation of multi-spacecraft missions including: MMS, Cluster, THEMIS, Van Allen Probes and Swarm.

Free Energy in Introductory Physics

Science.gov (United States)

Prentis, Jeffrey J.; Obsniuk, Michael J.

2016-01-01

Energy and entropy are two of the most important concepts in science. For all natural processes where a system exchanges energy with its environment, the energy of the system tends to decrease and the entropy of the system tends to increase. Free energy is the special concept that specifies how to balance the opposing tendencies to minimize energy…

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method

International Nuclear Information System (INIS)

Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao

2009-01-01

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids 'on-the-fly' QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

The new view of hydrophobic free energy.

Science.gov (United States)

Baldwin, Robert L

2013-04-17

In the new view, hydrophobic free energy is measured by the work of solute transfer of hydrocarbon gases from vapor to aqueous solution. Reasons are given for believing that older values, measured by solute transfer from a reference solvent to water, are not quantitatively correct. The hydrophobic free energy from gas-liquid transfer is the sum of two opposing quantities, the cavity work (unfavorable) and the solute-solvent interaction energy (favorable). Values of the interaction energy have been found by simulation for linear alkanes and are used here to find the cavity work, which scales linearly with molar volume, not accessible surface area. The hydrophobic free energy is the dominant factor driving folding as judged by the heat capacity change for transfer, which agrees with values for solvating hydrocarbon gases. There is an apparent conflict with earlier values of hydrophobic free energy from studies of large-to-small mutations and an explanation is given. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Thermodynamically consistent modeling and simulation of multi-component two-phase flow model with partial miscibility

KAUST Repository

Kou, Jisheng

2016-11-25

A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a latest alternative over the NPT-based framework to model the realistic fluids. The proposed model uses the Helmholtz free energy rather than Gibbs free energy in the NPT-based framework. Different from the classical routines, we combine the first law of thermodynamics and related thermodynamical relations to derive the entropy balance equation, and then we derive a transport equation of the Helmholtz free energy density. Furthermore, by using the second law of thermodynamics, we derive a set of unified equations for both interfaces and bulk phases that can describe the partial miscibility of two fluids. A relation between the pressure gradient and chemical potential gradients is established, and this relation leads to a new formulation of the momentum balance equation, which demonstrates that chemical potential gradients become the primary driving force of fluid motion. Moreover, we prove that the proposed model satisfies the total (free) energy dissipation with time. For numerical simulation of the proposed model, the key difficulties result from the strong nonlinearity of Helmholtz free energy density and tight coupling relations between molar densities and velocity. To resolve these problems, we propose a novel convex-concave splitting of Helmholtz free energy density and deal well with the coupling relations between molar densities and velocity through very careful physical observations with a mathematical rigor. We prove that the proposed numerical scheme can preserve the discrete (free) energy dissipation. Numerical tests are carried out to verify the effectiveness of the proposed method.

Thermodynamically consistent modeling and simulation of multi-component two-phase flow with partial miscibility

KAUST Repository

Kou, Jisheng

2017-12-09

A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is an attractive alternative recently over the NPT-based framework to model the realistic fluids. The proposed model uses the Helmholtz free energy rather than Gibbs free energy in the NPT-based framework. Different from the classical routines, we combine the first law of thermodynamics and related thermodynamical relations to derive the entropy balance equation, and then we derive a transport equation of the Helmholtz free energy density. Furthermore, by using the second law of thermodynamics, we derive a set of unified equations for both interfaces and bulk phases that can describe the partial miscibility of multiple fluids. A relation between the pressure gradient and chemical potential gradients is established, and this relation leads to a new formulation of the momentum balance equation, which demonstrates that chemical potential gradients become the primary driving force of fluid motion. Moreover, we prove that the proposed model satisfies the total (free) energy dissipation with time. For numerical simulation of the proposed model, the key difficulties result from the strong nonlinearity of Helmholtz free energy density and tight coupling relations between molar densities and velocity. To resolve these problems, we propose a novel convex-concave splitting of Helmholtz free energy density and deal well with the coupling relations between molar densities and velocity through very careful physical observations with a mathematical rigor. We prove that the proposed numerical scheme can preserve the discrete (free) energy dissipation. Numerical tests are carried out to verify the effectiveness of the proposed method.

Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State

OpenAIRE

Regnier, S.; Priest, E. R.

2008-01-01

To understand the physics of solar flares, including the local reorganization of the magnetic field and the acceleration of energetic particles, we have first to estimate the free magnetic energy available for such phenomena, which can be converted into kinetic and thermal energy. The free magnetic energy is the excess energy of a magnetic configuration compared to the minimum-energy state, which is a linear force-free field if the magnetic helicity of the configuration is conserved. We inves...

Electromagnetic energy harvester for harvesting acoustic energy

Indian Academy of Sciences (India)

Farid U Khan

Acoustics; energy harvesting; electromagnetic; Helmholtz resonator; sound pressure level; suspended coil. ... WSNs, which are supposed to operate for longer period of time. However ... several ambient energies such as wind, thermal, vibration, and solar are ..... textile plants in Northern India with specific reference to noise.

Guidelines for the analysis of free energy calculations.

Science.gov (United States)

Klimovich, Pavel V; Shirts, Michael R; Mobley, David L

2015-05-01

Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.

Magnetized Kelvin-Helmholtz instability: theory and simulations in the Earth's magnetosphere context

Science.gov (United States)

Faganello, Matteo; Califano, Francesco

2017-12-01

The Kelvin-Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth's magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin-Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can be adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.

MHD Kelvin-Helmholtz instability in non-hydrostatic equilibrium

International Nuclear Information System (INIS)

Laghouati, Y; Bouabdallah, A; Zizi, M; Alemany, A

2007-01-01

The present work deals with the linear stability of a magnetohydrodynamic shear flow so that a stratified inviscid fluid rotating about a vertical axis when a uniform magnetic field is applied in the direction of the streaming or zonal flow. In geophysical flow, the stability of the flow is determined by taking into account the nonhydrostatic condition depending on Richardson number R i and the deviation δ from hydrostatic equilibrium. According to Stone (Stone P H 1971 J. Fluid. Mech. 45 659), it is shown that such deviation δ decreases the growth rates of three kinds of instability which can appear as geostrophic (G), symmetric (S) and Kelvin-Helmholtz (K-H) instabilities. To be specific, the evolution of the flow is therefore considered in the light of the influence of magnetic field, particularly, on K-H instability. The results of this study are presented by the linear stability of a magnetohydrodynamic, with horizontal free-shear flow of stratified fluid, subject to rotation about the vertical axis and uniform magnetic field in the zonal direction. Results are discussed and compared to previous works as Chandrasekhar (Chandrasekhar S 1961 Hydrodynamic and hydromagnetic stability (Oxford: Clarendon Press) chapter 11 pp 481-513) and Stone

Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points.

Science.gov (United States)

Harris, Robert C; Deng, Nanjie; Levy, Ronald M; Ishizuka, Ryosuke; Matubayasi, Nobuyuki

2017-06-05

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

The free-energy principle: a unified brain theory?

Science.gov (United States)

Friston, Karl

2010-02-01

A free-energy principle has been proposed recently that accounts for action, perception and learning. This Review looks at some key brain theories in the biological (for example, neural Darwinism) and physical (for example, information theory and optimal control theory) sciences from the free-energy perspective. Crucially, one key theme runs through each of these theories - optimization. Furthermore, if we look closely at what is optimized, the same quantity keeps emerging, namely value (expected reward, expected utility) or its complement, surprise (prediction error, expected cost). This is the quantity that is optimized under the free-energy principle, which suggests that several global brain theories might be unified within a free-energy framework.

Free energy and heat capacity

International Nuclear Information System (INIS)

Kurata, M.; Devanathan, R.

2015-01-01

Free energy and heat capacity of actinide elements and compounds are important properties for the evaluation of the safety and reliable performance of nuclear fuel. They are essential inputs for models that describe complex phenomena that govern the behaviour of actinide compounds during nuclear fuels fabrication and irradiation. This chapter introduces various experimental methods to measure free energy and heat capacity to serve as inputs for models and to validate computer simulations. This is followed by a discussion of computer simulation of these properties, and recent simulations of thermophysical properties of nuclear fuel are briefly reviewed. (authors)

Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids

Energy Technology Data Exchange (ETDEWEB)

Sheng, Qin, E-mail: Qin_Sheng@baylor.edu [Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328 (United States); Sun, Hai-wei, E-mail: hsun@umac.mo [Department of Mathematics, University of Macau (Macao)

2016-11-15

This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman–Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.

Development of a Miniature, Two-Axis, Triple-Helmholtz-Driven Gimbal

Science.gov (United States)

Sharif, Boz; Joscelyn, Ed; Wilcox, Brian; Johnson, Michael R.

2000-01-01

This paper details the development of a Helmholtz-driven, 2-axis gimbal to position a flat mirror within 50 microradian (fine positioning) in a space environment. The gimbal is intended to travel on a deep space mission mounted on a miniature "rover" vehicle. The gimbal will perform both pointing and scanning functions. The goal for total mass of the gimbal was 25 grams. The primary challenge was to design and build a bearing system that would achieve the required accuracy in addition to supporting the relatively large mass of the mirror and the outer gimbal. The mechanism is subjected to 100-G loading without the aid of any additional caging mechanism. Additionally, it was desired to have the same level of accuracy during Earth-bound, 1-G testing. Due to the inherent lack of damping in a zero-G, vacuum environment; the ability of the gimbal to respond to very small amounts of input energy is paramount. Initial testing of the first prototype revealed exceedingly long damping times required even while exposed to the damping effects of air and 1-G friction. It is envisioned that fine positioning of the gimbal will be accomplished in very small steps to avoid large disturbances to the mirror. Various bearing designs, including materials, lubrication options and bearing geometry will be discussed. In addition various options for the Helmholtz coil design will be explored with specific test data given. Ground testing in the presence of 1-G was compounded by the local magnetic fields due to the "compass" effect on the gimbal. The test data will be presented and discussed. Additionally, rationale for estimating gimbal performance in a zero-G environment will be presented and discussed.

Voluntarism in early psychology: the case of Hermann von Helmholtz.

Science.gov (United States)

De Kock, Liesbet

2014-05-01

The failure to recognize the programmatic similarity between (post-)Kantian German philosophy and early psychology has impoverished psychology's historical self-understanding to a great extent. This article aims to contribute to recent efforts to overcome the gaps in the historiography of contemporary psychology, which are the result of an empiricist bias. To this end, we present an analysis of the way in which Hermann von Helmholtz's theory of perception resonates with Johann Gottlieb Fichte's Ego-doctrine. It will be argued that this indebtedness is particularly clear when focusing on the foundation of the differential awareness of subject and object in perception. In doing so, the widespread reception of Helmholtz's work as proto-positivist or strictly empiricist is challenged, in favor of the claim that important elements of his theorizing can only be understood properly against the background of Fichte's Ego-doctrine. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Standard free energy of formation of iron iodide

Science.gov (United States)

Khandkar, A.; Tare, V. B.; Wagner, J. B., Jr.

1983-01-01

An experiment is reported where silver iodide is used to determine the standard free energy of formation of iron iodide. By using silver iodide as a solid electrolyte, a galvanic cell, Ag/AgI/Fe-FeI2, is formulated. The standard free energy of formation of AgI is known, and hence it is possible to estimate the standard free energy of formation of FeI2 by measuring the open-circuit emf of the above cell as a function of temperature. The free standard energy of formation of FeI2 determined by this method is -38784 + 24.165T cal/mol. It is estimated that the maximum error associated with this method is plus or minus 2500 cal/mol.

Probing Free-Energy Surfaces with Differential Scanning Calorimetry

Science.gov (United States)

Sanchez-Ruiz, Jose M.

2011-05-01

Many aspects of protein folding can be understood in terms of projections of the highly dimensional energy landscape onto a few (or even only one) particularly relevant coordinates. These free-energy surfaces can be probed conveniently from experimental differential scanning calorimetry (DSC) thermograms, as DSC provides a direct relation with the protein partition function. Free-energy surfaces thus obtained are consistent with two fundamental scenarios predicted by the energy-landscape perspective: (a) well-defined macrostates separated by significant free-energy barriers, in some cases, and, in many other cases, (b) marginal or even vanishingly small barriers, which furthermore show a good correlation with kinetics for fast- and ultrafast-folding proteins. Overall, the potential of DSC to assess free-energy surfaces for a wide variety of proteins makes it possible to address fundamental issues, such as the molecular basis of the barrier modulations produced by natural selection in response to functional requirements or to ensure kinetic stability.

Energy buildup in sheared force-free magnetic fields

Science.gov (United States)

Wolfson, Richard; Low, Boon C.

1992-01-01

Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.

Coupled Kelvin-Helmholtz and Tearing Mode Instabilities at the Mercury's Magnetopause

Science.gov (United States)

Ivanovski, S. L.; Milillo, A.; Kartalev, M.; Massetti, S.

2018-05-01

A MHD approach for numerical simulations of coupled Kelvin-Helmholtz and tearing mode instabilities has been applied to Mercury’s magnetopause and used to perform a physical parameters study constrained by the MESSENGER data.

The outlooks of Helmholtz, Plank and Einstein on the unified physical theory

International Nuclear Information System (INIS)

Treder, G.Yu.

1982-01-01

The outlooks of Helmholtz, Planck and Einstein on the unified physical theory are exposed. Planck formulated the Einstein relativistic mechanics in the canonical form stemming from the suggested by Helmholtz approach that the principle of action is the unified formal principle of physics. Einstein and his companious proceeded from machroscopic fields in the attempts to prove the unified geometric field theory. The sense of Planck length as ''the smallest length in physics'' is determined, on the one hand, by the Heizenberg uncerntainty principle for the measurement process, and on the other hand by the universal proportionality between inertia and gravity. It results from geometrical nature and gravitational potential, i. e. from Einstein interpretation of the equivalence principle

Kelvin-Helmholtz evolution in subsonic cold streams feeding galaxies

Science.gov (United States)

Angulo, Adrianna; Coffing, S.; Kuranz, C.; Drake, R. P.; Klein, S.; Trantham, M.; Malamud, G.

2017-10-01

The most prolific star formers in cosmological history lie in a regime where dense filament structures carried substantial mass into the galaxy to sustain star formation without producing a shock. However, hydrodynamic instabilities present on the filament surface limit the ability of such structures to deliver dense matter deeply enough to sustain star formation. Simulations lack the finite resolution necessary to allow fair treatment of the instabilities present at the stream boundary. Using the Omega EP laser, we simulate this mode of galaxy formation with a cold, dense, filament structure within a hotter, subsonic flow and observe the interface evolution. Machined surface perturbations stimulate the development of the Kelvin-Helmholtz (KH) instability due to the resultant shear between the two media. A spherical crystal imaging system produces high-resolution radiographs of the KH structures along the filament surface. The results from the first experiments of this kind, using a rod with single-mode, long-wavelength modulations, will be discussed. This work is funded by the U.S. Department of Energy, through the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, Grant Number DE-NA0002956, and the National Laser User Facility Program, Grant Number DE-NA0002719, and through.

Calculating zeros: Non-equilibrium free energy calculations

International Nuclear Information System (INIS)

Oostenbrink, Chris; Gunsteren, Wilfred F. van

2006-01-01

Free energy calculations on three model processes with theoretically known free energy changes have been performed using short simulation times. A comparison between equilibrium (thermodynamic integration) and non-equilibrium (fast growth) methods has been made in order to assess the accuracy and precision of these methods. The three processes have been chosen to represent processes often observed in biomolecular free energy calculations. They involve a redistribution of charges, the creation and annihilation of neutral particles and conformational changes. At very short overall simulation times, the thermodynamic integration approach using discrete steps is most accurate. More importantly, reasonable accuracy can be obtained using this method which seems independent of the overall simulation time. In cases where slow conformational changes play a role, fast growth simulations might have an advantage over discrete thermodynamic integration where sufficient sampling needs to be obtained at every λ-point, but only if the initial conformations do properly represent an equilibrium ensemble. From these three test cases practical lessons can be learned that will be applicable to biomolecular free energy calculations

The Bogoliubov free energy functional II

DEFF Research Database (Denmark)

Napiórkowski, Marcin; Reuvers, Robin; Solovej, Jan Philip

2018-01-01

We analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit $a_0\\to a$, we determine the critical temperature to be $T_{\\rm{c}}=T_{\\rm{fc}}(1+1.49(\\rho^{1/3}a))$ to leading order. Here, $T......_{\\rm{fc}}$ is the critical temperature of the free Bose gas, $\\rho$ is the density of the gas, $a$ is the scattering length of the pair-interaction potential $V$, and $a_0=(8\\pi)^{-1}\\widehat{V}(0)$ its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee...

Free energy of activation. Definition, properties, and dependent variables with special reference to linear free energy relations

International Nuclear Information System (INIS)

Levine, R.D.

1979-01-01

The reaction rate constant is expressed as Z exp(-G/sub a//RT). Z is the binary collision frequency. G/sub a/, the free energy of activation, is shown to be the difference between the free energy of the reactive reactants and the free energy of all reactants. The results are derived from both a statistical mechanical and a collision theoretic point of view. While the later is more suitable for an ab-initio computation of the reaction rate, it is the former that lends itself to the search of systematics and of correlations and to compaction of data. Different thermodynamic-like routes to the characterization of G/sub a/ are thus explored. The two most promising ones appear to be the use of thermodynamic type cycles and the changes of dependent variables using the Legendre transform technique. The dependence of G/sub a/ on ΔG 0 , the standard free energy change in the reaction, is examined from the later point of view. It is shown that one can rigorously express this dependence as G/sub a/ = αΔG 0 + G/sub a/ 0 M(α). Here α is the Bronsted slope, α = -par. delta ln k(T)/par. delta(ΔG 0 /RT), G/sub a/ 0 is independent of ΔG 0 and M(α), the Legendre transform of G/sub a/, is a function only of α. For small changes in ΔG 0 , the general result reduces to the familiar ''linear'' free energy relation delta G/sub a/ = α delta ΔG 0 . It is concluded from general considerations that M(α) is a symmetric, convex function of α and hence that α is a monotonically increasing function of ΔG 0 . Experimental data appear to conform well to the form α = 1/[1 + exp(-ΔG 0 /G/sub s/ 0 )]. A simple interpretation of the ΔG 0 dependence of G/sub a/, based on an interpolation of the free energy from that of the reagents to that of the products, is offered. 4 figures, 69 references

The free-energy cost of interaction between DNA loops.

Science.gov (United States)

Huang, Lifang; Liu, Peijiang; Yuan, Zhanjiang; Zhou, Tianshou; Yu, Jianshe

2017-10-03

From the viewpoint of thermodynamics, the formation of DNA loops and the interaction between them, which are all non-equilibrium processes, result in the change of free energy, affecting gene expression and further cell-to-cell variability as observed experimentally. However, how these processes dissipate free energy remains largely unclear. Here, by analyzing a mechanic model that maps three fundamental topologies of two interacting DNA loops into a 4-state model of gene transcription, we first show that a longer DNA loop needs more mean free energy consumption. Then, independent of the type of interacting two DNA loops (nested, side-by-side or alternating), the promotion between them always consumes less mean free energy whereas the suppression dissipates more mean free energy. More interestingly, we find that in contrast to the mechanism of direct looping between promoter and enhancer, the facilitated-tracking mechanism dissipates less mean free energy but enhances the mean mRNA expression, justifying the facilitated-tracking hypothesis, a long-standing debate in biology. Based on minimal energy principle, we thus speculate that organisms would utilize the mechanisms of loop-loop promotion and facilitated tracking to survive in complex environments. Our studies provide insights into the understanding of gene expression regulation mechanism from the view of energy consumption.

Free energy of superfluid 3He

International Nuclear Information System (INIS)

Rainer, D.; Serene, J.W.

1976-01-01

A systematic scheme is presented for calculating the free energy of superfluid Fermi liquids by an asymptotic expansion in the small parameter T/subc//T/subF/. This scheme is used to evaluate the strong-coupling corrections to the free energy of superfluid 3 He. It is shown that the leading corrections can be expressed in terms of the normal-state quasiparticle scattering amplitude, and the strong-coupling results are discussed using the s-p approximation for the scattering amplitude

Two numerical methods for an inverse problem for the 2-D Helmholtz equation

CERN Document Server

Gryazin, Y A; Lucas, T R

2003-01-01

Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.

Information-to-free-energy conversion: Utilizing thermal fluctuations.

Science.gov (United States)

Toyabe, Shoichi; Muneyuki, Eiro

2013-01-01

Maxwell's demon is a hypothetical creature that can convert information to free energy. A debate that has lasted for more than 100 years has revealed that the demon's operation does not contradict the laws of thermodynamics; hence, the demon can be realized physically. We briefly review the first experimental demonstration of Maxwell's demon of Szilard's engine type that converts information to free energy. We pump heat from an isothermal environment by using the information about the thermal fluctuations of a Brownian particle and increase the particle's free energy.

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

Science.gov (United States)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

Calculating Free Energies Using Average Force

Science.gov (United States)

Darve, Eric; Pohorille, Andrew; DeVincenzi, Donald L. (Technical Monitor)

2001-01-01

A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Intramolecular Association within the SAFT Framework

DEFF Research Database (Denmark)

Avlund, Ane Søgaard; Kontogeorgis, Georgios; Chapman, Walter G.

2011-01-01

A general theory for modelling intramolecular association within the SAFT framework is proposed. Sear and Jackson [Phys. Rev. E. 50 (1), 386 (1994)] and Ghonasgi and Chapman [J. Chem. Phys. 102 (6), 2585 (1995)] have previously extended SAFT to include intramolecular association for chains with two...... the contribution to the Helmholtz free energy from association (inter- as well as intramolecularly) at equilibrium. Sear and Jackson rederived the contribution to the Helmholtz free energy from association from the theory by Wertheim [J. Stat. Phys. 42 (3–4), 459 (1986)] with inclusion of intramolecular...

Surface free energy of alkali and transition metal nanoparticles

International Nuclear Information System (INIS)

Aqra, Fathi; Ayyad, Ahmed

2014-01-01

Graphical abstract: Size dependent surface free energy of spherical, cubic and disk Au nanoparticles. - Highlights: • A model to account for the surface free energy of metallic nanoparticles is described. • The model requires only the cohesive energy of the nanoparticle. • The surface free energy of a number of metallic nanoparticles has been calculated, and the obtained values agree well with existing data. • Surface energy falls down very fast when the number of atoms is less than hundred. • The model is applicable to any metallic nanoparticle. - Abstract: This paper addresses an interesting issue on the surface free energy of metallic nanoparticles as compared to the bulk material. Starting from a previously reported equation, a theoretical model, that involves a specific term for calculating the cohesive energy of nanoparticle, is established in a view to describe the behavior of surface free energy of metallic nanoparticles (using different shapes of particle: sphere, cube and disc). The results indicate that the behavior of surface energy is very appropriate for spherical nanoparticle, and thus, it is the most realistic shape of a nanoparticle. The surface energy of copper, silver, gold, platinum, tungsten, molybdenum, tantalum, paladium and alkali metallic nanoparticles is only prominent in the nanoscale size, and it decreases with the decrease of nanoparticle size. Thus, the surface free energy plays a more important role in determining the properties of nanoparticles than in bulk materials. It differs from shape to another, and falls down as the number of atoms (nanoparticle size) decreases. In the case of spherical nanoparticles, the onset of the sharp decrease in surface energy is observed at about 110 atom. A decrease of 16% and 45% in surface energy is found by moving from bulk to 110 atom and from bulk to 5 atom, respectively. The predictions are consistent with the reported data

Free-energy analysis of spin models on hyperbolic lattice geometries.

Science.gov (United States)

Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej

2016-04-01

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Implicit ligand theory for relative binding free energies

Science.gov (United States)

Nguyen, Trung Hai; Minh, David D. L.

2018-03-01

Implicit ligand theory enables noncovalent binding free energies to be calculated based on an exponential average of the binding potential of mean force (BPMF)—the binding free energy between a flexible ligand and rigid receptor—over a precomputed ensemble of receptor configurations. In the original formalism, receptor configurations were drawn from or reweighted to the apo ensemble. Here we show that BPMFs averaged over a holo ensemble yield binding free energies relative to the reference ligand that specifies the ensemble. When using receptor snapshots from an alchemical simulation with a single ligand, the new statistical estimator outperforms the original.

QM/MM free energy simulations: recent progress and challenges

Science.gov (United States)

Lu, Xiya; Fang, Dong; Ito, Shingo; Okamoto, Yuko; Ovchinnikov, Victor

2016-01-01

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections. PMID:27563170

Improved free-energy landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding energy.

Science.gov (United States)

Heenan, Patrick R; Yu, Hao; Siewny, Matthew G W; Perkins, Thomas T

2018-03-28

Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged as a powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium free energies (ΔG 0 ) from non-equilibrium single-molecule force spectroscopy records. The combination of these two advances in single-molecule studies deduced the free-energy of the model membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the reconstruction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-fold higher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated with the force probe and determined the molecular free-energy landscape of the molecule under study, bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid (aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly high value. Hence, while average unfolding ΔG 0 per aa is a useful metric, the derived high-resolution landscape details significant local variation from the mean. More generally, we demonstrated that, as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy landscapes from AFM data.

Holographic free energy and thermodynamic geometry

Science.gov (United States)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-12-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

Holographic free energy and thermodynamic geometry

International Nuclear Information System (INIS)

Ghorai, Debabrata; Gangopadhyay, Sunandan

2016-01-01

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

Holographic free energy and thermodynamic geometry

Energy Technology Data Exchange (ETDEWEB)

Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)

2016-12-15

We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

On the TAP Free Energy in the Mixed p-Spin Models

Science.gov (United States)

Chen, Wei-Kuo; Panchenko, Dmitry

2018-05-01

Thouless et al. (Phys Mag 35(3):593-601, 1977), derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy on the extended configuration space of local magnetizations with an Onsager correction term. In the setting of mixed p-spin models with Ising spins, we prove that the free energy can indeed be written as the supremum of the TAP free energy over the space of local magnetizations whose Edwards-Anderson order parameter (self-overlap) is to the right of the support of the Parisi measure. Furthermore, for generic mixed p-spin models, we prove that the free energy is equal to the TAP free energy evaluated on the local magnetization of any pure state.

Free energy from molecular dynamics with multiple constraints

NARCIS (Netherlands)

den Otter, Wouter K.; Briels, Willem J.

2000-01-01

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to

Free energy distribution function of a random Ising ferromagnet

International Nuclear Information System (INIS)

Dotsenko, Victor; Klumov, Boris

2012-01-01

We study the free energy distribution function of a weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg–Landau Hamiltonian. It is shown that besides the usual Gaussian 'body' this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much slower than the right one (for large positive values of the free energy). It is argued that at the critical point the free energy of the random Ising ferromagnet in dimensions D < 4 is described by a non-trivial universal distribution function which is non-self-averaging

Acoustic response of Helmholtz dampers in the presence of hot grazing flow

Science.gov (United States)

Ćosić, B.; Wassmer, D.; Terhaar, S.; Paschereit, C. O.

2015-01-01

Thermoacoustic instabilities are high amplitude instabilities of premixed gas turbine combustors. Cooled passive dampers are used to attenuate or suppress these instabilities in the combustion chamber. For the first time, the influence of temperature differences between the grazing flow in the combustor and the cross-flow emanating from the Helmholtz damper is comprehensively investigated in the linear and nonlinear amplitude regime. The flow field inside the resonator and in the vicinity of the neck is measured with high-speed particle image velocimetry for various amplitudes and at different momentum-flux ratios of grazing and purging flow. Seeding is used as a tracer to qualitatively assess the mixing of the grazing and purging flow as well as the ingestion into the neck of the resonator. Experimentally, the acoustic response for various temperature differences between grazing and purging flow is investigated. The multi-microphone method, in combination with two microphones flush-mounted in the resonator volume and two microphones in the plane of the resonator entrance, is used to determine the impedance of the Helmholtz resonator in the linear and nonlinear amplitude regime for various temperatures and different momentum-flux ratios. Additionally, a thermocouple was used to measure the temperature in the neck. The acoustic response and the temperature measurements are used to obtain the virtual neck length and the effective area jump from a detailed impedance model. This model is extended to include the observed acoustic energy dissipation caused by the density gradients at the neck vicinity. A clear correlation between temperature differences and changes of the mass end-correction is confirmed. The capabilities of the impedance model are demonstrated.

A third note: Helmholtz, Palestrina, and the Early History of Musicology

NARCIS (Netherlands)

Kursell, J.

2015-01-01

This contribution focuses on Hermann von Helmholtz’s work on Renaissance composer Giovanni Pierluigi da Palestrina. Helmholtz used his scientific concept of distortion to analyze this music and, reversely, to find corroboration for the concept in his musical analyses. In this, his work interlocked

Measuring excess free energies of self-assembled membrane structures.

Science.gov (United States)

Norizoe, Yuki; Daoulas, Kostas Ch; Müller, Marcus

2010-01-01

Using computer simulation of a solvent-free, coarse-grained model for amphiphilic membranes, we study the excess free energy of hourglass-shaped connections (i.e., stalks) between two apposed bilayer membranes. In order to calculate the free energy by simulation in the canonical ensemble, we reversibly transfer two apposed bilayers into a configuration with a stalk in three steps. First, we gradually replace the intermolecular interactions by an external, ordering field. The latter is chosen such that the structure of the non-interacting system in this field closely resembles the structure of the original, interacting system in the absence of the external field. The absence of structural changes along this path suggests that it is reversible; a fact which is confirmed by expanded-ensemble simulations. Second, the external, ordering field is changed as to transform the non-interacting system from the apposed bilayer structure to two-bilayers connected by a stalk. The final external field is chosen such that the structure of the non-interacting system resembles the structure of the stalk in the interacting system without a field. On the third branch of the transformation path, we reversibly replace the external, ordering field by non-bonded interactions. Using expanded-ensemble techniques, the free energy change along this reversible path can be obtained with an accuracy of 10(-3)k(B)T per molecule in the n VT-ensemble. Calculating the chemical potential, we obtain the free energy of a stalk in the grandcanonical ensemble, and employing semi-grandcanonical techniques, we calculate the change of the excess free energy upon altering the molecular architecture. This computational strategy can be applied to compute the free energy of self-assembled phases in lipid and copolymer systems, and the excess free energy of defects or interfaces.

Use of linear free energy relationship to predict Gibbs free energies of formation of pyrochlore phases (CaMTi2O7)

International Nuclear Information System (INIS)

Xu, H.; Wang, Y.

1999-01-01

In this letter, a linear free energy relationship is used to predict the Gibbs free energies of formation of crystalline phases of pyrochlore and zirconolite families with stoichiometry of MCaTi 2 O 7 (or, CaMTi 2 O 7 ,) from the known thermodynamic properties of aqueous tetravalent cations (M 4+ ). The linear free energy relationship for tetravalent cations is expressed as ΔG f,M v X 0 =a M v X ΔG n,M 4+ 0 +b M v X +β M v X r M 4+ , where the coefficients a M v X , b M v X , and β M v X characterize a particular structural family of M v X, r M 4+ is the ionic radius of M 4+ cation, ΔG f,M v X 0 is the standard Gibbs free energy of formation of M v X, and ΔG n,M 4+ 0 is the standard non-solvation energy of cation M 4+ . The coefficients for the structural family of zirconolite with the stoichiometry of M 4+ CaTi 2 O 7 are estimated to be: a M v X =0.5717, b M v X =-4284.67 (kJ/mol), and β M v X =27.2 (kJ/mol nm). The coefficients for the structural family of pyrochlore with the stoichiometry of M 4+ CaTi 2 O 7 are estimated to be: a M v X =0.5717, b M v X =-4174.25 (kJ/mol), and β M v X =13.4 (kJ/mol nm). Using the linear free energy relationship, the Gibbs free energies of formation of various zirconolite and pyrochlore phases are calculated. (orig.)

Boundary conditions, energies and gravitational heat in general relativity (a classical analysis)

International Nuclear Information System (INIS)

Francaviglia, M; Raiteri, M

2004-01-01

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of general relativity. When the variation of the energy is written in a covariant form, it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so-called covariant ADM correction term. When specific boundary conditions are analysed one sees that the Komar energy is related to the gravitational heat while the ADM correction term plays the role of the Helmholtz free energy. These properties allow one to establish, inside a classical geometric framework, a formal analogy between gravitation and the laws governing the evolution of a thermodynamical system. The analogy applies to stationary spacetimes admitting multiple causal horizons as well as to AdS Taub-bolt solutions

From free energy to expected energy: Improving energy-based value function approximation in reinforcement learning.

Science.gov (United States)

Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji

2016-12-01

Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Hierarchical Protein Free Energy Landscapes from Variationally Enhanced Sampling.

Science.gov (United States)

Shaffer, Patrick; Valsson, Omar; Parrinello, Michele

2016-12-13

In recent work, we demonstrated that it is possible to obtain approximate representations of high-dimensional free energy surfaces with variationally enhanced sampling ( Shaffer, P.; Valsson, O.; Parrinello, M. Proc. Natl. Acad. Sci. , 2016 , 113 , 17 ). The high-dimensional spaces considered in that work were the set of backbone dihedral angles of a small peptide, Chignolin, and the high-dimensional free energy surface was approximated as the sum of many two-dimensional terms plus an additional term which represents an initial estimate. In this paper, we build on that work and demonstrate that we can calculate high-dimensional free energy surfaces of very high accuracy by incorporating additional terms. The additional terms apply to a set of collective variables which are more coarse than the base set of collective variables. In this way, it is possible to build hierarchical free energy surfaces, which are composed of terms that act on different length scales. We test the accuracy of these free energy landscapes for the proteins Chignolin and Trp-cage by constructing simple coarse-grained models and comparing results from the coarse-grained model to results from atomistic simulations. The approach described in this paper is ideally suited for problems in which the free energy surface has important features on different length scales or in which there is some natural hierarchy.

Regeneralized London free energy for high-Tc vortex lattices

Directory of Open Access Journals (Sweden)

M. A. Shahzamanian

2006-09-01

Full Text Available   The London free-energy is regeneralized by the Ginsburg-Landau free-energy density in the presence of both d and s order parameters. We have shown that the strength of the s-d coupling, makes an important rule to determine the form of the lattice vortex. Appearance of the ratios of the coherence length to penetration depth in the higher order corrections of the free-energy density will truncate these corrections for even large values of .

Calibration of Helmholtz Coils for the characterization of MEMS magnetic sensor using fluxgate magnetometer with DAS1 magnetic range data acquisition system

Science.gov (United States)

Ahmad, Farooq; Dennis, John Ojur; Md Khir, Mohd Haris; Hamid, Nor Hisham

2012-09-01

This paper presents the calibration of Helmholtz coils for the characterization of MEMS Magnetic sensor using Fluxgate magnetometer with DAS1 Magnetic Range Data Acquisition System. The Helmholtz coils arrangement is often used to generate a uniform magnetic field in space. In the past, standard magnets were used to calibrate the Helmholtz coils. A method is presented here for calibrating these coils using a Fluxgate magnetometer and known current source, which is easier and results in greater accuracy.

Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains

Science.gov (United States)

2016-06-01

solve the Helmholtz equation as ∂Ω goes through significant change in its shape and topology — applications for which implicit representation of the...boundary-value problems for the wave equation and maxwell’s equations. Russian Math . Surv., 1965. [16] S. Reutskiy. The method of fundamental

Levy-free part in energy tax is not wanted

International Nuclear Information System (INIS)

Gilijamse, W.

1995-01-01

The Dutch government proposed to implement an energy levy for small-scale consumers in 1996. The yields will be reimbursed by means of a reduction of the tax burden. By applying a levy-free tax allowance the tax reduction can be limited. However, it appears that this allowance does not work: it reduces the energy saving impact of the energy levy, because it does not stimulate investments in energy saving housing construction and energy saving heat supply. It also interferes with a just compensation of income. It is recommended to cancel the levy-free tax allowance and to realize compensation by raising the tax free allowance in the income tax. 2 figs., 1 tab., 6 refs

Kelvin-Helmholtz instability in a weakly ionized layer

OpenAIRE

Shadmehri, Mohsen; Downes, Turlough P.

2007-01-01

We study the linear theory of Kelvin-Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer's thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on th...

Free-energy coarse-grained potential for C60

International Nuclear Information System (INIS)

Edmunds, D. M.; Tangney, P.; Vvedensky, D. D.; Foulkes, W. M. C.

2015-01-01

We propose a new deformable free energy method for generating a free-energy coarse-graining potential for C 60 . Potentials generated from this approach exhibit a strong temperature dependence and produce excellent agreement with benchmark fully atomistic molecular dynamics simulations. Parameter sets for analytical fits to this potential are provided at four different temperatures

Semi-analytic solution to planar Helmholtz equation

Directory of Open Access Journals (Sweden)

Tukač M.

2013-06-01

Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.

Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Sigmund, Ole

2009-01-01

The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology...... information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential...... equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers....

Funnel metadynamics as accurate binding free-energy method

Science.gov (United States)

Limongelli, Vittorio; Bonomi, Massimiliano; Parrinello, Michele

2013-01-01

A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein–ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein–ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science. PMID:23553839

Surface free energy for systems with integrable boundary conditions

International Nuclear Information System (INIS)

Goehmann, Frank; Bortz, Michael; Frahm, Holger

2005-01-01

The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions

Comparative exploration of hydrogen sulfide and water transmembrane free energy surfaces via orthogonal space tempering free energy sampling.

Science.gov (United States)

Lv, Chao; Aitchison, Erick W; Wu, Dongsheng; Zheng, Lianqing; Cheng, Xiaolin; Yang, Wei

2016-03-05

Hydrogen sulfide (H2 S), a commonly known toxic gas compound, possesses unique chemical features that allow this small solute molecule to quickly diffuse through cell membranes. Taking advantage of the recent orthogonal space tempering (OST) method, we comparatively mapped the transmembrane free energy landscapes of H2 S and its structural analogue, water (H2 O), seeking to decipher the molecular determinants that govern their drastically different permeabilities. As revealed by our OST sampling results, in contrast to the highly polar water solute, hydrogen sulfide is evidently amphipathic, and thus inside membrane is favorably localized at the interfacial region, that is, the interface between the polar head-group and nonpolar acyl chain regions. Because the membrane binding affinity of H2 S is mainly governed by its small hydrophobic moiety and the barrier height inbetween the interfacial region and the membrane center is largely determined by its moderate polarity, the transmembrane free energy barriers to encounter by this toxic molecule are very small. Moreover when H2 S diffuses from the bulk solution to the membrane center, the above two effects nearly cancel each other, so as to lead to a negligible free energy difference. This study not only explains why H2 S can quickly pass through cell membranes but also provides a practical illustration on how to use the OST free energy sampling method to conveniently analyze complex molecular processes. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Estimating Atomic Contributions to Hydration and Binding Using Free Energy Perturbation.

Science.gov (United States)

Irwin, Benedict W J; Huggins, David J

2018-05-08

We present a general method called atom-wise free energy perturbation (AFEP), which extends a conventional molecular dynamics free energy perturbation (FEP) simulation to give the contribution to a free energy change from each atom. AFEP is derived from an expansion of the Zwanzig equation used in the exponential averaging method by defining that the system total energy can be partitioned into contributions from each atom. A partitioning method is assumed and used to group terms in the expansion to correspond to individual atoms. AFEP is applied to six example free energy changes to demonstrate the method. Firstly, the hydration free energies of methane, methanol, methylamine, methanethiol, and caffeine in water. AFEP highlights the atoms in the molecules that interact favorably or unfavorably with water. Finally AFEP is applied to the binding free energy of human immunodeficiency virus type 1 protease to lopinavir, and AFEP reveals the contribution of each atom to the binding free energy, indicating candidate areas of the molecule to improve to produce a more strongly binding inhibitor. FEP gives a single value for the free energy change and is already a very useful method. AFEP gives a free energy change for each "part" of the system being simulated, where part can mean individual atoms, chemical groups, amino acids, or larger partitions depending on what the user is trying to measure. This method should have various applications in molecular dynamics studies of physical, chemical, or biochemical phenomena, specifically in the field of computational drug discovery.

[Scientific theoretical founding of medicine as a natural science by Hermann von Helmholtz (1821-1894)].

Science.gov (United States)

Neumann, J N

1994-01-01

In this study an attempt will be made to discuss the epistemological problems in the theory and practice of modern technical medicine in the writings of Hermann von Helmholz. An inquiry into the relationship between von Helmholtz' thinking and the critical philosophy of Immanuel Kant is followed by the characteristics of von Helmholtz' philosophy of science which he himself called "empirical theory". The question of medicine as a science finally leads to the main problem of medical epistemology, viz., the relationship between theoretical knowledge and practice in medicine. In this context the anthropological dimension is brought into consideration.

Calculation of the surface free energy of fcc copper nanoparticles

International Nuclear Information System (INIS)

Jia Ming; Lai Yanqing; Tian Zhongliang; Liu Yexiang

2009-01-01

Using molecular dynamics simulations with the modified analytic embedded-atom method we calculate the Gibbs free energy and surface free energy for fcc Cu bulk, and further obtain the Gibbs free energy of nanoparticles. Based on the Gibbs free energy of nanoparticles, we have investigated the heat capacity of copper nanoparticles. Calculation results indicate that the Gibbs free energy and the heat capacity of nanoparticles can be divided into two parts: bulk quantity and surface quantity. The molar heat capacity of the bulk sample is lower compared with the molar heat capacity of nanoparticles, and this difference increases with the decrease in the particle size. It is also observed that the size effect on the thermodynamic properties of Cu nanoparticles is not really significant until the particle is less than about 20 nm. It is the surface atoms that decide the size effect on the thermodynamic properties of nanoparticles

Characterization of strain rate sensitivity and activation volume using the indentation relaxation test

International Nuclear Information System (INIS)

Xu Baoxing; Chen Xi; Yue Zhufeng

2010-01-01

We present the possibility of extracting the strain rate sensitivity, activation volume and Helmholtz free energy (for dislocation activation) using just one indentation stress relaxation test, and the approach is demonstrated with polycrystalline copper. The Helmholtz free energy measured from indentation relaxation agrees well with that from the conventional compression relaxation test, which validates the proposed approach. From the indentation relaxation test, the measured indentation strain rate sensitivity exponent is found to be slightly larger, and the indentation activation volume much smaller, than their counterparts from the compression test. The results indicate the involvement of multiple dislocation mechanisms in the indentation test.

Collisionless Kelvin-Helmholtz instability and vortex-induced reconnection in the external region of the Earth magnetotail

International Nuclear Information System (INIS)

Pegoraro, F; Faganello, M; Califano, F

2008-01-01

In a magnetized plasma streaming with a non uniform velocity, the Kelvin-Helmholtz instability plays a major role in mixing different plasma regions and in stretching the magnetic field lines leading to the formation of layers with a sheared magnetic field where magnetic field line reconnection can take place. A relevant example is provided by the formation of a mixing layer between the Earth's magnetosphere and the solar wind at low latitudes during northward periods. In the considered configuration, in the presence of a magnetic field nearly perpendicular to the plane defined by the velocity field and its inhomogeneity direction, velocity shear drives a Kelvin-Helmholtz instability which advects and distorts the magnetic field configuration. If the Alfven velocity associated to the in-plane magnetic field is sufficiently weak with respect to the variation of the fluid velocity in the plasma, the Kelvin-Helmholtz instability generates fully rolled-up vortices which advect the magnetic field lines into a complex configuration, causing the formation of current layers along the inversion curves of the in-plane magnetic field component. Pairing of the vortices generated by the Kelvin-Helmholtz instability is a well know phenomenon in two-dimensional hydrodynamics. Here we investigate the development of magnetic reconnection during the vortex pairing process and show that completely different magnetic structures are produced depending on how fast the reconnection process develops on the time scale set by the pairing process.

Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression.

Science.gov (United States)

Mones, Letif; Bernstein, Noam; Csányi, Gábor

2016-10-11

Practical free energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the free energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the free energy surface so that free energy barriers are eliminated. Most schemes use the final bias as their best estimate of the free energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final free energy reconstruction itself. We find that biasing with metadynamics, measuring a free energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.

Cosmological constant versus free energy for heterotic strings

International Nuclear Information System (INIS)

Alvarez, E.; Osorio, M.A.R.

1988-01-01

A detailed analysis is made of the modular-invariant formulation of the free energy of heterotic strings. Several instances are pointed out in which a duality formula can be obtained, and its physical implications are discussed. The interplay between the free energy of a given heterotic string and the cosmological constant of the toroidal compactification of another heterotic string is emphasized. (orig.)

Relationship between wave energy and free energy from pickup ions in the Comet Halley environment

Science.gov (United States)

Huddleston, D. E.; Johnstone, A. D.

1992-01-01

The free energy available from the implanted heavy ion population at Comet Halley is calculated by assuming that the initial unstable velocity space ring distribution of the ions evolves toward a bispherical shell. Ultimately this free energy adds to the turbulence in the solar wind. Upstream and downstream free energies are obtained separately for the conditions observed along the Giotto spacecraft trajectory. The results indicate that the waves are mostly upstream propagating in the solar wind frame. The total free energy density always exceeds the measured wave energy density because, as expected in the nonlinear process of ion scattering, the available energy is not all immediately released. An estimate of the amount which has been released can be obtained from the measured oxygen ion distributions and again it exceeds that observed. The theoretical analysis is extended to calculate the k spectrum of the cometary-ion-generated turbulence.

Heavy quark free energies for three quark systems at finite temperature

International Nuclear Information System (INIS)

Huebner, Kay; Karsch, Frithjof; Kaczmarek, Olaf; Vogt, Oliver

2008-01-01

We study the free energy of static three quark systems in singlet, octet, decuplet, and average color channels in the quenched approximation and in 2-flavor QCD at finite temperature. We show that in the high temperature phase singlet and decuplet free energies of three quark systems are well described by the sum of the free energies of three diquark systems plus self-energy contributions of the three quarks. In the confining low temperature phase we find evidence for a Y-shaped flux tube in SU(3) pure gauge theory, which is less evident in 2-flavor QCD due to the onset of string breaking. We also compare the short distance behavior of octet and decuplet free energies to the free energies of single static quarks in the corresponding color representations.

Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates

Directory of Open Access Journals (Sweden)

Ya-Juan Hao

2013-01-01

Full Text Available The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.

The elastic free energy of a tandem modular protein under force.

Science.gov (United States)

Valle-Orero, Jessica; Eckels, Edward C; Stirnemann, Guillaume; Popa, Ionel; Berkovich, Ronen; Fernandez, Julio M

2015-05-01

Recent studies have provided a theoretical framework for including entropic elasticity in the free energy landscape of proteins under mechanical force. Accounting for entropic elasticity using polymer physics models has helped explain the hopping behavior seen in single molecule experiments in the low force regime. Here, we expand on the construction of the free energy of a single protein domain under force proposed by Berkovich et al. to provide a free energy landscape for N tandem domains along a continuous polypeptide. Calculation of the free energy of individual domains followed by their concatenation provides a continuous free energy landscape whose curvature is dominated by the worm-like chain at forces below 20 pN. We have validated our free energy model using Brownian dynamics and reproduce key features of protein folding. This free energy model can predict the effects of changes in the elastic properties of a multidomain protein as a consequence of biological modifications such as phosphorylation or the formation of disulfide bonds. This work lays the foundations for the modeling of tissue elasticity, which is largely determined by the properties of tandem polyproteins. Copyright © 2015. Published by Elsevier Inc.

Virtual substitution scan via single-step free energy perturbation.

Science.gov (United States)

Chiang, Ying-Chih; Wang, Yi

2016-02-05

With the rapid expansion of our computing power, molecular dynamics (MD) simulations ranging from hundreds of nanoseconds to microseconds or even milliseconds have become increasingly common. The majority of these long trajectories are obtained from plain (vanilla) MD simulations, where no enhanced sampling or free energy calculation method is employed. To promote the 'recycling' of these trajectories, we developed the Virtual Substitution Scan (VSS) toolkit as a plugin of the open-source visualization and analysis software VMD. Based on the single-step free energy perturbation (sFEP) method, VSS enables the user to post-process a vanilla MD trajectory for a fast free energy scan of substituting aryl hydrogens by small functional groups. Dihedrals of the functional groups are sampled explicitly in VSS, which improves the performance of the calculation and is found particularly important for certain groups. As a proof-of-concept demonstration, we employ VSS to compute the solvation free energy change upon substituting the hydrogen of a benzene molecule by 12 small functional groups frequently considered in lead optimization. Additionally, VSS is used to compute the relative binding free energy of four selected ligands of the T4 lysozyme. Overall, the computational cost of VSS is only a fraction of the corresponding multi-step FEP (mFEP) calculation, while its results agree reasonably well with those of mFEP, indicating that VSS offers a promising tool for rapid free energy scan of small functional group substitutions. This article is protected by copyright. All rights reserved. © 2016 Wiley Periodicals, Inc.

Accelerated weight histogram method for exploring free energy landscapes

Energy Technology Data Exchange (ETDEWEB)

Lindahl, V.; Lidmar, J.; Hess, B. [Department of Theoretical Physics and Swedish e-Science Research Center, KTH Royal Institute of Technology, 10691 Stockholm (Sweden)

2014-07-28

Calculating free energies is an important and notoriously difficult task for molecular simulations. The rapid increase in computational power has made it possible to probe increasingly complex systems, yet extracting accurate free energies from these simulations remains a major challenge. Fully exploring the free energy landscape of, say, a biological macromolecule typically requires sampling large conformational changes and slow transitions. Often, the only feasible way to study such a system is to simulate it using an enhanced sampling method. The accelerated weight histogram (AWH) method is a new, efficient extended ensemble sampling technique which adaptively biases the simulation to promote exploration of the free energy landscape. The AWH method uses a probability weight histogram which allows for efficient free energy updates and results in an easy discretization procedure. A major advantage of the method is its general formulation, making it a powerful platform for developing further extensions and analyzing its relation to already existing methods. Here, we demonstrate its efficiency and general applicability by calculating the potential of mean force along a reaction coordinate for both a single dimension and multiple dimensions. We make use of a non-uniform, free energy dependent target distribution in reaction coordinate space so that computational efforts are not wasted on physically irrelevant regions. We present numerical results for molecular dynamics simulations of lithium acetate in solution and chignolin, a 10-residue long peptide that folds into a β-hairpin. We further present practical guidelines for setting up and running an AWH simulation.

Free energy surfaces in the superconducting mixed state

Science.gov (United States)

Finnemore, D. K.; Fang, M. M.; Bansal, N. P.; Farrell, D. E.

1989-01-01

The free energy surface for Tl2Ba2Ca2Cu3O1O has been measured as a function of temperature and magnetic field to determine the fundamental thermodynamic properties of the mixed state. The change in free energy, G(H)-G(O), is found to be linear in temperature over a wide range indicating that the specific heat is independent of field.

Free neutron-proton analyzing power at medium energies

International Nuclear Information System (INIS)

Newsom, C.R.

1980-01-01

In recent years, increasing efforts have been made to measure the nucleon-nucleon polarization parameters. To date, no free neutron-proton spin correlated parameters have been published in the energy range 500 to 800 MeV. Existing analyzing power data is of low precision and in most cases was obtained by quasi-free proton scattering. As a first step in determining the neutron-proton scattering matrix, the free neutron-proton analyzing power has been measured at the Los Alamos Physics Facility as a function of energy and angle. The experiment was performed by scattering a neutron beam from a polarized proton target. The neutron beam was generated by scattering 800 MeV protons from a Beryllium target and using the neutrons produced at 0 degrees. The incident energy ranged from 300 MeV to 800 MeV. The energy spread of the neutron beam made it possible to measure the analyzing power at different energies simultaneously. Angular distributions were taken from 60 to 170 degrees in the center of mass system (c.m.)

Melting temperature and structural transformation of some rare-earth metals

International Nuclear Information System (INIS)

Vu Van Hung; Hoang Van Tich; Dang Thanh Hai

2009-01-01

the pressure dependence of the melting temperatures of rare-earth metals is studied using the equation of states derived from the statistical moment (SMM). SMM studies were carried out order to calculate the Helmholtz free energy of hcp, bcc Dy and fcc, bcc Ce metals at a wide range of temperatures. the stable phase of Dy and Ce metals can be determined by examining the Helmholtz free energy at a given temperature, i, e. the phase that gives the lowest free energy will be stable. For example, we found that at T lower than 1750 K the hcp Dy metal is stable. At T higher than 1750 K the bcc Dy metal is also stable. Thus 1750 K marks the phase transition temperature of Dy metal. These findings are in agreement with previous experiments. (author)

Finite-size corrections to the free energies of crystalline solids

NARCIS (Netherlands)

Polson, J.M.; Trizac, E.; Pronk, S.; Frenkel, D.

2000-01-01

We analyze the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading (ln N/N) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (N → ∞), we estimate the free

Temperature dependence of grain boundary free energy and elastic constants

International Nuclear Information System (INIS)

Foiles, Stephen M.

2010-01-01

This work explores the suggestion that the temperature dependence of the grain boundary free energy can be estimated from the temperature dependence of the elastic constants. The temperature-dependent elastic constants and free energy of a symmetric Σ79 tilt boundary are computed for an embedded atom method model of Ni. The grain boundary free energy scales with the product of the shear modulus times the lattice constant for temperatures up to about 0.75 the melting temperature.

Effect of plasma density profile of tokamak on Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Tang Fulin

1984-01-01

The purpose of this paper is to study the effect of radial distribution of plasma density profile of tokamak on Kelvin-Helmholtz instability caused by toroidal rotation. The effect of radial distribution of plasma rotational velocity on stability is also examine for comparison. It is found that within the range of tokamak parameters the only radial distribution of plasma rotational velocity cannot induce Kelvin-Helmholtz instability. On the contrary, when there is a radial distribution of plasma density, i.e. P 01 =P 0 e -tx and V 0 1 = const, plasma becomes unstable, and instability will increase proportionally to the value of t. Meanwhile when the value of t remains constant, the instability growth rate will decrease if P 0 grows or the distance between plasma and wall of container decreases too. It shows that the Kelvin-Helmoltz instability is not only influenced by the steepness of density profile but also by the inertia of plasma in central region, which is helpful for depressing the instability. (author). 5 refs, 4 figs, 2 tabs

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes

Science.gov (United States)

2015-01-01

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect

A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator

Science.gov (United States)

Zhao, Xiang; Cai, Li; Yu, Dianlong; Lu, Zhimiao; Wen, Jihong

2017-06-01

Acoustic metasurfaces (AMSs) are able to manipulate wavefronts at an anomalous angle through a subwavelength layer. Their application provide a new way to control sound waves in addition to traditional materials. In this work, we introduced the AMS into the design of a Helmholtz resonator (HR) and studied the acoustic transmission through the modified HR in a pipe with one branch. The variation of sound insulation capacity with the phase gradient of the AMS was studied, and the results show that the AMS can remarkably lower the frequency band of the sound insulation without increasing the size. Our investigation provides a new degree of freedom for acoustic control with a Helmholtz resonator, which is of great significance in acoustic metasurface theory and sound insulation design.

Free energy evaluation in polymer translocation via Jarzynski equality

Energy Technology Data Exchange (ETDEWEB)

Mondaini, Felipe, E-mail: fmondaini@if.ufrj.br [Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petrópolis, 25.620-003, RJ (Brazil); Moriconi, L., E-mail: moriconi@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, 21945-970, Rio de Janeiro, RJ (Brazil)

2014-05-01

We perform, with the help of cloud computing resources, extensive Langevin simulations, which provide free energy estimates for unbiased three-dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic (FENE) potential. Analysing data for polymers with different lengths, the free energy profile is noted to have interesting finite-size scaling properties.

Free energy evaluation in polymer translocation via Jarzynski equality

International Nuclear Information System (INIS)

Mondaini, Felipe; Moriconi, L.

2014-01-01

We perform, with the help of cloud computing resources, extensive Langevin simulations, which provide free energy estimates for unbiased three-dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic (FENE) potential. Analysing data for polymers with different lengths, the free energy profile is noted to have interesting finite-size scaling properties.

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

Science.gov (United States)

Lapelosa, Mauro; Gallicchio, Emilio; Levy, Ronald M.

2011-01-01

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations. PMID:22368530

The Common Data Acquisition Platform in the Helmholtz Association

International Nuclear Information System (INIS)

Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

2017-01-01

Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ''Matter and Technology'': ''Detector Technology and Systems'' and ''Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

The Common Data Acquisition Platform in the Helmholtz Association

Science.gov (United States)

Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

2017-04-01

Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ``Matter and Technology'': ``Detector Technology and Systems'' and ``Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

Computational Approach to Explore the B/A Junction Free Energy in DNA.

Science.gov (United States)

Kulkarni, Mandar; Mukherjee, Arnab

2016-01-04

Protein-DNA interactions induce conformational changes in DNA such as B- to A-form transitions at a local level. Such transitions are associated with a junction free energy cost at the boundary of two different conformations in a DNA molecule. In this study, we performed umbrella sampling simulations to find the free energy values of the B-A transition at the dinucleotide and trinucleotide level of DNA. Using a combination of dinucleotide and trinucleotide free energy costs obtained from simulations, we calculated the B/A junction free energy. Our study shows that the B/A junction free energy is 0.52 kcal mol(-1) for the A-philic GG step and 1.59 kcal mol(-1) for the B-philic AA step. This observation is in agreement with experimentally derived values. After excluding junction effects, we obtained an absolute free energy cost for the B- to A-form conversion for all the dinucleotide steps. These absolute free energies may be used for predicting the propensity of structural transitions in DNA. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Calculation of the beam injector steering system using Helmholtz coils

International Nuclear Information System (INIS)

Passaro, A.; Sircilli Neto, F.; Migliano, A.C.C.

1991-03-01

In this work, a preliminary evaluation of the beam injector steering system of the IEAv electron linac is presented. From the existing injector configuration and with the assumptions of monoenergetic beam (100 keV) and uniform magnetic field, two pairs of Helmholtz coils were calculated for the steering system. Excitations of 105 A.turn and 37 A.turn were determined for the first and second coils, respectively. (author)

Free energy functionals for polarization fluctuations: Pekar factor revisited.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Newton, Marshall D; Matyushov, Dmitry V

2017-02-14

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekar's perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).

Free energy functionals for polarization fluctuations: Pekar factor revisited

International Nuclear Information System (INIS)

Dinpajooh, Mohammadhasan; Newton, Marshall D.; Matyushov, Dmitry V.

2017-01-01

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. This separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom, within dielectric continuum models. The main qualitative prediction of Pekar’s perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. We study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. But, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).

Gibbs free energy of formation of liquid lanthanide-bismuth alloys

International Nuclear Information System (INIS)

Sheng Jiawei; Yamana, Hajimu; Moriyama, Hirotake

2001-01-01

The linear free energy relationship developed by Sverjensky and Molling provides a way to predict Gibbs free energies of liquid Ln-Bi alloys formation from the known thermodynamic properties of aqueous trivalent lanthanides (Ln 3(5(6+ ). The Ln-Bi alloys are divided into two isostructural families named as the LnBi 2 (Ln=La, Ce, Pr, Nd and Pm) and LnBi (Ln=Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb). The calculated Gibbs free energy values are well agreed with experimental data

Assignment of Side-Chain Conformation Using Adiabatic Energy Mapping, Free Energy Perturbation, and Molecular Dynamic Simulations

DEFF Research Database (Denmark)

Frimurer, Thomas M.; Günther, Peter H.; Sørensen, Morten Dahl

1999-01-01

adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)......adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)...

Black and gray Helmholtz-Kerr soliton refraction

International Nuclear Information System (INIS)

Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

2011-01-01

Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposal of positive or negative lensing operations on soliton arrays at planar boundaries.

A Short Essay on the Uses of Free Energy

Science.gov (United States)

Koutandos, Spyridon

2013-01-01

In this article we examine cases of more classical and less classical nature compared to results found by quantum mechanics and attribute a form of Free Energy discontinuity for each case within a boundary layer. The concept of a boundary layer is broadened as to include areas of first or second variations of the Gibbs free energy. It is…

Linear free energy relationships between aqueous phase hydroxyl radical reaction rate constants and free energy of activation.

Science.gov (United States)

Minakata, Daisuke; Crittenden, John

2011-04-15

The hydroxyl radical (HO(•)) is a strong oxidant that reacts with electron-rich sites on organic compounds and initiates complex radical chain reactions in aqueous phase advanced oxidation processes (AOPs). Computer based kinetic modeling requires a reaction pathway generator and predictions of associated reaction rate constants. Previously, we reported a reaction pathway generator that can enumerate the most important elementary reactions for aliphatic compounds. For the reaction rate constant predictor, we develop linear free energy relationships (LFERs) between aqueous phase literature-reported HO(•) reaction rate constants and theoretically calculated free energies of activation for H-atom abstraction from a C-H bond and HO(•) addition to alkenes. The theoretical method uses ab initio quantum mechanical calculations, Gaussian 1-3, for gas phase reactions and a solvation method, COSMO-RS theory, to estimate the impact of water. Theoretically calculated free energies of activation are found to be within approximately ±3 kcal/mol of experimental values. Considering errors that arise from quantum mechanical calculations and experiments, this should be within the acceptable errors. The established LFERs are used to predict the HO(•) reaction rate constants within a factor of 5 from the experimental values. This approach may be applied to other reaction mechanisms to establish a library of rate constant predictions for kinetic modeling of AOPs.

A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator

Directory of Open Access Journals (Sweden)

Xiang Zhao

2017-06-01

Full Text Available Acoustic metasurfaces (AMSs are able to manipulate wavefronts at an anomalous angle through a subwavelength layer. Their application provide a new way to control sound waves in addition to traditional materials. In this work, we introduced the AMS into the design of a Helmholtz resonator (HR and studied the acoustic transmission through the modified HR in a pipe with one branch. The variation of sound insulation capacity with the phase gradient of the AMS was studied, and the results show that the AMS can remarkably lower the frequency band of the sound insulation without increasing the size. Our investigation provides a new degree of freedom for acoustic control with a Helmholtz resonator, which is of great significance in acoustic metasurface theory and sound insulation design.

Emotional valence and the free-energy principle.

Science.gov (United States)

Joffily, Mateus; Coricelli, Giorgio

2013-01-01

The free-energy principle has recently been proposed as a unified Bayesian account of perception, learning and action. Despite the inextricable link between emotion and cognition, emotion has not yet been formulated under this framework. A core concept that permeates many perspectives on emotion is valence, which broadly refers to the positive and negative character of emotion or some of its aspects. In the present paper, we propose a definition of emotional valence in terms of the negative rate of change of free-energy over time. If the second time-derivative of free-energy is taken into account, the dynamics of basic forms of emotion such as happiness, unhappiness, hope, fear, disappointment and relief can be explained. In this formulation, an important function of emotional valence turns out to regulate the learning rate of the causes of sensory inputs. When sensations increasingly violate the agent's expectations, valence is negative and increases the learning rate. Conversely, when sensations increasingly fulfil the agent's expectations, valence is positive and decreases the learning rate. This dynamic interaction between emotional valence and learning rate highlights the crucial role played by emotions in biological agents' adaptation to unexpected changes in their world.

Emotional valence and the free-energy principle.

Directory of Open Access Journals (Sweden)

Mateus Joffily

Full Text Available The free-energy principle has recently been proposed as a unified Bayesian account of perception, learning and action. Despite the inextricable link between emotion and cognition, emotion has not yet been formulated under this framework. A core concept that permeates many perspectives on emotion is valence, which broadly refers to the positive and negative character of emotion or some of its aspects. In the present paper, we propose a definition of emotional valence in terms of the negative rate of change of free-energy over time. If the second time-derivative of free-energy is taken into account, the dynamics of basic forms of emotion such as happiness, unhappiness, hope, fear, disappointment and relief can be explained. In this formulation, an important function of emotional valence turns out to regulate the learning rate of the causes of sensory inputs. When sensations increasingly violate the agent's expectations, valence is negative and increases the learning rate. Conversely, when sensations increasingly fulfil the agent's expectations, valence is positive and decreases the learning rate. This dynamic interaction between emotional valence and learning rate highlights the crucial role played by emotions in biological agents' adaptation to unexpected changes in their world.

Direct measurement of the free energy of aging hard sphere colloidal glasses.

Science.gov (United States)

Zargar, Rojman; Nienhuis, Bernard; Schall, Peter; Bonn, Daniel

2013-06-21

The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology.

Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics.

Science.gov (United States)

Tao, Peng; Sodt, Alexander J; Shao, Yihan; König, Gerhard; Brooks, Bernard R

2014-10-14

The calculations of potential of mean force along complex chemical reactions or rare events pathways are of great interest because of their importance for many areas in chemistry, molecular biology, and material science. The major difficulty for free energy calculations comes from the great computational cost for adequate sampling of the system in high-energy regions, especially close to the reaction transition state. Here, we present a method, called FEG-RBD, in which the free energy gradients were obtained from rigid body dynamics simulations. Then the free energy gradients were integrated along a reference reaction pathway to calculate free energy profiles. In a given system, the reaction coordinates defining a subset of atoms (e.g., a solute, or the quantum mechanics (QM) region of a quantum mechanics/molecular mechanics simulation) are selected to form a rigid body during the simulation. The first-order derivatives (gradients) of the free energy with respect to the reaction coordinates are obtained through the integration of constraint forces within the rigid body. Each structure along the reference reaction path is separately subjected to such a rigid body simulation. The individual free energy gradients are integrated along the reference pathway to obtain the free energy profile. Test cases provided demonstrate both the strengths and weaknesses of the FEG-RBD method. The most significant benefit of this method comes from the fast convergence rate of the free energy gradient using rigid-body constraints instead of restraints. A correction to the free energy due to approximate relaxation of the rigid-body constraint is estimated and discussed. A comparison with umbrella sampling using a simple test case revealed the improved sampling efficiency of FEG-RBD by a factor of 4 on average. The enhanced efficiency makes this method effective for calculating the free energy of complex chemical reactions when the reaction coordinate can be unambiguously defined by a

CFD simulation of Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Strubelj, L.; Tiselj, I.

2005-01-01

Kelvin-Helmholtz instability appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. The experiment of Thorpe [1] used as a benchmark in the present paper, is made in a rectangular glass tube filled with two immiscible fluids of various densities. We simulated the growth of instability with CFX-5.7 code and compared simulation with analytical solution. It was found that surface tension force, which stabilizes growth of waves, actually has a destabilizing effect in simulation, unless very small timestep and residual is used. In CFX code system of nonlinear Navier-Stokes equations is linearised and solved iterative in each timestep, until prescribed residual is achieved. On the other hand, simulation without surface tension force is more stable than analytical result predicts. (author)

Constructing a multidimensional free energy surface like a spider weaving a web.

Science.gov (United States)

Chen, Changjun

2017-10-15

Complete free energy surface in the collective variable space provides important information of the reaction mechanisms of the molecules. But, sufficient sampling in the collective variable space is not easy. The space expands quickly with the number of the collective variables. To solve the problem, many methods utilize artificial biasing potentials to flatten out the original free energy surface of the molecule in the simulation. Their performances are sensitive to the definitions of the biasing potentials. Fast-growing biasing potential accelerates the sampling speed but decreases the accuracy of the free energy result. Slow-growing biasing potential gives an optimized result but needs more simulation time. In this article, we propose an alternative method. It adds the biasing potential to a representative point of the molecule in the collective variable space to improve the conformational sampling. And the free energy surface is calculated from the free energy gradient in the constrained simulation, not given by the negative of the biasing potential as previous methods. So the presented method does not require the biasing potential to remove all the barriers and basins on the free energy surface exactly. Practical applications show that the method in this work is able to produce the accurate free energy surfaces for different molecules in a short time period. The free energy errors are small in the cases of various biasing potentials. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A Third Note: Helmholtz, Palestrina, and the Early History of Musicology.

Science.gov (United States)

Kursell, Julia

2015-06-01

This contribution focuses on Hermann von Helmholtz's work on Renaissance composer Giovanni Pierluigi da Palestrina. Helmholtz used his scientific concept of distortion to analyze this music and, reversely, to find corroboration for the concept in his musical analyses. In this, his work interlocked with nineteenth-century aesthetic and scholarly ideals. His eagerness to use the latest products of historical scholarship in early music reveals a specific view of music history. Historical documents of music provide the opportunity for the discovery of new experimental research topics and thereby also reveal insights into hearing under different conditions. The essay argues that this work occupies a peculiar position in the history of musicology; it falls under the header of "systematic musicology," which eventually emerged as a discipline of musicology at the end of the nineteenth century. That this discipline has a history at all is easily overlooked, as many of its contributors were scientists with an interest in music. A history of musicology therefore must consider at least the following two caveats: parts of it take place outside the institutionalized field of musicology, and any history of musicology must, in the last instance, be embedded in a history of music.

Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies.

Science.gov (United States)

Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton

2013-08-15

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

A Python tool to set up relative free energy calculations in GROMACS.

Science.gov (United States)

Klimovich, Pavel V; Mobley, David L

2015-11-01

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper (LOMAP; Liu et al. in J Comput Aided Mol Des 27(9):755-770, 2013), recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge (Mobley et al. in J Comput Aided Mol Des 28(4):135-150, 2014). Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations.

Reconstruction of extended sources for the Helmholtz equation

International Nuclear Information System (INIS)

Kress, Rainer; Rundell, William

2013-01-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler ‘equivalent point source’ problem, and which uses a Newton scheme to improve the corresponding initial approximation. (paper)

Reconstruction of extended sources for the Helmholtz equation

KAUST Repository

Kress, Rainer

2013-02-26

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler \\'equivalent point source\\' problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2013 IOP Publishing Ltd.

Minimum free-energy paths for the self-organization of polymer brushes.

Science.gov (United States)

Gleria, Ignacio; Mocskos, Esteban; Tagliazucchi, Mario

2017-03-22

A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy. The theoretical methodology introduced in this work allows us to predict the minimum free-energy path connecting these two minima as well as the morphology of the system along the path. It is shown that the transition between the homogeneous brush and the aggregates may involve a free-energy barrier or be barrierless depending on the relative stability of the two morphologies and the chain length and grafting density of the polymer. In the case where a free-energy barrier exists, one of the morphologies is a metastable structure and, therefore, the properties of the brush as the quality of the solvent is cycled are expected to display hysteresis. The theory is also applied to study the adhesion/deadhesion transition between two opposing surfaces modified by identical polymer brushes and it is shown that this process may also require surpassing a free-energy barrier.

HelmholtzZentrum Muenchen Deutsches Forschungszentrum fuer Gesundheit und Umwelt. Annual report 2011; HelmholtzZentrum Muenchen Deutsches Forschungszentrum fuer Gesundheit und Umwelt. Jahresbericht 2011

Energy Technology Data Exchange (ETDEWEB)

NONE

2012-11-01

The contribution under consideration is the annual report 2011 of the German Research Centre for Environmental Health (HelmholtzZentrum Munich, Federal Republic of Germany). The most important component of this annual report are the scientific highlights according to the following topics: (1) Systems researches for the health (M. Hrabe de Angelis); (2) Mechanisms of the interaction between genes and environment (M. Goetz); (3) Research of the metabolism (M. Tschoep); (4) Research of lungs and allergies (O. Eickelberg); (5) Technologies for the bio medicine (V. Ntziachristos); (6) Natural basis of existence (J. Durner).

Free energy option and its relevance to improve domestic energy demands in southern Nigeria

Directory of Open Access Journals (Sweden)

Moses Eterigho Emetere

2016-11-01

Full Text Available The aim of this paper is to seek an energy option that would benefit the growing energy demands. Domestic energy demands in southern Nigeria had increased greatly due to failing power programs and seasonal migrations. The fossil fuel option is gradually fading away due to environmental pollution and recent dynamic cost. The renewable energy option had been celebrated with little success in the coastal area of southern Nigeria. At the moment, the renewable energy option is very expensive with little guarantee on its efficiency with time. The data set used for this study was obtained from the Davis weather installation in Covenant University. The free energy option was considered. The cost and its environmental implication for domestic use were comparatively discussed alongside other energy options — using the Life cycle cost analysis. It was found out that free energy option is more affordable and efficient for domestic use.

Heavy-quark free energies, internal-energy and entropy contributions

International Nuclear Information System (INIS)

Kaczmarek, O.

2009-01-01

We present lattice QCD results on heavy-quark free energies, extract from its temperature dependence the entropy and internal-energy contributions, and discuss the onset of medium effects that lead to screening of static quark-antiquark sources in a thermal medium. The detailed analysis of the temperature and distance dependence of the different contributions indicate the complex non-perturbative nature of strongly interacting matter. We shall discuss the necessity to include those effects in studies on the behavior of heavy quarks, heavy-quark bound states and their dissociation in the quark-gluon plasma phase. (orig.)

Archive of Geosample Information from the GEOMAR Helmholtz Centre for Ocean Research Kiel Core Repository

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — The GEOMAR Helmholtz Centre for Ocean Research Kiel made a one-time contribution to the Index to Marine and Lacustrine Geological Samples (IMLGS) database of...

Mass and free energy of Lovelock black holes

International Nuclear Information System (INIS)

Kastor, David; Traschen, Jennie; Ray, Sourya

2011-01-01

An explicit formula for the ADM mass of an asymptotically AdS black hole in a generic Lovelock gravity theory is presented, identical in form to that in Einstein gravity, but multiplied by a function of the Lovelock coupling constants and the AdS curvature radius. A Gauss' law-type formula relates the mass, which is an integral at infinity, to an expression depending instead on the horizon radius. This and other thermodynamic quantities, such as the free energy, are then analyzed in the limits of small and large horizon radius, yielding results that are independent of the detailed choice of Lovelock couplings. In even dimensions, the temperature diverges in both limits, implying the existence of a minimum temperature for black holes. The negative free energy of sufficiently large black holes implies the existence of a Hawking-Page transition. In odd dimensions, the temperature still diverges for large black holes, which again have negative free energy. However, the temperature vanishes as the horizon radius tends to zero and sufficiently small black holes have positive specific heat.

An ab initio approach to free-energy reconstruction using logarithmic mean force dynamics

International Nuclear Information System (INIS)

Nakamura, Makoto; Obata, Masao; Morishita, Tetsuya; Oda, Tatsuki

2014-01-01

We present an ab initio approach for evaluating a free energy profile along a reaction coordinate by combining logarithmic mean force dynamics (LogMFD) and first-principles molecular dynamics. The mean force, which is the derivative of the free energy with respect to the reaction coordinate, is estimated using density functional theory (DFT) in the present approach, which is expected to provide an accurate free energy profile along the reaction coordinate. We apply this new method, first-principles LogMFD (FP-LogMFD), to a glycine dipeptide molecule and reconstruct one- and two-dimensional free energy profiles in the framework of DFT. The resultant free energy profile is compared with that obtained by the thermodynamic integration method and by the previous LogMFD calculation using an empirical force-field, showing that FP-LogMFD is a promising method to calculate free energy without empirical force-fields

Overview of direct air free cooling and thermal energy storage potential energy savings in data centres

International Nuclear Information System (INIS)

Oró, Eduard; Depoorter, Victor; Pflugradt, Noah; Salom, Jaume

2015-01-01

In the last years the total energy demand of data centres has experienced a dramatic increase which is expected to continue. This is why data centres industry and researchers are working on implementing energy efficiency measures and integrating renewable energy to overcome energy dependence and to reduce operational costs and CO 2 emissions. The cooling system of these unique infrastructures can account for 40% of the total energy consumption. To reduce the energy consumption, free cooling strategies are used more and more, but so far there has been little research about the potential of thermal energy storage (TES) solutions to match energy demand and energy availability. Hence, this work intends to provide an overview of the potential of the integration of direct air free cooling strategy and TES systems into data centres located at different European locations. For each location, the benefit of using direct air free cooling is evaluated energetically and economically for a data centre of 1250 kW. The use of direct air free cooling is shown to be feasible. This does not apply the TES systems by itself. But when using TES in combination with an off-peak electricity tariff the operational cooling cost can be drastically reduced. - Highlights: • The total annual hours for direct air free cooling in data centres are calculated. • The potential of TES integration in data centres is evaluated. • The implementation of TES to store the ambient air cold is not recommended. • TES is feasible if combined with redundant chillers and off-peak electricity price. • The cooling electricity cost is being reduced up to 51%, depending on the location

Free Energy Self-Averaging in Protein-Sized Random Heteropolymers

International Nuclear Information System (INIS)

Chuang, Jeffrey; Grosberg, Alexander Yu.; Kardar, Mehran

2001-01-01

Current theories of heteropolymers are inherently macroscopic, but are applied to mesoscopic proteins. To compute the free energy over sequences, one assumes self-averaging -- a property established only in the macroscopic limit. By enumerating the states and energies of compact 18, 27, and 36mers on a lattice with an ensemble of random sequences, we test the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is valid at the scale of real proteins. The results validate sequence design methods which exponentially speed up computational design and simplify experimental realizations

Density-space potential phase difference in a Kelvin--Helmholtz instability

International Nuclear Information System (INIS)

Glowienka, J.C.; Jennings, W.C.; Hickok, R.L.

1974-01-01

The low-frequency instability found in a hollow cathode discharge in helium was studied using an ion beam probe as a primary diagnostic tool. Three aspects of the instability are discussed: the location and amplitude of the oscillation and its correlation with the shape of the space potential; the phase angle between density and space potential oscillations; and the comparison of the data with three known instability models: Kelvin--Helmholtz, Rayleigh--Taylor, and drift waves--for mode identification. (U.S.)

Calculation of free-energy differences from computer simulations of initial and final states

International Nuclear Information System (INIS)

Hummer, G.; Szabo, A.

1996-01-01

A class of simple expressions of increasing accuracy for the free-energy difference between two states is derived based on numerical thermodynamic integration. The implementation of these formulas requires simulations of the initial and final (and possibly a few intermediate) states. They involve higher free-energy derivatives at these states which are related to the moments of the probability distribution of the perturbation. Given a specified number of such derivatives, these integration formulas are optimal in the sense that they are exact to the highest possible order of free-energy perturbation theory. The utility of this approach is illustrated for the hydration free energy of water. This problem provides a quite stringent test because the free energy is a highly nonlinear function of the charge so that even fourth order perturbation theory gives a very poor estimate of the free-energy change. Our results should prove most useful for complex, computationally demanding problems where free-energy differences arise primarily from changes in the electrostatic interactions (e.g., electron transfer, charging of ions, protonation of amino acids in proteins). copyright 1996 American Institute of Physics

Evaluation of the accuracy of the free-energy-minimization method

International Nuclear Information System (INIS)

Najafabadi, R.; Srolovitz, D.J.

1995-01-01

We have made a detailed comparison between three competing methods for determining the free energies of solids and their defects: the thermodynamic integration of Monte Carlo (TIMC) data, the quasiharmonic (QH) model, and the free-energy-minimization (FEM) method. The accuracy of these methods decreases from the TIMC to QH to FEM method, while the computational efficiency improves in that order. All three methods yield perfect crystal lattice parameters and free energies at finite temperatures which are in good agreement for three different Cu interatomic potentials [embedded atom method (EAM), Morse and Lennard-Jones]. The FEM error (relative to the TIMC) in the (001) surface free energy and in the vacancy formation energy were found to be much larger for the EAM potential than for the other two potentials. Part of the errors in the FEM determination of the free energies are associated with anharmonicities in the interatomic potentials, with the remainder attributed to decoupling of the atomic vibrations. The anharmonicity of the EAM potential was found to be unphysically large compared with experimental vacancy formation entropy determinations. Based upon these results, we show that the FEM method provides a reasonable compromise between accuracy and computational demands. However, the accuracy of this approach is sensitive to the choice of interatomic potential and the nature of the defect to which it is being applied. The accuracy of the FEM is best in high-symmetry environments (perfect crystal, high-symmetry defects, etc.) and when used to describe materials where the anharmonicity is not too large

A fast tomographic method for searching the minimum free energy path

International Nuclear Information System (INIS)

Chen, Changjun; Huang, Yanzhao; Xiao, Yi; Jiang, Xuewei

2014-01-01

Minimum Free Energy Path (MFEP) provides a lot of important information about the chemical reactions, like the free energy barrier, the location of the transition state, and the relative stability between reactant and product. With MFEP, one can study the mechanisms of the reaction in an efficient way. Due to a large number of degrees of freedom, searching the MFEP is a very time-consuming process. Here, we present a fast tomographic method to perform the search. Our approach first calculates the free energy surfaces in a sequence of hyperplanes perpendicular to a transition path. Based on an objective function and the free energy gradient, the transition path is optimized in the collective variable space iteratively. Applications of the present method to model systems show that our method is practical. It can be an alternative approach for finding the state-to-state MFEP

Metadyn View: Fast web-based viewer of free energy surfaces calculated by metadynamics

Science.gov (United States)

Hošek, Petr; Spiwok, Vojtěch

2016-01-01

Metadynamics is a highly successful enhanced sampling technique for simulation of molecular processes and prediction of their free energy surfaces. An in-depth analysis of data obtained by this method is as important as the simulation itself. Although there are several tools to compute free energy surfaces from metadynamics data, they usually lack user friendliness and a build-in visualization part. Here we introduce Metadyn View as a fast and user friendly viewer of bias potential/free energy surfaces calculated by metadynamics in Plumed package. It is based on modern web technologies including HTML5, JavaScript and Cascade Style Sheets (CSS). It can be used by visiting the web site and uploading a HILLS file. It calculates the bias potential/free energy surface on the client-side, so it can run online or offline without necessity to install additional web engines. Moreover, it includes tools for measurement of free energies and free energy differences and data/image export.

Using the fast fourier transform in binding free energy calculations.

Science.gov (United States)

Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L

2018-04-30

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Alternative Energy: A Guide to Free Information for Educators.

Science.gov (United States)

White, Janet A.

This guide was compiled to help teachers and students locate free educational materials (both lessons and nontechnical background references) on renewable energy resources and energy conservation. The 214 entries are arranged by these topic areas: (1) energy efficiency and renewables; (2) biomass; (3) hydropower; (4) solar thermal energy; (5)…

The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity

Science.gov (United States)

Orazzo, Annagrazia; Hoepffner, Jérôme

2012-11-01

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.

Linearly decoupled energy-stable numerical methods for multi-component two-phase compressible flow

KAUST Repository

Kou, Jisheng

2017-12-06

In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure a consistency relationship with the mass balance equations. Moreover, we propose a component-wise SAV approach for a multi-component fluid, which requires solving a sequence of linear, separate mass balance equations. We prove that the methods have the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.

Chemical Denaturants Smoothen Ruggedness on the Free Energy Landscape of Protein Folding.

Science.gov (United States)

Malhotra, Pooja; Jethva, Prashant N; Udgaonkar, Jayant B

2017-08-08

To characterize experimentally the ruggedness of the free energy landscape of protein folding is challenging, because the distributed small free energy barriers are usually dominated by one, or a few, large activation free energy barriers. This study delineates changes in the roughness of the free energy landscape by making use of the observation that a decrease in ruggedness is accompanied invariably by an increase in folding cooperativity. Hydrogen exchange (HX) coupled to mass spectrometry was used to detect transient sampling of local energy minima and the global unfolded state on the free energy landscape of the small protein single-chain monellin. Under native conditions, local noncooperative openings result in interconversions between Boltzmann-distributed intermediate states, populated on an extremely rugged "uphill" energy landscape. The cooperativity of these interconversions was increased by selectively destabilizing the native state via mutations, and further by the addition of a chemical denaturant. The perturbation of stability alone resulted in seven backbone amide sites exchanging cooperatively. The size of the cooperatively exchanging and/or unfolding unit did not depend on the extent of protein destabilization. Only upon the addition of a denaturant to a destabilized mutant variant did seven additional backbone amide sites exchange cooperatively. Segmentwise analysis of the HX kinetics of the mutant variants further confirmed that the observed increase in cooperativity was due to the smoothing of the ruggedness of the free energy landscape of folding of the protein by the chemical denaturant.

Designed azurins show lower reorganization free energies for intraprotein electron transfer

DEFF Research Database (Denmark)

Farver, Ole; Marshall, Nicholas M; Wherland, Scot

2013-01-01

Low reorganization free energies are necessary for fast electron transfer (ET) reactions. Hence, rational design of redox proteins with lower reorganization free energies has been a long-standing challenge, promising to yield a deeper understanding of the underlying principles of ET reactivity...

Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2018-01-01

Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.

Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations

Directory of Open Access Journals (Sweden)

Federico Fogolari

2018-02-01

Full Text Available Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.

Free energy change of off-eutectic binary alloys on solidification

Science.gov (United States)

Ohsaka, K.; Trinh, E. H.; Lin, J.-C.; Perepezko, J. H.

1991-01-01

A formula for the free energy difference between the undercooled liquid phase and the stable solid phase is derived for off-eutectic binary alloys in which the equilibrium solid/liquid transition takes place over a certain temperature range. The free energy change is then evaluated numerically for a Bi-25 at. pct Cd alloy modeled as a sub-subregular solution.

The Magnetic Free Energy in Active Regions

Science.gov (United States)

Metcalf, Thomas R.; Mickey, Donald L.; LaBonte, Barry J.

2001-01-01

The magnetic field permeating the solar atmosphere governs much of the structure, morphology, brightness, and dynamics observed on the Sun. The magnetic field, especially in active regions, is thought to provide the power for energetic events in the solar corona, such as solar flares and Coronal Mass Ejections (CME) and is believed to energize the hot coronal plasma seen in extreme ultraviolet or X-rays. The question remains what specific aspect of the magnetic flux governs the observed variability. To directly understand the role of the magnetic field in energizing the solar corona, it is necessary to measure the free magnetic energy available in active regions. The grant now expiring has demonstrated a new and valuable technique for observing the magnetic free energy in active regions as a function of time.

Variational Approach to Enhanced Sampling and Free Energy Calculations

Science.gov (United States)

Valsson, Omar; Parrinello, Michele

2014-08-01

The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.

Knot soliton in DNA and geometric structure of its free-energy density.

Science.gov (United States)

Wang, Ying; Shi, Xuguang

2018-03-01

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Free energy barriers to evaporation of water in hydrophobic confinement.

Science.gov (United States)

Sharma, Sumit; Debenedetti, Pablo G

2012-11-08

We use umbrella sampling Monte Carlo and forward and reverse forward flux sampling (FFS) simulation techniques to compute the free energy barriers to evaporation of water confined between two hydrophobic surfaces separated by nanoscopic gaps, as a function of the gap width, at 1 bar and 298 K. The evaporation mechanism for small (1 × 1 nm(2)) surfaces is found to be fundamentally different from that for large (3 × 3 nm(2)) surfaces. In the latter case, the evaporation proceeds via the formation of a gap-spanning tubular cavity. The 1 × 1 nm(2) surfaces, in contrast, are too small to accommodate a stable vapor cavity. Accordingly, the associated free energy barriers correspond to the formation of a critical-sized cavity for sufficiently large confining surfaces, and to complete emptying of the gap region for small confining surfaces. The free energy barriers to evaporation were found to be of O(20kT) for 14 Å gaps, and to increase by approximately ~5kT with every 1 Å increase in the gap width. The entropy contribution to the free energy of evaporation was found to be independent of the gap width.

Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level

Science.gov (United States)

Olsson, Martin A.; Söderhjelm, Pär

2016-01-01

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. PMID:27117350

Free energy change of a dislocation due to a Cottrell atmosphere

Science.gov (United States)

Sills, R. B.; Cai, W.

2018-06-01

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel-hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation's line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank-Read source using discrete dislocation dynamics.

THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING

Energy Technology Data Exchange (ETDEWEB)

DeRosa, M. L.; Schrijver, C. J. [Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover St. B/252, Palo Alto, CA 94304 (United States); Wheatland, M. S.; Gilchrist, S. A. [Sydney Institute for Astronomy, School of Physics, The University of Sydney, Sydney, NSW 2006 (Australia); Leka, K. D.; Barnes, G. [NorthWest Research Associates, 3380 Mitchell Ln., Boulder, CO 80301 (United States); Amari, T.; Canou, A. [CNRS, Centre de Physique Théorique de l’École Polytechnique, F-91128, Palaiseau Cedex (France); Thalmann, J. K. [Institute of Physics/IGAM, University of Graz, Universitätsplatz 5, A-8010 Graz (Austria); Valori, G. [Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT (United Kingdom); Wiegelmann, T. [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077, Göttingen (Germany); Malanushenko, A. [Department of Physics, Montana State University, Bozeman, MT 59717 (United States); Sun, X. [W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States); Régnier, S. [Department of Mathematics and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle-Upon-Tyne, NE1 8ST (United Kingdom)

2015-10-01

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.

A Short Essay on the Uses of Free Energy

OpenAIRE

Koutandos, Spyridon

2013-01-01

In this article we examine cases of more classical and less classical nature compared to results found by quantum mechanics and attribute a form of Free Energy discontinuity for each case within a boundary layer. The concept of a boundary layer is broadened as to include areas of first or second variations of the Gibbs free energy. It is constructive to think not only of implosions like boundary layers but also of explosion like ones. Situations such as boiling and the passage of electric cur...

Breaking the polar-nonpolar division in solvation free energy prediction.

Science.gov (United States)

Wang, Bao; Wang, Chengzhang; Wu, Kedi; Wei, Guo-Wei

2018-02-05

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature-function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson-Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave-one-out test gives an optimal root-mean-square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94

The Use of Helmholtz Resonance for Measuring the Volume of Liquids and Solids

Directory of Open Access Journals (Sweden)

Clive E. Davies

2010-11-01

Full Text Available An experimental investigation was undertaken to ascertain the potential of using Helmholtz resonance for volume determination and the factors that may influence accuracy. The uses for a rapid non-interference volume measurement system range from agricultural produce and mineral sampling through to liquid fill measurements. By weighing the sample the density can also measured indirectly.

Characterizing permanent magnet blocks with Helmholtz coils

Science.gov (United States)

Carnegie, D. W.; Timpf, J.

1992-08-01

Most of the insertion devices to be installed at the Advanced Photon Source will utilize permanent magnets in their magnetic structures. The quality of the spectral output is sensitive to the errors in the field of the device which are related to variations in the magnetic properties of the individual blocks. The Advanced Photon Source will have a measurement facility to map the field in the completed insertion devices and equipment to test and modify the magnetic strength of the individual magnet blocks. One component of the facility, the Helmholtz coil permanent magnet block measurement system, has been assembled and tested. This system measures the total magnetic moment vector of a block with a precision better than 0.01% and a directional resolution of about 0.05°. The design and performance of the system will be presented.

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

Computation of Hemagglutinin Free Energy Difference by the Confinement Method

Science.gov (United States)

2017-01-01

Hemagglutinin (HA) mediates membrane fusion, a crucial step during influenza virus cell entry. How many HAs are needed for this process is still subject to debate. To aid in this discussion, the confinement free energy method was used to calculate the conformational free energy difference between the extended intermediate and postfusion state of HA. Special care was taken to comply with the general guidelines for free energy calculations, thereby obtaining convergence and demonstrating reliability of the results. The energy that one HA trimer contributes to fusion was found to be 34.2 ± 3.4kBT, similar to the known contributions from other fusion proteins. Although computationally expensive, the technique used is a promising tool for the further energetic characterization of fusion protein mechanisms. Knowledge of the energetic contributions per protein, and of conserved residues that are crucial for fusion, aids in the development of fusion inhibitors for antiviral drugs. PMID:29151344

Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures.

Science.gov (United States)

Bishop, Kevin P; Roy, Pierre-Nicholas

2018-03-14

Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.

Low energy quasi free scattering on nuclear surface

Energy Technology Data Exchange (ETDEWEB)

Shiyuan, S.

1983-05-01

The result of RGM calculation of low energy /sup 3/He(n, n)/sup 3/ He total elastic cross section does not agree well with experimental data for E/sub n/<1 MeV. This discrepancy can be improved by assuming lwo energy quasi-free scattering of particles beyond the nuclear surface.

Development of a high-sensitivity and portable cell using Helmholtz resonance for noninvasive blood glucose-level measurement based on photoacoustic spectroscopy.

Science.gov (United States)

Tachibana, K; Okada, K; Kobayashi, R; Ishihara, Y

2016-08-01

We describe the possibility of high-sensitivity noninvasive blood glucose measurement based on photoacoustic spectroscopy (PAS). The demand for noninvasive blood glucose-level measurement has increased due to the explosive increase in diabetic patients. We have developed a noninvasive blood glucose-level measurement based on PAS. The conventional method uses a straight-type resonant cell. However, the cell volume is large, which results in a low detection sensitivity and difficult portability. In this paper, a small-sized Helmholtz-type resonant cell is proposed to improve detection sensitivity and portability by reducing the cell dead volume. First, the acoustic property of the small-sized Helmholtz-type resonant cell was evaluated by performing an experiment using a silicone rubber. As a result, the detection sensitivity of the small-sized Helmholtz-type resonant cell was approximately two times larger than that of the conventional straight-type resonant cell. In addition, the inside volume was approximately 30 times smaller. Second, the detection limits of glucose concentration were estimated by performing an experiment using glucose solutions. The experimental results showed that a glucose concentration of approximately 1% was detected by the small-sized Helmholtz-type resonant cell. Although these results on the sensitivity of blood glucose-level measurement are currently insufficient, they suggest that miniaturization of a resonance cell is effective in the application of noninvasive blood glucose-level measurement.

Free Energy and Internal Combustion Engine Cycles

OpenAIRE

Harris, William D.

2012-01-01

The performance of one type (Carnot) of Internal Combustion Engine (ICE) cycle is analyzed within the framework of thermodynamic free energies. ICE performance is different from that of an External Combustion Engine (ECE) which is dictated by Carnot's rule.

Free energy surfaces from nonequilibrium processes without work measurement

Science.gov (United States)

Adib, Artur B.

2006-04-01

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such "clamp-and-release" processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations and analyzed in the context of tethered single-molecule experiments.

Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics

Directory of Open Access Journals (Sweden)

Clinton D. Stoner

2000-08-01

Full Text Available Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to convert spontaneously into thermal energy and for thermal energy to distribute spontaneously and uniformly within the accessible space. The fact that free energy is a Second-Law, expendable energy that makes it possible for thermodynamic work to be done at finite rates is emphasized. Entropy, as originally defined, is pointed out to be the capacity factor for thermal energy that is hidden with respect to temperature; it serves to evaluate the practical quality of thermal energy and to account for changes in the amounts of latent thermal energies in systems maintained at constant temperature. With entropy thus operationally defined, it is possible to see that TDS° of the Gibbs standard free energy relation DG°= DH°-TDS° serves to account for differences or changes in nonthermal energies that do not contribute to DG° and that, since DH° serves to account for differences or changes in total energy, complete enthalpy-entropy (DH° - TDS° compensation must invariably occur in isothermal processes for which TDS° is finite. A major objective was to clarify the means by which free energy is transferred and conserved in sequences of biological reactions coupled by freely diffusible intermediates. In achieving this objective it was found necessary to distinguish between a 'characteristic free energy' possessed by all First-Law energies in amounts equivalent to the amounts of the energies themselves and a 'free energy of concentration' that is intrinsically mechanical and relatively elusive in that it can appear to be free of First-Law energy. The findings in this regard serve to clarify the fact that the transfer of chemical potential energy from one

Effect of cold plasma on the Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Melander, B.G.

1978-01-01

The thesis studies the effect of a two-component plasma (hot and cold) on the shear driven Kelvin-Helmholtz instability. An ion distribution with a shear flow parallel to the ambient magnetic field and a density gradient parallel to the shear direction is used. Both the electrostatic and electromagnetic versions of the instability are studied in the limit of hydromagnetic frequencies. The dispersion relation is obtained in the electrostatic case by solving the Vlasov equation for the perturbed ion and electron densities and then using the quasineutrality condition. In the electromagnetic case the coupled Vlasov and Maxwell's equations are solved to obtain the dispersion relation

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

Science.gov (United States)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Coarse-grained versus atomistic simulations : realistic interaction free energies for real proteins

NARCIS (Netherlands)

May, Ali; Pool, René; van Dijk, Erik; Bijlard, Jochem; Abeln, Sanne; Heringa, Jaap; Feenstra, K Anton

2014-01-01

MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full

Free energy minimization and information gain: The devil is in the details

NARCIS (Netherlands)

Kwisthout, J.H.P.; Rooij, I.J.E.I. van

2015-01-01

Contrary to Friston's previous work, this paper describes free energy minimization using categorical probability distributions over discrete states. This alternative mathematical framework exposes a fundamental, yet unnoticed challenge for the free energy principle. When considering discrete state

Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins

NARCIS (Netherlands)

May, A.; Pool, R.; van Dijk, E.; Bijlard, J.; Abeln, S.; Heringa, J.; Feenstra, K.A.

2014-01-01

MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full

A Free Energy Model for Hysteresis Ferroelectric Materials

National Research Council Canada - National Science Library

Smith, Ralph C; Ounaies, Zoubeida; Seelecke, Stefan; Smith, Joshua

2003-01-01

This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques...

Arbitrage-free valuation of energy derivatives

International Nuclear Information System (INIS)

Amin, K.; Ng, V.; Pirrong, C.

1999-01-01

This chapter focuses on techniques available for valuing energy-contingent claims and develops an arbitrage-free framework to value energy derivatives. The relationship between the spot, forward and futures prices is explained. Option valuation with deterministic convenience yields is discussed using an extension of the Black (1976) framework, and details of the risk-neutral valuation of European options, and valuation of American and European-style options are given. Option valuations with stochastic convenience yields, the evolution of the term structure of convenience yield, and a tree approach to valuing American and other options are discussed. Applications and limitations of the models for pricing energy derivative products are considered. The stochastic differential equation for the futures prices when the convenience yields are stochastic is presented in an appendix

Advancing Drug Discovery through Enhanced Free Energy Calculations.

Science.gov (United States)

Abel, Robert; Wang, Lingle; Harder, Edward D; Berne, B J; Friesner, Richard A

2017-07-18

A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates

Is the Free Vacuum Energy Infinite?

International Nuclear Information System (INIS)

Shirazi, S. M.; Razmi, H.

2015-01-01

Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks

Free-market approach to energy proposed in new study

International Nuclear Information System (INIS)

Anon.

1992-01-01

This paper reports that a free-market approach to energy use, intensified R and D and an emphasis on conservation and clean fuels such as natural gas can result in significant reductions in emissions of greenhouse gases, without any major new federal policy initiatives, according to a new study, An Alternative Energy Future, sponsored by Alliance to Save Energy, AGA and Solar Energy Industries Assn

Free energy minimization to predict RNA secondary structures and computational RNA design.

Science.gov (United States)

Churkin, Alexander; Weinbrand, Lina; Barash, Danny

2015-01-01

Determining the RNA secondary structure from sequence data by computational predictions is a long-standing problem. Its solution has been approached in two distinctive ways. If a multiple sequence alignment of a collection of homologous sequences is available, the comparative method uses phylogeny to determine conserved base pairs that are more likely to form as a result of billions of years of evolution than by chance. In the case of single sequences, recursive algorithms that compute free energy structures by using empirically derived energy parameters have been developed. This latter approach of RNA folding prediction by energy minimization is widely used to predict RNA secondary structure from sequence. For a significant number of RNA molecules, the secondary structure of the RNA molecule is indicative of its function and its computational prediction by minimizing its free energy is important for its functional analysis. A general method for free energy minimization to predict RNA secondary structures is dynamic programming, although other optimization methods have been developed as well along with empirically derived energy parameters. In this chapter, we introduce and illustrate by examples the approach of free energy minimization to predict RNA secondary structures.

Preliminary analysis of resonance effect by Helmholtz-Schrödinger method

International Nuclear Information System (INIS)

Er-Yan, Yan; Fan-Bao, Meng; Hong-Ge, Ma; Chao-Yang, Chen

2010-01-01

The Helmholtz-Schrödinger method is employed to study the electric field standing wave caused by coupling through a simple slot. There is a good agreement between the numerical results and the resonant conditions presented by the Helmholtz—Schrödinger method. Thus, it can be used in similar cases where the amplitude of the electric field is the important quantity or eigenfunctions of the Schrödinger equation are needed for complicated quantum structures with hard wall boundary conditions. (general)

Analysis of the Bogoliubov free energy functional

DEFF Research Database (Denmark)

Reuvers, Robin

In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used to describe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubov free energy functional', we demonstrate existence of minimizers as well as the presence...

Advanced Graphene-Based Binder-Free Electrodes for High-Performance Energy Storage.

Science.gov (United States)

Ji, Junyi; Li, Yang; Peng, Wenchao; Zhang, Guoliang; Zhang, Fengbao; Fan, Xiaobin

2015-09-23

The increasing demand for energy has triggered tremendous research effort for the development of high-performance and durable energy-storage devices. Advanced graphene-based electrodes with high electrical conductivity and ion accessibility can exhibit superior electrochemical performance in energy-storage devices. Among them, binder-free configurations can enhance the electron conductivity of the electrode, which leads to a higher capacity by avoiding the addition of non-conductive and inactive binders. Graphene, a 2D material, can be fabricated into a porous and flexible structure with an interconnected conductive network. Such a conductive structure is favorable for both electron and ion transport to the entire electrode surface. In this review, the main processes used to prepare binder-free graphene-based hybrids with high porosity and well-designed electron conductive networks are summarized. Then, the applications of free-standing binder-free graphene-based electrodes in energy-storage devices are discussed. Future research aspects with regard to overcoming the technological bottlenecks are also proposed. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Free energy of formation of lanthanum nickelate

International Nuclear Information System (INIS)

Sreedharan, O.M.; Chandrasekharaiah, M.S.; Karkhanavala, M.D.

1976-01-01

The ΔG 0 /sub f/ of La 2 NiO 4 (s) was determined from the measured emf in the range 1123 to 1373 0 K of the solid oxide electrolyte galvanic cell. The emf data were fitted to a linear equation by the method of least squares. From these data, the standard free-energy change, ΔG 0 , for the reaction NiO(s) + La 2 O 3 (s) = La 2 NiO 4 (s) was calculated. Combining these emf data with the best available free energy of formation data for NiO(s) and La 2 O 3 (s), the following expression for ΔG 0 /sub f/(La 2 NiO 4 (s)) was derived as ΔG 0 /sub f/(La 2 NiO 4 (s)/kJ mole -1 = -2057.0 + 322.8 x 10 -3 T +- 17.30

Binding free energy analysis of protein-protein docking model structures by evERdock.

Science.gov (United States)

Takemura, Kazuhiro; Matubayasi, Nobuyuki; Kitao, Akio

2018-03-14

To aid the evaluation of protein-protein complex model structures generated by protein docking prediction (decoys), we previously developed a method to calculate the binding free energies for complexes. The method combines a short (2 ns) all-atom molecular dynamics simulation with explicit solvent and solution theory in the energy representation (ER). We showed that this method successfully selected structures similar to the native complex structure (near-native decoys) as the lowest binding free energy structures. In our current work, we applied this method (evERdock) to 100 or 300 model structures of four protein-protein complexes. The crystal structures and the near-native decoys showed the lowest binding free energy of all the examined structures, indicating that evERdock can successfully evaluate decoys. Several decoys that show low interface root-mean-square distance but relatively high binding free energy were also identified. Analysis of the fraction of native contacts, hydrogen bonds, and salt bridges at the protein-protein interface indicated that these decoys were insufficiently optimized at the interface. After optimizing the interactions around the interface by including interfacial water molecules, the binding free energies of these decoys were improved. We also investigated the effect of solute entropy on binding free energy and found that consideration of the entropy term does not necessarily improve the evaluations of decoys using the normal model analysis for entropy calculation.

Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation.

Science.gov (United States)

Ding, Xinqiang; Vilseck, Jonah Z; Hayes, Ryan L; Brooks, Charles L

2017-06-13

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

The inverted free energy landscape of an intrinsically disordered peptide by simulations and experiments.

Science.gov (United States)

Granata, Daniele; Baftizadeh, Fahimeh; Habchi, Johnny; Galvagnion, Celine; De Simone, Alfonso; Camilloni, Carlo; Laio, Alessandro; Vendruscolo, Michele

2015-10-26

The free energy landscape theory has been very successful in rationalizing the folding behaviour of globular proteins, as this representation provides intuitive information on the number of states involved in the folding process, their populations and pathways of interconversion. We extend here this formalism to the case of the Aβ40 peptide, a 40-residue intrinsically disordered protein fragment associated with Alzheimer's disease. By using an advanced sampling technique that enables free energy calculations to reach convergence also in the case of highly disordered states of proteins, we provide a precise structural characterization of the free energy landscape of this peptide. We find that such landscape has inverted features with respect to those typical of folded proteins. While the global free energy minimum consists of highly disordered structures, higher free energy regions correspond to a large variety of transiently structured conformations with secondary structure elements arranged in several different manners, and are not separated from each other by sizeable free energy barriers. From this peculiar structure of the free energy landscape we predict that this peptide should become more structured and not only more compact, with increasing temperatures, and we show that this is the case through a series of biophysical measurements.

Use of linear free energy relationship to predict Gibbs free energies of formation of zirconolite phases (MZrTi2O7 and MHfTi2O7)

International Nuclear Information System (INIS)

Xu, H.

1999-01-01

In this letter, the Sverjensky-Molling equation derived from a linear free energy relationship is used to calculate the Gibbs free energies of formation of zirconolite crystalline phases (MZrTi 2 O 7 and MHfTi 2 O 7 ) from the known thermodynamic properties of the corresponding aqueous divalent cations (M 2+ ). Sverjensky-Molling equation is expressed as ΔG 0 f,M v X =a M v X ΔG 0 n,M 2+ +b M v X +β M v X r M 2+ , where the coefficients a M v X , b M v X , and β M v X characterize a particular structural family of M v X, r M 2+ is the ionic radius of M 2+ cation, ΔG f,M v X 0 is the standard Gibbs free energy of formation of M v X, and ΔG 0 n,M 2+ is the standard non-solvation energy of cation M 2+ . This relationship can be used to predict the Gibbs free energies of formation of various fictive phases (such as BaZrTi 2 O 7 , SrZrTi 2 O 7 , PbZrTi 2 O 7 , etc.) that may form solid solution with CaZrTi 2 O 7 in actual Synroc-based nuclear waste forms. Based on obtained linear free energy relationships, it is predicted that large cations (e.g., Ba and Ra) prefer to be in perovskite structure, and small cations (e.g., Ca, Zn, and Cd) prefer to be in zirconolite structure. (orig.)

Free-Free Transitions in the Presence of Laser Fields at Very Low Incident Electron Energy

Science.gov (United States)

Bhatia, A. K.; Sinha, Chandana

2010-01-01

We study the free-free transition in electron-hydrogenic systems in ground state in presence of an external laser field at very loud incident energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen to be monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser in a nonperturbative manner by choosing a Volkov wave function for it. The scattering weave function for the electron is solved numerically by taking into account the effect of the electron exchange, short-range as well as of the long-range interactions to get the S and P wave phase shifts while for the higher angular momentum phase shifts the exchange approximation has only been considered. We calculate the laser assisted differential cross sections (LADCS) for the aforesaid free-free transition process for single photon absorption/emission. The laser intensity is chosen to be much less than the atomic field intensity. A strong suppression is noted in the LADCS as compared to the field free (FF) cross sections. Unlike the FF ones, the LADCS exhibit some oscillations having a distinct maximum at a low value of the scattering angle depending on the laser parameters as well as on the incident energies.

Free-energy landscape of a hyperstable RNA tetraloop.

Science.gov (United States)

Miner, Jacob C; Chen, Alan A; García, Angel E

2016-06-14

We report the characterization of the energy landscape and the folding/unfolding thermodynamics of a hyperstable RNA tetraloop obtained through high-performance molecular dynamics simulations at microsecond timescales. Sampling of the configurational landscape is conducted using temperature replica exchange molecular dynamics over three isochores at high, ambient, and negative pressures to determine the thermodynamic stability and the free-energy landscape of the tetraloop. The simulations reveal reversible folding/unfolding transitions of the tetraloop into the canonical A-RNA conformation and the presence of two alternative configurations, including a left-handed Z-RNA conformation and a compact purine Triplet. Increasing hydrostatic pressure shows a stabilizing effect on the A-RNA conformation and a destabilization of the left-handed Z-RNA. Our results provide a comprehensive description of the folded free-energy landscape of a hyperstable RNA tetraloop and highlight the significant advances of all-atom molecular dynamics in describing the unbiased folding of a simple RNA secondary structure motif.

The calculation of surface free energy based on embedded atom method for solid nickel

International Nuclear Information System (INIS)

Luo Wenhua; Hu Wangyu; Su Kalin; Liu Fusheng

2013-01-01

Highlights: ► A new solution for accurate prediction of surface free energy based on embedded atom method was proposed. ► The temperature dependent anisotropic surface energy of solid nickel was obtained. ► In isotropic environment, the approach does not change most predictions of bulk material properties. - Abstract: Accurate prediction of surface free energy of crystalline metals is a challenging task. The theory calculations based on embedded atom method potentials often underestimate surface free energy of metals. With an analytical charge density correction to the argument of the embedding energy of embedded atom method, an approach to improve the prediction for surface free energy is presented. This approach is applied to calculate the temperature dependent anisotropic surface energy of bulk nickel and surface energies of nickel nanoparticles, and the obtained results are in good agreement with available experimental data.

Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems

Science.gov (United States)

Swinburne, Thomas D.; Marinica, Mihai-Cosmin

2018-03-01

The calculation of free energy differences for thermally activated mechanisms in the solid state are routinely hindered by the inability to define a set of collective variable functions that accurately describe the mechanism under study. Even when possible, the requirement of descriptors for each mechanism under study prevents implementation of free energy calculations in the growing range of automated material simulation schemes. We provide a solution, deriving a path-based, exact expression for free energy differences in the solid state which does not require a converged reaction pathway, collective variable functions, Gram matrix evaluations, or probability flux-based estimators. The generality and efficiency of our method is demonstrated on a complex transformation of C 15 interstitial defects in iron and double kink nucleation on a screw dislocation in tungsten, the latter system consisting of more than 120 000 atoms. Both cases exhibit significant anharmonicity under experimentally relevant temperatures.

Towards accurate free energy calculations in ligand protein-binding studies.

Science.gov (United States)

Steinbrecher, Thomas; Labahn, Andreas

2010-01-01

Cells contain a multitude of different chemical reaction paths running simultaneously and quite independently next to each other. This amazing feat is enabled by molecular recognition, the ability of biomolecules to form stable and specific complexes with each other and with their substrates. A better understanding of this process, i.e. of the kinetics, structures and thermodynamic properties of biomolecule binding, would be invaluable in the study of biological systems. In addition, as the mode of action of many pharmaceuticals is based upon their inhibition or activation of biomolecule targets, predictive models of small molecule receptor binding are very helpful tools in rational drug design. Since the goal here is normally to design a new compound with a high inhibition strength, one of the most important thermodynamic properties is the binding free energy DeltaG(0). The prediction of binding constants has always been one of the major goals in the field of computational chemistry, because the ability to reliably assess a hypothetical compound's binding properties without having to synthesize it first would save a tremendous amount of work. The different approaches to this question range from fast and simple empirical descriptor methods to elaborate simulation protocols aimed at putting the computation of free energies onto a solid foundation of statistical thermodynamics. While the later methods are still not suited for the screenings of thousands of compounds that are routinely performed in computational drug design studies, they are increasingly put to use for the detailed study of protein ligand interactions. This review will focus on molecular mechanics force field based free energy calculations and their application to the study of protein ligand interactions. After a brief overview of other popular methods for the calculation of free energies, we will describe recent advances in methodology and a variety of exemplary studies of molecular dynamics

Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields

International Nuclear Information System (INIS)

El Gawhary, Omar

2017-01-01

The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics. (paper)

Free Energy Reconstruction from Logarithmic Mean-Force Dynamics Using Multiple Nonequilibrium Trajectories.

Science.gov (United States)

Morishita, Tetsuya; Yonezawa, Yasushige; Ito, Atsushi M

2017-07-11

Efficient and reliable estimation of the mean force (MF), the derivatives of the free energy with respect to a set of collective variables (CVs), has been a challenging problem because free energy differences are often computed by integrating the MF. Among various methods for computing free energy differences, logarithmic mean-force dynamics (LogMFD) [ Morishita et al., Phys. Rev. E 2012 , 85 , 066702 ] invokes the conservation law in classical mechanics to integrate the MF, which allows us to estimate the free energy profile along the CVs on-the-fly. Here, we present a method called parallel dynamics, which improves the estimation of the MF by employing multiple replicas of the system and is straightforwardly incorporated in LogMFD or a related method. In the parallel dynamics, the MF is evaluated by a nonequilibrium path-ensemble using the multiple replicas based on the Crooks-Jarzynski nonequilibrium work relation. Thanks to the Crooks relation, realizing full-equilibrium states is no longer mandatory for estimating the MF. Additionally, sampling in the hidden subspace orthogonal to the CV space is highly improved with appropriate weights for each metastable state (if any), which is hardly achievable by typical free energy computational methods. We illustrate how to implement parallel dynamics by combining it with LogMFD, which we call logarithmic parallel dynamics (LogPD). Biosystems of alanine dipeptide and adenylate kinase in explicit water are employed as benchmark systems to which LogPD is applied to demonstrate the effect of multiple replicas on the accuracy and efficiency in estimating the free energy profiles using parallel dynamics.

Interaction Free Energies of Eight Sodium Salts and a Phosphatidylcholine Membrane

DEFF Research Database (Denmark)

Wang, C. H.; Ge, Y.; Mortensen, J.

2011-01-01

Many recent reports have discussed specific effects of anions on the properties of lipid membranes and possible roles of such effects within biochemistry. One key parameter in both theoretical and experimental treatments of membrane-salt interactions is the net affinity, that is, the free energy...... salts by dialysis equilibrium measurements. This method provides model free thermodynamic data and allows investigations in the dilute concentration range where solution nonideality and perturbation of membrane structure is limited. The transfer free energy of DMPC from water to salt solutions, Delta mu...

Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations.

Science.gov (United States)

König, Gerhard; Brooks, Bernard R

2015-05-01

Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence. The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered. We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled. The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision. The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue

Reply to Comment on 'On the importance of the free energy for elasticity under pressure'

International Nuclear Information System (INIS)

Marcus, P M; Qiu, S L

2004-01-01

All criticisms by Steinle-Neumann and Cohen of the correctness of our calculations of equilibrium structure and elastic constants under pressure from the Gibbs free energy are answered and the criticisms are rejected. The difference between the free energy and the internal energy as functions of structure is described to clarify the use of the free energy. The meaning of elastic constants in a system under pressure is discussed in order to derive the basic quadratic expansion of the free energy in the strains. The coefficients in the expansion are the elastic constants under pressure and are in agreement with well-known work. We give reasons why calculations based on the Gibbs free energy are simpler and more accurate than the usual calculations based on minima of the energy at constant volume. (reply)

A simple free energy for the isotropic-nematic phase transition of rods

NARCIS (Netherlands)

Tuinier, R.

2016-01-01

A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant

Variationally Optimized Free-Energy Flooding for Rate Calculation

Science.gov (United States)

McCarty, James; Valsson, Omar; Tiwary, Pratyush; Parrinello, Michele

2015-08-01

We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways.

BFEE: A User-Friendly Graphical Interface Facilitating Absolute Binding Free-Energy Calculations.

Science.gov (United States)

Fu, Haohao; Gumbart, James C; Chen, Haochuan; Shao, Xueguang; Cai, Wensheng; Chipot, Christophe

2018-03-26

Quantifying protein-ligand binding has attracted the attention of both theorists and experimentalists for decades. Many methods for estimating binding free energies in silico have been reported in recent years. Proper use of the proposed strategies requires, however, adequate knowledge of the protein-ligand complex, the mathematical background for deriving the underlying theory, and time for setting up the simulations, bookkeeping, and postprocessing. Here, to minimize human intervention, we propose a toolkit aimed at facilitating the accurate estimation of standard binding free energies using a geometrical route, coined the binding free-energy estimator (BFEE), and introduced it as a plug-in of the popular visualization program VMD. Benefitting from recent developments in new collective variables, BFEE can be used to generate the simulation input files, based solely on the structure of the complex. Once the simulations are completed, BFEE can also be utilized to perform the post-treatment of the free-energy calculations, allowing the absolute binding free energy to be estimated directly from the one-dimensional potentials of mean force in simulation outputs. The minimal amount of human intervention required during the whole process combined with the ergonomic graphical interface makes BFEE a very effective and practical tool for the end-user.

Thermodynamic free energy methods to investigate shape transitions in bilayer membranes.

Science.gov (United States)

Ramakrishnan, N; Tourdot, Richard W; Radhakrishnan, Ravi

2016-06-01

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.

Temperature effects on the nuclear symmetry energy and symmetry free energy with an isospin and momentum dependent interaction

International Nuclear Information System (INIS)

Xu, Jun; Ma, Hong-Ru; Chen, Lie-Wen; Li, Bao-An

2007-01-01

Within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, we investigate the temperature dependence of the symmetry energy E sym (ρ,T) and symmetry free energy F sym (ρ,T) for hot, isospin asymmetric nuclear matter. It is shown that the symmetry energy E sym (ρ,T) generally decreases with increasing temperature while the symmetry free energy F sym (ρ,T) exhibits opposite temperature dependence. The decrement of the symmetry energy with temperature is essentially due to the decrement of the potential energy part of the symmetry energy with temperature. The difference between the symmetry energy and symmetry free energy is found to be quite small around the saturation density of nuclear matter. While at very low densities, they differ significantly from each other. In comparison with the experimental data of temperature dependent symmetry energy extracted from the isotopic scaling analysis of intermediate mass fragments (IMF's) in heavy-ion collisions, the resulting density and temperature dependent symmetry energy E sym (ρ,T) is then used to estimate the average freeze-out density of the IMF's

Interfacial free energy and stiffness of aluminum during rapid solidification

International Nuclear Information System (INIS)

Brown, Nicholas T.; Martinez, Enrique; Qu, Jianmin

2017-01-01

Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11 to 34 K/nm. The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parameters remain independent of the non-equilibrium conditions applied in this analysis. As a result, the relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.

Energy of Force-Free Magnetic Fields in Relation to Coronal Mass Ejections

International Nuclear Information System (INIS)

Choe, G.S.; Cheng, C.Z.

2002-01-01

In typical observations of coronal mass ejections (CMEs), a magnetic structure of a helmet-shaped closed configuration bulges out and eventually opens up. However, a spontaneous transition between these field configurations has been regarded to be energetically impossible in force-free fields according to the Aly-Sturrock theorem. The theorem states that the maximum energy state of force-free fields with a given boundary normal field distribution is the open field. The theorem implicitly assumes the existence of the maximum energy state, which may not be taken for granted. In this study, we have constructed force-free fields containing tangential discontinuities in multiple flux systems. These force-free fields can be generated from a potential field by footpoint motions that do not conserve the boundary normal field distribution. Some of these force-free fields are found to have more magnetic energy than the corresponding open fields. The constructed force-free configurations are compared with observational features of CME-bearing active regions. Possible mechanisms of CMEs are also discussed

Efficient free energy calculations for compounds with multiple stable conformations separated by high energy barriers

NARCIS (Netherlands)

Hritz, J.; Oostenbrink, C.

2009-01-01

Compounds with high intramolecular energy barriers represent challenging targets for free energy calculations because of the difficulty to obtain sufficient conformational sampling. Existing approaches are therefore computationally very demanding, thus preventing practical applications for such

A Variational Approach to Enhanced Sampling and Free Energy Calculations

Science.gov (United States)

Parrinello, Michele

2015-03-01

The presence of kinetic bottlenecks severely hampers the ability of widely used sampling methods like molecular dynamics or Monte Carlo to explore complex free energy landscapes. One of the most popular methods for addressing this problem is umbrella sampling which is based on the addition of an external bias which helps overcoming the kinetic barriers. The bias potential is usually taken to be a function of a restricted number of collective variables. However constructing the bias is not simple, especially when the number of collective variables increases. Here we introduce a functional of the bias which, when minimized, allows us to recover the free energy. We demonstrate the usefulness and the flexibility of this approach on a number of examples which include the determination of a six dimensional free energy surface. Besides the practical advantages, the existence of such a variational principle allows us to look at the enhanced sampling problem from a rather convenient vantage point.

Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

DEFF Research Database (Denmark)

Miansari, Mo; Miansari, Me; Barari, Amin

2009-01-01

In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

CAN THE STABILITY OF PROTEIN MUTANTS BE PREDICTED BY FREE-ENERGY CALCULATIONS

NARCIS (Netherlands)

YUNYU, S; MARK, AE; WANG, CX; HUANG, FH; BERENDSEN, HJC; VANGUNSTEREN, WF

The use of free energy simulation techniques in the study of protein stability is critically evaluated. Results from two simulations of the thermostability mutation Asn218 to Ser218 in Subtilisin are presented. It is shown that components of the free energy change can be highly sensitive to the

FESetup: Automating Setup for Alchemical Free Energy Simulations.

Science.gov (United States)

Loeffler, Hannes H; Michel, Julien; Woods, Christopher

2015-12-28

FESetup is a new pipeline tool which can be used flexibly within larger workflows. The tool aims to support fast and easy setup of alchemical free energy simulations for molecular simulation packages such as AMBER, GROMACS, Sire, or NAMD. Post-processing methods like MM-PBSA and LIE can be set up as well. Ligands are automatically parametrized with AM1-BCC, and atom mappings for a single topology description are computed with a maximum common substructure search (MCSS) algorithm. An abstract molecular dynamics (MD) engine can be used for equilibration prior to free energy setup or standalone. Currently, all modern AMBER force fields are supported. Ease of use, robustness of the code, and automation where it is feasible are the main development goals. The project follows an open development model, and we welcome contributions.

Nonlocal Free Energy of a Spatially Inhomogeneous Superconductor

International Nuclear Information System (INIS)

Grigorishin, K.V.; Lev, B.I.

2012-01-01

The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude. The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter. Moreover, the nonlocality of the magnetic response is the consequence of order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low- and high-temperature limit at the condition of slowness of spatial variations of the order parameter. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

Effects of temperature and pressure on thermodynamic properties of Cd0.50 Zn0.50 Se alloy

Science.gov (United States)

Aarifeen, Najm ul; Afaq, A.

2017-09-01

Thermodynamic properties of \\text{C}{{\\text{d}}0.50} \\text{Z}{{\\text{n}}0.50} Se alloy are studied using quasi harmonic model for pressure range 0-10 GPa and temperature range 0-1000 K. The structural optimization is obtained by self consistent field calculations and full-potential linear muffin-tin orbital method with GGA+U as an exchange correlation functional where U=2.3427 eV is the hubbard potential. The effects of temperature and pressure on the bulk modulus, Helmholtz free energy, internal energy, entropy, Debye temperature, Grüneisen parameter, thermal expansion coefficient and heat capacities of the material are observed and discussed. The bulk modulus, Helmholtz free energy and Debye temperature are found to decrease with increasing temperature while there is an increasing behavior when the pressure rises. Whereas internal energy has increasing trend with rises in temperature and it almost remains insensitive to pressure. The entropy of the system increases (decreases) with a rise of pressure (temperature).

Modeling free energy availability from Hadean hydrothermal systems to the first metabolism.

Science.gov (United States)

Simoncini, E; Russell, M J; Kleidon, A

2011-12-01

Off-axis Hydrothermal Systems (HSs) are seen as the possible setting for the emergence of life. As the availability of free energy is a general requirement to drive any form of metabolism, we ask here under which conditions free energy generation by geologic processes is greatest and relate these to the conditions found at off-axis HSs. To do so, we present a conceptual model in which we explicitly capture the energetics of fluid motion and its interaction with exothermic reactions to maintain a state of chemical disequilibrium. Central to the interaction is the temperature at which the exothermic reactions take place. This temperature not only sets the equilibrium constant of the chemical reactions and thereby the distance of the actual state to chemical equilibrium, but these reactions also shape the temperature gradient that drives convection and thereby the advection of reactants to the reaction sites and the removal of the products that relate to geochemical free energy generation. What this conceptual model shows is that the positive feedback between convection and the chemical kinetics that is found at HSs favors a greater rate of free energy generation than in the absence of convection. Because of the lower temperatures and because the temperature of reactions is determined more strongly by these dynamics rather than an external heat flux, the conditions found at off-axis HSs should result in the greatest rates of geochemical free energy generation. Hence, we hypothesize from these thermodynamic considerations that off-axis HSs seem most conducive for the emergence of protometabolic pathways as these provide the greatest, abiotic generation rates of chemical free energy.

The Kelvin-Helmholtz instability on the magnetopause

International Nuclear Information System (INIS)

Kivelson, M.G.; California Univ., Los Angeles; Pu, Z.-Y.

1984-01-01

Conditions for the development of Kelvin-Helmholtz (K-H) waves on the magnetopause have been known for more than 15 years; more recently, spacecraft observations have stimulated further examination of the properties of K-H waves. For a magnetopause with no boundary layer, two different modes of surface waves have been identified and their properties have been investigated for various assumed orientations of magnetic field and flow velocity vectors. The power radiated into the magnetosphere from the velocity shear at the boundary has been estimated. Other calculations have focused on the consequences of finite thickness boundary layers, both uniform and non-uniform. The boundary layer is found to modify the wave modes present at the magnetopause and to yield a criterion for the wavelength of the fastest growing surface waves. The paper concludes by questioning the extent to which the inferences from boundary layer models are model dependent and identifies areas where further work is needed or anticipated. (author)

Free energy simulations with the AMOEBA polarizable force field and metadynamics on GPU platform.

Science.gov (United States)

Peng, Xiangda; Zhang, Yuebin; Chu, Huiying; Li, Guohui

2016-03-05

The free energy calculation library PLUMED has been incorporated into the OpenMM simulation toolkit, with the purpose to perform enhanced sampling MD simulations using the AMOEBA polarizable force field on GPU platform. Two examples, (I) the free energy profile of water pair separation (II) alanine dipeptide dihedral angle free energy surface in explicit solvent, are provided here to demonstrate the accuracy and efficiency of our implementation. The converged free energy profiles could be obtained within an affordable MD simulation time when the AMOEBA polarizable force field is employed. Moreover, the free energy surfaces estimated using the AMOEBA polarizable force field are in agreement with those calculated from experimental data and ab initio methods. Hence, the implementation in this work is reliable and would be utilized to study more complicated biological phenomena in both an accurate and efficient way. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach.

Science.gov (United States)

Burusco, Kepa K; Bruce, Neil J; Alibay, Irfan; Bryce, Richard A

2015-10-26

Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Inequalities for magnetic-flux free energies and confinement in lattice gauge theories

International Nuclear Information System (INIS)

Yoneya, T.

1982-01-01

Rigorous inequalities among magnetic-flux free energies of tori with varying diameters are derived in lattice gauge theories. From the inequalities, it follows that if the magnetic-flux free energy vanishes in the limit of large uniform dilatation of a torus, the free energy must always decrease exponentially with the area of the cross section of the torus. The latter property is known to be sufficient for permanent confinement of static quarks. As a consequence of this property, a lower bound V(R) >= const x R for the static quark-antiquark potential is obtained in three-dimensional U(n) lattice gauge theory for sufficiently large R. (orig.)

Energy efficient structure-free data aggregation and delivery in WSN

Directory of Open Access Journals (Sweden)

Prabhudutta Mohanty

2016-11-01

Full Text Available In Wireless Sensor Networks (WSNs, the energy consumption due to the sensed data transmission is more than processing data locally within the sensor node. The data aggregation is one of the techniques to conserve energy by eliminating the redundant data transmission in dense WSNs. In this paper, we propose an energy efficient structure-free data aggregation and delivery (ESDAD protocol, which aggregates the redundant data in the intermediate nodes. In the proposed protocol, waiting time for packets at each intermediate node is calculated very sensibly so that data can be aggregated efficiently in the routing path. The sensed data packets are transmitted judicially to the aggregation point for data aggregation. The ESDAD protocol computes a cost function for structure-free, next-hop node selection and performs near source data aggregation. The buffer of each node is partitioned to maintain different types of flows for fair and efficient data delivery. The transmission rates of the sources and intermediate nodes are adjusted during congestion. The performance of the proposed protocol is evaluated through extensive simulations. The simulation results reveal that it outperforms the existing structure-free protocols in terms of energy efficiency, reliability and on-time delivery ratio.

Direct evaluation of free energy for large system through structure integration approach.

Science.gov (United States)

Takeuchi, Kazuhito; Tanaka, Ryohei; Yuge, Koretaka

2015-09-30

We propose a new approach, 'structure integration', enabling direct evaluation of configurational free energy for large systems. The present approach is based on the statistical information of lattice. Through first-principles-based simulation, we find that the present method evaluates configurational free energy accurately in disorder states above critical temperature.

Tinker-OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs.

Science.gov (United States)

Harger, Matthew; Li, Daniel; Wang, Zhi; Dalby, Kevin; Lagardère, Louis; Piquemal, Jean-Philip; Ponder, Jay; Ren, Pengyu

2017-09-05

The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU-based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker-OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200-fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host-guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Re-examining the tetraphenyl-arsonium/tetraphenyl-borate (TATB) hypothesis for single-ion solvation free energies

Science.gov (United States)

Pollard, Travis P.; Beck, Thomas L.

2018-06-01

Attempts to establish an absolute single-ion hydration free energy scale have followed multiple strategies. Two central themes consist of (1) employing bulk pair thermodynamic data and an underlying interfacial-potential-free model to partition the hydration free energy into individual contributions [Marcus, Latimer, and tetraphenyl-arsonium/tetraphenyl-borate (TATB) methods] or (2) utilizing bulk thermodynamic and cluster data to estimate the free energy to insert a proton into water, including in principle an interfacial potential contribution [the cluster pair approximation (CPA)]. While the results for the hydration free energy of the proton agree remarkably well between the three approaches in the first category, the value differs from the CPA result by roughly +10 kcal/mol, implying a value for the effective electrochemical surface potential of water of -0.4 V. This paper provides a computational re-analysis of the TATB method for single-ion free energies using quasichemical theory. A previous study indicated a significant discrepancy between the free energies of hydration for the TA cation and the TB anion. We show that the main contribution to this large computed difference is an electrostatic artifact arising from modeling interactions in periodic boundaries. No attempt is made here to develop more accurate models for the local ion/solvent interactions that may lead to further small free energy differences between the TA and TB ions, but the results clarify the primary importance of interfacial potential effects for analysis of the various free energy scales. Results are also presented, related to the TATB assumption in the organic solvents dimethyl sulfoxide and 1,2-dichloroethane.

Computational scheme for pH-dependent binding free energy calculation with explicit solvent.

Science.gov (United States)

Lee, Juyong; Miller, Benjamin T; Brooks, Bernard R

2016-01-01

We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations. © 2015 The Protein Society.

Interfacial free energy governs single polystyrene chain collapse in water and aqueous solutions.

Science.gov (United States)

Li, Isaac T S; Walker, Gilbert C

2010-05-12

The hydrophobic interaction is significantly responsible for driving protein folding and self-assembly. To understand it, the thermodynamics, the role of water structure, the dewetting process surrounding hydrophobes, and related aspects have undergone extensive investigations. Here, we examine the hypothesis that polymer-solvent interfacial free energy is adequate to describe the energetics of the collapse of a hydrophobic homopolymer chain at fixed temperature, which serves as a much simplified model for studying the hydrophobic collapse of a protein. This implies that changes in polymer-solvent interfacial free energy should be directly proportional to the force to extend a collapsed polymer into a bad solvent. To test this hypothesis, we undertook single-molecule force spectroscopy on a collapsed, single, polystyrene chain in water-ethanol and water-salt mixtures where we measured the monomer solvation free energy from an ensemble average conformations. Different proportions within the binary mixture were used to create solvents with different interfacial free energies with polystyrene. In these mixed solvents, we observed a linear correlation between the interfacial free energy and the force required to extend the chain into solution, which is a direct measure of the solvation free energy per monomer on a single chain at room temperature. A simple analytical model compares favorably with the experimental results. This knowledge supports a common assumption that explicit water solvent may not be necessary for cases whose primary concerns are hydrophobic interactions and hydrophobic hydration.

Characterizing structural transitions using localized free energy landscape analysis.

Directory of Open Access Journals (Sweden)

Nilesh K Banavali

Full Text Available Structural changes in molecules are frequently observed during biological processes like replication, transcription and translation. These structural changes can usually be traced to specific distortions in the backbones of the macromolecules involved. Quantitative energetic characterization of such distortions can greatly advance the atomic-level understanding of the dynamic character of these biological processes.Molecular dynamics simulations combined with a variation of the Weighted Histogram Analysis Method for potential of mean force determination are applied to characterize localized structural changes for the test case of cytosine (underlined base flipping in a GTCAGCGCATGG DNA duplex. Free energy landscapes for backbone torsion and sugar pucker degrees of freedom in the DNA are used to understand their behavior in response to the base flipping perturbation. By simplifying the base flipping structural change into a two-state model, a free energy difference of upto 14 kcal/mol can be attributed to the flipped state relative to the stacked Watson-Crick base paired state. This two-state classification allows precise evaluation of the effect of base flipping on local backbone degrees of freedom.The calculated free energy landscapes of individual backbone and sugar degrees of freedom expectedly show the greatest change in the vicinity of the flipping base itself, but specific delocalized effects can be discerned upto four nucleotide positions away in both 5' and 3' directions. Free energy landscape analysis thus provides a quantitative method to pinpoint the determinants of structural change on the atomic scale and also delineate the extent of propagation of the perturbation along the molecule. In addition to nucleic acids, this methodology is anticipated to be useful for studying conformational changes in all macromolecules, including carbohydrates, lipids, and proteins.

Severe accident research activities at Helmholtz-Zentrum Dresden-Rossendorf (HZDR)

Energy Technology Data Exchange (ETDEWEB)

Wilhelm, Polina; Jobst, Matthias; Schaefer, Frank; Kliem, Soeren [Helmholtz-Zentrum Dresden-Rossendorf e.V., Dresden (Germany)

2016-05-15

In the frame of the nuclear safety research program of the Helmholtz Association HZDR performs fundamental and applied research to assess and to reduce the risks related to the nuclear fuel cycle and the production of electricity in nuclear power plants. One of the research topics focuses on the safety aspects of current and future reactor designs. This includes the development and application of methods for analyses of transients and postulated accidents, covering the whole spectrum from normal operation till severe accident sequences including core degradation. This paper gives an overview of the severe accident research activities at the Reactor Safety Division at the Institute of Resource Ecology.

Connecting science and the musical arts in teaching tone quality: Integrating Helmholtz motion and master violin teachers' pedagogies

Science.gov (United States)

Collins, Cheri D.

Is it possible for students to achieve better tone quality from even their factory-made violins? All violins, regardless of cost, have a common capacity for good tone in certain frequencies. These signature modes outline the first position range of a violin (196-600 hertz). To activate this basic capacity of all violins, the string must fully vibrate. To accomplish this the bow must be pulled across the string with enough pressure (relative to its speed and contact point) for the horsehairs to catch. This friction permits the string to vibrate in Helmholtz Motion, which produces a corner that travels along the edge of the string between the bridge and the nut. Creating this corner is the most fundamental technique for achieving good tone. The findings of celebrated scientists Ernest Chladni, Hermann von Helmholtz, and John Schelleng will be discussed and the tone-production pedagogy of master teachers Carl Flesch, Ivan Galamian, Robert Gerle, and Simon Fischer will be investigated. Important connections between the insights of these scientists and master teachers are evident. Integrating science and art can provide teachers with a better understanding of the characteristics of good tone. This can help their students achieve the best possible sound from their instruments. In the private studio the master teacher may not use the words "Helmholtz Motion." Yet through modeling and listening students are able to understand and create a quality tone. Music teachers without experience in string performance may be assigned to teach strings in classroom and ensembles settings. As a result modeling good tone is not always possible. However, all teachers and conductors can understand the fundamental behavior of string vibration and adapt their instruction strategies towards student success. Better tonal quality for any string instrument is ultimately achieved. Mastery and use of the Helmholtz Motion benefits teachers and students alike. Simple practice exercises for teaching

Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

International Nuclear Information System (INIS)

Burinskaya, T. M.; Shevelev, M. M.; Rauch, J.-L.

2011-01-01

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.

Applications for Energy Recovering Free Electron Lasers

Energy Technology Data Exchange (ETDEWEB)

George Neil

2007-08-01

The availability of high-power, high-brilliance sources of tunable photons from energy-recovered Free Electron Lasers is opening up whole new fields of application of accelerators in industry. This talk will review some of the ideas that are already being put into production, and some of the newer ideas that are still under development.

Iterative solution of the Helmholtz equation

Energy Technology Data Exchange (ETDEWEB)

Larsson, E.; Otto, K. [Uppsala Univ. (Sweden)

1996-12-31

We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.

Exploration, Novelty, Surprise and Free Energy Minimisation

Directory of Open Access Journals (Sweden)

Philipp eSchwartenbeck

2013-10-01

Full Text Available This paper reviews recent developments under the free energy principle that introduce a normative perspective on classical economic (utilitarian decision-making based on (active Bayesian inference. It has been suggested that the free energy principle precludes novelty and complexity, because it assumes that biological systems – like ourselves - try to minimise the long-term average of surprise to maintain their homeostasis. However, recent formulations show that minimising surprise leads naturally to concepts such as exploration and novelty bonuses. In this approach, agents infer a policy that minimises surprise by minimising the difference (or relative entropy between likely and desired outcomes, which involves both pursuing the goal-state that has the highest expected utility (often termed ‘exploitation’ and visiting a number of different goal-states (‘exploration’. Crucially, the opportunity to visit new states increases the value of the current state. Casting decision-making problems within a variational framework, therefore, predicts that our behaviour is governed by both the entropy and expected utility of future states. This dissolves any dialectic between minimising surprise and exploration or novelty seeking.

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

KAUST Repository

Fan, Xiaolin; Kou, Jisheng; Qiao, Zhonghua; Sun, Shuyu

2017-01-01

are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic

AlaScan: A Graphical User Interface for Alanine Scanning Free-Energy Calculations.

Science.gov (United States)

Ramadoss, Vijayaraj; Dehez, François; Chipot, Christophe

2016-06-27

Computation of the free-energy changes that underlie molecular recognition and association has gained significant importance due to its considerable potential in drug discovery. The massive increase of computational power in recent years substantiates the application of more accurate theoretical methods for the calculation of binding free energies. The impact of such advances is the application of parent approaches, like computational alanine scanning, to investigate in silico the effect of amino-acid replacement in protein-ligand and protein-protein complexes, or probe the thermostability of individual proteins. Because human effort represents a significant cost that precludes the routine use of this form of free-energy calculations, minimizing manual intervention constitutes a stringent prerequisite for any such systematic computation. With this objective in mind, we propose a new plug-in, referred to as AlaScan, developed within the popular visualization program VMD to automate the major steps in alanine-scanning calculations, employing free-energy perturbation as implemented in the widely used molecular dynamics code NAMD. The AlaScan plug-in can be utilized upstream, to prepare input files for selected alanine mutations. It can also be utilized downstream to perform the analysis of different alanine-scanning calculations and to report the free-energy estimates in a user-friendly graphical user interface, allowing favorable mutations to be identified at a glance. The plug-in also assists the end-user in assessing the reliability of the calculation through rapid visual inspection.

Incorporating the effect of ionic strength in free energy calculations using explicit ions

NARCIS (Netherlands)

Donnini, S; Mark, AE; Juffer, AH; Villa, Alessandra

2005-01-01

The incorporation of explicit ions to mimic the effect of ionic strength or to neutralize the overall charge on a system in free energy calculations using molecular dynamics simulations is investigated. The difference in the free energy of hydration between two triosephosphate isomerase inhibitors

Solid/liquid interfacial free energies in binary systems

Science.gov (United States)

Nason, D.; Tiller, W. A.

1973-01-01

Description of a semiquantitative technique for predicting the segregation characteristics of smooth interfaces between binary solid and liquid solutions in terms of readily available thermodynamic parameters of the bulk solutions. A lattice-liquid interfacial model and a pair-bonded regular solution model are employed in the treatment with an accommodation for liquid interfacial entropy. The method is used to calculate the interfacial segregation and the free energy of segregation for solid-liquid interfaces between binary solutions for the (111) boundary of fcc crystals. The zone of compositional transition across the interface is shown to be on the order of a few atomic layers in width, being moderately narrower for ideal solutions. The free energy of the segregated interface depends primarily upon the solid composition and the heats of fusion of the component atoms, the composition difference of the solutions, and the difference of the heats of mixing of the solutions.

Absolute Hydration Free Energy of Proton from First Principles Electronic Structure Calculations

International Nuclear Information System (INIS)

Zhan, Chang-Guo; Dixon, David A.

2001-01-01

The absolute hydration free energy of the proton, DGhyd298(H+), is one of the fundamental quantities for the thermodynamics of aqueous systems. Its exact value remains unknown despite extensive experimental and computational efforts. We report a first-principles determination of DGhyd298(H+) by using the latest developments in electronic structure theory and massively parallel computers. DGhyd298(H+) is accurately predicted to be -262.4 kcal/mol based on high-level, first-principles solvation-included electronic structure calculations. The absolute hydration free energies of other cations can be obtained by using appropriate available thermodynamic data in combination with this value. The high accuracy of the predicted absolute hydration free energy of proton is confirmed by applying the same protocol to predict DGhyd298(Li+)

Extrapolation procedures for calculating high-temperature gibbs free energies of aqueous electrolytes

International Nuclear Information System (INIS)

Tremaine, P.R.

1979-01-01

Methods for calculating high-temprature Gibbs free energies of mononuclear cations and anions from room-temperature data are reviewed. Emphasis is given to species required for oxide solubility calculations relevant to mass transport situations in the nuclear industry. Free energies predicted by each method are compared to selected values calculated from recently reported solubility studies and other literature data. Values for monatomic ions estimated using the assumption anti C 0 p(T) = anti C 0 p(298) agree best with experiment to 423 K. From 423 K to 523 K, free energies from an electrostatic model for ion hydration are more accurate. Extrapolations for hydrolyzed species are limited by a lack of room-temperature entropy data and expressions for estimating these entropies are discussed. (orig.) [de

Hydrogen role in a carbon-free energy mix

International Nuclear Information System (INIS)

2014-02-01

Among the energy storage technologies under development today, there is today an increasing interest towards the hydrogen-based ones. Hydrogen generation allows to store electricity, while its combustion can supply electrical, mechanical or heat energy. The French Atomic Energy Commission (CEA) started to work on hydrogen technologies at the end of the 1990's in order to reinforce its economical interest. The development of these technologies is one of the 34 French industrial programs presented in September 2013 by the French Minister of productive recovery. This paper aims at identifying the hydrogen stakes in a carbon-free energy mix and at highlighting the remaining technological challenges to be met before reaching an industrial development level

Minimal Self-Models and the Free Energy Principle

Directory of Open Access Journals (Sweden)

Jakub eLimanowski

2013-09-01

Full Text Available The term "minimal phenomenal selfhood" describes the basic, pre-reflective experience of being a self (Blanke & Metzinger, 2009. Theoretical accounts of the minimal self have long recognized the importance and the ambivalence of the body as both part of the physical world, and the enabling condition for being in this world (Gallagher, 2005; Grafton, 2009. A recent account of minimal phenomenal selfhood (MPS, Metzinger, 2004a centers on the consideration that minimal selfhood emerges as the result of basic self-modeling mechanisms, thereby being founded on pre-reflective bodily processes. The free energy principle (FEP, Friston, 2010 is a novel unified theory of cortical function that builds upon the imperative that self-organizing systems entail hierarchical generative models of the causes of their sensory input, which are optimized by minimizing free energy as an approximation of the log-likelihood of the model. The implementation of the FEP via predictive coding mechanisms and in particular the active inference principle emphasizes the role of embodiment for predictive self-modeling, which has been appreciated in recent publications. In this review, we provide an overview of these conceptions and illustrate thereby the potential power of the FEP in explaining the mechanisms underlying minimal selfhood and its key constituents, multisensory integration, interoception, agency, perspective, and the experience of mineness. We conclude that the conceptualization of MPS can be well mapped onto a hierarchical generative model furnished by the free energy principle and may constitute the basis for higher-level, cognitive forms of self-referral, as well as the understanding of other minds.

The Maximum Free Magnetic Energy Allowed in a Solar Active Region

Science.gov (United States)

Moore, Ronald L.; Falconer, David A.

2009-01-01

Two whole-active-region magnetic quantities that can be measured from a line-of-sight magnetogram are (sup L) WL(sub SG), a gauge of the total free energy in an active region's magnetic field, and sup L(sub theta), a measure of the active region's total magnetic flux. From these two quantities measured from 1865 SOHO/MDI magnetograms that tracked 44 sunspot active regions across the 0.5 R(sub Sun) central disk, together with each active region's observed production of CMEs, X flares, and M flares, Falconer et al (2009, ApJ, submitted) found that (1) active regions have a maximum attainable free magnetic energy that increases with the magnetic size (sup L) (sub theta) of the active region, (2) in (Log (sup L)WL(sub SG), Log(sup L) theta) space, CME/flare-productive active regions are concentrated in a straight-line main sequence along which the free magnetic energy is near its upper limit, and (3) X and M flares are restricted to large active regions. Here, from (a) these results, (b) the observation that even the greatest X flares produce at most only subtle changes in active region magnetograms, and (c) measurements from MSFC vector magnetograms and from MDI line-of-sight magnetograms showing that practically all sunspot active regions have nearly the same area-averaged magnetic field strength: =- theta/A approximately equal to 300 G, where theta is the active region's total photospheric flux of field stronger than 100 G and A is the area of that flux, we infer that (1) the maximum allowed ratio of an active region's free magnetic energy to its potential-field energy is 1, and (2) any one CME/flare eruption releases no more than a small fraction (less than 10%) of the active region's free magnetic energy. This work was funded by NASA's Heliophysics Division and NSF's Division of Atmospheric Sciences.

Observation of the Kelvin–Helmholtz Instability in a Solar Prominence

Science.gov (United States)

Yang, Heesu; Xu, Zhi; Lim, Eun-Kyung; Kim, Sujin; Cho, Kyung-Suk; Kim, Yeon-Han; Chae, Jongchul; Cho, Kyuhyoun; Ji, Kaifan

2018-04-01

Many solar prominences end their lives in eruptions or abrupt disappearances that are associated with dynamical or thermal instabilities. Such instabilities are important because they may be responsible for energy transport and conversion. We present a clear observation of a streaming kink-mode Kelvin–Helmholtz Instability (KHI) taking place in a solar prominence using the Hα Lyot filter installed at the New Vacuum Solar Telescope, Fuxian-lake Solar Observatory in Yunnan, China. On one side of the prominence, a series of plasma blobs floated up from the chromosphere and streamed parallel to the limb. The plasma stream was accelerated to about 20–60 km s‑1 and then undulated. We found that 2″- and 5″-size vortices formed, floated along the stream, and then broke up. After the 5″-size vortex, a plasma ejection out of the stream was detected in the Solar Dynamics Observatory/Atmospheric Imaging Assembly images. Just before the formation of the 5″-size vortex, the stream displayed an oscillatory transverse motion with a period of 255 s with the amplitude growing at the rate of 0.001 s‑1. We attribute this oscillation of the stream and the subsequent formation of the vortex to the KHI triggered by velocity shear between the stream, guided by the magnetic field and the surrounding media. The plasma ejection suggests the transport of prominence material into the upper layer by the KHI in its nonlinear stage.

Energy of Force-Free Magnetic Fields in Relation to Coronal Mass Ejections; TOPICAL

International Nuclear Information System (INIS)

G.S. Choe; C.Z. Cheng

2002-01-01

In typical observations of coronal mass ejections (CMEs), a magnetic structure of a helmet-shaped closed configuration bulges out and eventually opens up. However, a spontaneous transition between these field configurations has been regarded to be energetically impossible in force-free fields according to the Aly-Sturrock theorem. The theorem states that the maximum energy state of force-free fields with a given boundary normal field distribution is the open field. The theorem implicitly assumes the existence of the maximum energy state, which may not be taken for granted. In this study, we have constructed force-free fields containing tangential discontinuities in multiple flux systems. These force-free fields can be generated from a potential field by footpoint motions that do not conserve the boundary normal field distribution. Some of these force-free fields are found to have more magnetic energy than the corresponding open fields. The constructed force-free configurations are compared with observational features of CME-bearing active regions. Possible mechanisms of CMEs are also discussed

ENERGY BUDGETS IN FREE-LIVING GREEN IGUANAS IN A SEASONAL ENVIRONMENT

NARCIS (Netherlands)

LICHTENBELT, WDV; WESSELINGH, RA; VOGEL, JT; ALBERS, KBM

Using a variety of techniques we estimated energy expenditure and allocation of energy in free-living green iguanas (Iguana iguana) in a seasonal environment on Curacao, Netherlands Antilles. 1) Daily energy expenditure (DEE) was measured by means of the doubly labeled water (DLW) technique, using

Of the Helmholtz Club, South-Californian seedbed for visual and cognitive neuroscience, and its patron Francis Crick.

Science.gov (United States)

Aicardi, Christine

2014-03-01

Taking up the view that semi-institutional gatherings such as clubs, societies, research schools, have been instrumental in creating sheltered spaces from which many a 20th-century project-driven interdisciplinary research programme could develop and become established within the institutions of science, the paper explores the history of one such gathering from its inception in the early 1980s into the 2000s, the Helmholtz Club, which brought together scientists from such various research fields as neuroanatomy, neurophysiology, psychophysics, computer science and engineering, who all had an interest in the study of the visual system and of higher cognitive functions relying on visual perception such as visual consciousness. It argues that British molecular biologist turned South Californian neuroscientist Francis Crick had an early and lasting influence over the Helmholtz Club of which he was a founding pillar, and that from its inception, the club served as a constitutive element in his long-term plans for a neuroscience of vision and of cognition. Further, it argues that in this role, the Helmholtz Club served many purposes, the primary of which was to be a social forum for interdisciplinary discussion, where 'discussion' was not mere talk but was imbued with an epistemic value and as such, carefully cultivated. Finally, it questions what counts as 'doing science' and in turn, definitions of success and failure-and provides some material evidence towards re-appraising the successfulness of Crick's contribution to the neurosciences. Copyright © 2013 The Author. Published by Elsevier Ltd.. All rights reserved.

Impact of domain knowledge on blinded predictions of binding energies by alchemical free energy calculations

Science.gov (United States)

Mey, Antonia S. J. S.; Jiménez, Jordi Juárez; Michel, Julien

2018-01-01

The Drug Design Data Resource (D3R) consortium organises blinded challenges to address the latest advances in computational methods for ligand pose prediction, affinity ranking, and free energy calculations. Within the context of the second D3R Grand Challenge several blinded binding free energies predictions were made for two congeneric series of Farsenoid X Receptor (FXR) inhibitors with a semi-automated alchemical free energy calculation workflow featuring FESetup and SOMD software tools. Reasonable performance was observed in retrospective analyses of literature datasets. Nevertheless, blinded predictions on the full D3R datasets were poor due to difficulties encountered with the ranking of compounds that vary in their net-charge. Performance increased for predictions that were restricted to subsets of compounds carrying the same net-charge. Disclosure of X-ray crystallography derived binding modes maintained or improved the correlation with experiment in a subsequent rounds of predictions. The best performing protocols on D3R set1 and set2 were comparable or superior to predictions made on the basis of analysis of literature structure activity relationships (SAR)s only, and comparable or slightly inferior, to the best submissions from other groups.

Energy and the NAFTA [North American Free Trade Agreement

International Nuclear Information System (INIS)

Plourde, A.

1993-01-01

A review is presented of the implications of the North American Free Trade Agreement (NAFTA) for the energy industry. This agreement expands the coverage accorded to energy in the Canada-US Free Trade Agreement (FTA), and is of limited significance with respect to Canada-US relations, but is quite important to these two countries' energy trade with Mexico. With respect to Canada-US trade, the most important departure from the FTA is that NAFTA tends to ensure a greater degree of respect for the terms of negotiated contracts, in particular by requiring the parties to make efforts to secure compliance with the national treatment provisions of the NAFTA by subfederal regulatory entities. Mexico's constitution severely restricts foreign participation in the activities of its energy industries, including basic petrochemicals. While NAFTA accomodates these restrictions, Canadian and US companies will have opportunities to bid on contracts for goods and services and construction in the Mexican energy sector on an equal footing with their Mexican counterparts. NAFTA also provides expanded opportunities for foreign investment and control in electricity generation for own-use, cogeneration and public service purposes. The parties are explicitly allowed to extend activity incentives to their respective oil and gas industries. 9 refs

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control.

Science.gov (United States)

Klimchitskaya, G L; Mostepanenko, V M

2017-07-12

The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO 2 and Al 2 O 3 films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO 2 , Al 2 O 3 and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control

Science.gov (United States)

Klimchitskaya, G. L.; Mostepanenko, V. M.

2017-07-01

The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO2 and Al2O3 films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO2, Al2O3 and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.

Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics.

Science.gov (United States)

Awasthi, Shalini; Kapil, Venkat; Nair, Nisanth N

2016-06-15

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Fast exploration of an optimal path on the multidimensional free energy surface

Science.gov (United States)

Chen, Changjun

2017-01-01

In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules. PMID:28542475

Molecular dynamics simulations and free energy profile of ...

Indian Academy of Sciences (India)

aDepartment of Chemical Engineering, bDepartment of Chemistry, Amirkabir University of Technology,. 15875-4413 ... Lipid bilayers; Paracetamol; free energy; molecular dynamics simulation; membrane. 1. ..... bilayer is less favourable due to the hydrophobic nature .... Orsi M and Essex J W 2010 Soft Matter 6 3797. 54.

THE ROLE OF KELVIN–HELMHOLTZ INSTABILITY FOR PRODUCING LOOP-TOP HARD X-RAY SOURCES IN SOLAR FLARES

Energy Technology Data Exchange (ETDEWEB)

Fang, Xia; Yuan, Ding; Xia, Chun; Doorsselaere, Tom Van; Keppens, Rony [Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium)

2016-12-10

We propose a model for the formation of loop-top hard X-ray (HXR) sources in solar flares through the inverse Compton mechanism, scattering the surrounding soft X-ray (SXR) photons to higher energy HXR photons. We simulate the consequences of a flare-driven energy deposit in the upper chromosphere in the impulsive phase of single loop flares. The consequent chromosphere evaporation flows from both footpoints reach speeds up to hundreds of kilometers per second, and we demonstrate how this triggers Kelvin–Helmholtz instability (KHI) in the loop top, under mildly asymmetric conditions, or more toward the loop flank for strongly asymmetric cases. The KHI vortices further fragment the magnetic topology into multiple magnetic islands and current sheets, and the hot plasma within leads to a bright loop-top SXR source region. We argue that the magnetohydrodynamic turbulence that appears at the loop apex could be an efficient accelerator of non-thermal particles, which the island structures can trap at the loop-top. These accelerated non-thermal particles can upscatter the surrounding thermal SXR photons emitted by the extremely hot evaporated plasma to HXR photons.

Diffusion in multicomponent systems: a free energy approach

International Nuclear Information System (INIS)

Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian

2004-01-01

This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (M aa , M ab , M ba , and M bb ), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ ac and χ bc ) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested

Towards a Continental Energy Market: From the Energy Crisis to the Free Trade Agreement, 1970-88.

Science.gov (United States)

Bennett, Paul W.

1989-01-01

Discusses the impact the 1973 oil embargo and resulting energy crisis had on Canadian energy policies, which eventually led in 1987 to the enactment of the Free Trade Agreement between Canada and the United States. Includes excerpts of three documents which reveal much about the shift in Canadian policy toward a continental energy market. (LS)

Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

International Nuclear Information System (INIS)

Wei, T; Qin, H H; Shi, R

2008-01-01

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

Prior Flaring as a Complement to Free Magnetic Energy for Forecasting Solar Eruptions

Science.gov (United States)

Falconer, David A.; Moore, Ronald L.; Barghouty, Abdulnasser F.; Khazanov, Igor

2012-01-01

From a large database of (1) 40,000 SOHO/MDI line-of-sight magnetograms covering the passage of 1,300 sunspot active regions across the 30 deg radius central disk of the Sun, (2) a proxy of each active region's free magnetic energy measured from each of the active region's central-disk-passage magnetograms, and (3) each active region's full-disk-passage history of production of major flares and fast coronal mass ejections (CMEs), we find new statistical evidence that (1) there are aspects of an active region's magnetic field other than the free energy that are strong determinants of the active region's productivity of major flares and fast CMEs in the coming few days, (2) an active region's recent productivity of major flares, in addition to reflecting the amount of free energy in the active region, also reflects these other determinants of coming productivity of major eruptions, and (3) consequently, the knowledge of whether an active region has recently had a major flare, used in combination with the active region's free-energy proxy measured from a magnetogram, can greatly alter the forecast chance that the active region will have a major eruption in the next few days after the time of the magnetogram. The active-region magnetic conditions that, in addition to the free energy, are reflected by recent major flaring are presumably the complexity and evolution of the field.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis.

Science.gov (United States)

Kearns, F L; Hudson, P S; Boresch, S; Woodcock, H L

2016-01-01

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples. © 2016 Elsevier Inc. All rights reserved.

PRIOR FLARING AS A COMPLEMENT TO FREE MAGNETIC ENERGY FOR FORECASTING SOLAR ERUPTIONS

International Nuclear Information System (INIS)

Falconer, David A.; Moore, Ronald L.; Barghouty, Abdulnasser F.; Khazanov, Igor

2012-01-01

From a large database of (1) 40,000 SOHO/MDI line-of-sight magnetograms covering the passage of 1300 sunspot active regions across the 30° radius central disk of the Sun, (2) a proxy of each active region's free magnetic energy measured from each of the active region's central-disk-passage magnetograms, and (3) each active region's full-disk-passage history of production of major flares and fast coronal mass ejections (CMEs), we find new statistical evidence that (1) there are aspects of an active region's magnetic field other than the free energy that are strong determinants of the active region's productivity of major flares and fast CMEs in the coming few days; (2) an active region's recent productivity of major flares, in addition to reflecting the amount of free energy in the active region, also reflects these other determinants of coming productivity of major eruptions; and (3) consequently, the knowledge of whether an active region has recently had a major flare, used in combination with the active region's free-energy proxy measured from a magnetogram, can greatly alter the forecast chance that the active region will have a major eruption in the next few days after the time of the magnetogram. The active-region magnetic conditions that, in addition to the free energy, are reflected by recent major flaring are presumably the complexity and evolution of the field.

Postselection-free energy-time entanglement

International Nuclear Information System (INIS)

Strekalov, D.V.; Pittman, T.B.; Sergienko, A.V.; Shih, Y.H.; Kwiat, P.G.

1996-01-01

We report a two-photon interference experiment that realizes a postselection-free test of Bell close-quote s inequality based on energy-time entanglement. In contrast with all previous experiments of this type, the employed entangled states are obtained without the use of a beam splitter or a short coincidence window to open-quote open-quote throw away close-quote close-quote unwanted amplitudes. A (95.0±1.4)% interference fringe visibility is observed, implying a strong violation of the Bell inequality. The scheme is very compact and has demonstrated excellent stability, suggesting that it may be useful, for example, in practical quantum cryptography. copyright 1996 The American Physical Society

Effect of Atomic Charges on Octanol–Water Partition Coefficient Using Alchemical Free Energy Calculation

Directory of Open Access Journals (Sweden)

Koji Ogata

2018-02-01

Full Text Available The octanol–water partition coefficient (logPow is an important index for measuring solubility, membrane permeability, and bioavailability in the drug discovery field. In this paper, the logPow values of 58 compounds were predicted by alchemical free energy calculation using molecular dynamics simulation. In free energy calculations, the atomic charges of the compounds are always fixed. However, they must be recalculated for each solvent. Therefore, three different sets of atomic charges were tested using quantum chemical calculations, taking into account vacuum, octanol, and water environments. The calculated atomic charges in the different environments do not necessarily influence the correlation between calculated and experimentally measured ∆Gwater values. The largest correlation coefficient values of the solvation free energy in water and octanol were 0.93 and 0.90, respectively. On the other hand, the correlation coefficient of logPow values calculated from free energies, the largest of which was 0.92, was sensitive to the combination of the solvation free energies calculated from the calculated atomic charges. These results reveal that the solvent assumed in the atomic charge calculation is an important factor determining the accuracy of predicted logPow values.

Sparse RNA folding revisited: space-efficient minimum free energy structure prediction.

Science.gov (United States)

Will, Sebastian; Jabbari, Hosna

2016-01-01

RNA secondary structure prediction by energy minimization is the central computational tool for the analysis of structural non-coding RNAs and their interactions. Sparsification has been successfully applied to improve the time efficiency of various structure prediction algorithms while guaranteeing the same result; however, for many such folding problems, space efficiency is of even greater concern, particularly for long RNA sequences. So far, space-efficient sparsified RNA folding with fold reconstruction was solved only for simple base-pair-based pseudo-energy models. Here, we revisit the problem of space-efficient free energy minimization. Whereas the space-efficient minimization of the free energy has been sketched before, the reconstruction of the optimum structure has not even been discussed. We show that this reconstruction is not possible in trivial extension of the method for simple energy models. Then, we present the time- and space-efficient sparsified free energy minimization algorithm SparseMFEFold that guarantees MFE structure prediction. In particular, this novel algorithm provides efficient fold reconstruction based on dynamically garbage-collected trace arrows. The complexity of our algorithm depends on two parameters, the number of candidates Z and the number of trace arrows T; both are bounded by [Formula: see text], but are typically much smaller. The time complexity of RNA folding is reduced from [Formula: see text] to [Formula: see text]; the space complexity, from [Formula: see text] to [Formula: see text]. Our empirical results show more than 80 % space savings over RNAfold [Vienna RNA package] on the long RNAs from the RNA STRAND database (≥2500 bases). The presented technique is intentionally generalizable to complex prediction algorithms; due to their high space demands, algorithms like pseudoknot prediction and RNA-RNA-interaction prediction are expected to profit even stronger than "standard" MFE folding. SparseMFEFold is free

Adhesion Evaluation of Asphalt-Aggregate Interface Using Surface Free Energy Method

Directory of Open Access Journals (Sweden)

Jie Ji

2017-02-01

Full Text Available The influence of organic additives (Sasobit and RH and water on the adhesion of the asphalt-aggregate interface was studied according to the surface free energy theory. Two asphalt binders (SK-70 and SK-90, and two aggregate types (limestone and basalt were used in this study. The sessile drop method was employed to test surface free energy components of asphalt, organic additives and aggregates. The adhesion models of the asphalt-aggregate interface in dry and wet conditions were established, and the adhesion work was calculated subsequently. The energy ratios were built to evaluate the effect of organic additives and water on the adhesiveness of the asphalt-aggregate interface. The results indicate that the addition of organic additives can enhance the adhesion of the asphalt-aggregate interface in dry conditions, because organic additives reduced the surface free energy of asphalt. However, the organic additives have hydrophobic characteristics and are sensitive to water. As a result, the adhesiveness of the asphalt-aggregate interface of the asphalt containing organic additives in wet conditions sharply decreased due to water damage to asphalt and organic additives. Furthermore, the compatibility of asphalt, aggregate with organic additive was noted and discussed.

Peptide Free Energy Landscapes Calibrated by Molecular Orbital Calculations

OpenAIRE

Ono, S.; Kuroda, M.; Higo, J.; Kamiya, N.; Nakajima, N.; Nakamura, H.

2002-01-01

Free energy landscapes of peptide conformations werecalibrated by ab initiomolecular orbital calculations, after enhancedconformational sampling using the multicanonical molecular dynamicssimulations. Three different potentials of mean force for an isolateddipeptide were individually obtained using the conventional force fields,AMBER parm94, AMBER parm96, and CHARMm22. Each potential ofmean force was calibrated based on the umbrella sampling algorithm fromthe adiabatic energy map that was cal...

How to deal with multiple binding poses in alchemical relative protein-ligand binding free energy calculations.

Science.gov (United States)

Kaus, Joseph W; Harder, Edward; Lin, Teng; Abel, Robert; McCammon, J Andrew; Wang, Lingle

2015-06-09

Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the

How To Deal with Multiple Binding Poses in Alchemical Relative Protein–Ligand Binding Free Energy Calculations

Science.gov (United States)

2016-01-01

Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the

Enhancing DC Glow Discharge Tube Museuum Displays using a Theremin Controlled Helmholtz Coil to Demonstrate Magnetic Confinement

Science.gov (United States)

Siu, Theodore; Wissel, Stephanie; Guttadora, Larry; Liao, Susan; Zwicker, Andrew

2010-11-01

Since their discovery in the mid 1800's, DC glow discharge apparatuses have commonly been used for spectral analysis, the demonstration of the Frank-Hertz experiment, and to study plasma breakdown voltages following from the Paschen Curve. A DC glow discharge tube museum display was outfitted with a Helmholtz Coil electromagnet in order to demonstrate magnetic confinement for a science museum display. A device commonly known as a ``theremin'' was designed and built in order to externally control the Helmholtz Coil current and the plasma current. Originally a musical instrument, a theremin has two variable capacitors connected to two radio frequency oscillators which determine pitch and volume. Using a theremin to control current and ``play'' the plasma adds appeal and durability by providing a new innovative means of interacting with a museum exhibit. Educationally, students can use the display to not only learn about plasma properties but also electronic properties of the human body.

Analysis and control of a hybrid vehicle powered by free-piston energy converter

OpenAIRE

Hansson, Jörgen

2006-01-01

The introduction of hybrid powertrains has made it possible to utilise unconventional engines as primary power units in vehicles. The free-piston energy converter (FPEC) is such an engine. It is a combination of a free-piston combustion engine and a linear electrical machine. The main features of this configuration are high efficiency and a rapid transient response. In this thesis the free-piston energy converter as part of a hybrid powertrain is studied. One issue of the FPEC is the generati...

Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics

Science.gov (United States)

Lau, Gabriel V.; Hunt, Patricia A.; Müller, Erich A.; Jackson, George; Ford, Ian J.

2015-12-01

Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the "mitosis" or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.

Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics

Energy Technology Data Exchange (ETDEWEB)

Lau, Gabriel V.; Müller, Erich A.; Jackson, George [Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Hunt, Patricia A. [Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT (United Kingdom)

2015-12-28

Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the “mitosis” or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.

Kelvin-Helmholtz instability: the ``atom'' of geophysical turbulence?

Science.gov (United States)

Smyth, William

2017-11-01

Observations of small-scale turbulence in Earth's atmosphere and oceans have most commonly been interpreted in terms of the Kolmogorov theory of isotropic turbulence, despite the fact that the observed turbulence is significantly anisotropic due to density stratification and sheared large-scale flows. I will describe an alternative picture in which turbulence consists of distinct events that occur sporadically in space and time. The simplest model for an individual event is the ``Kelvin-Helmholtz (KH) ansatz'', in which turbulence relieves the dynamic instability of a localized shear layer. I will summarize evidence that the KH ansatz is a valid description of observed turbulence events, using microstructure measurements from the equatorial Pacific ocean as an example. While the KH ansatz has been under study for many decades and is reasonably well understood, the bigger picture is much less clear. How are the KH events distributed in space and time? How do different events interact with each other? I will describe some tentative steps toward a more thorough understanding.

Efficient approach to obtain free energy gradient using QM/MM MD simulation

International Nuclear Information System (INIS)

Asada, Toshio; Koseki, Shiro; Ando, Kanta

2015-01-01

The efficient computational approach denoted as charge and atom dipole response kernel (CDRK) model to consider polarization effects of the quantum mechanical (QM) region is described using the charge response and the atom dipole response kernels for free energy gradient (FEG) calculations in the quantum mechanical/molecular mechanical (QM/MM) method. CDRK model can reasonably reproduce energies and also energy gradients of QM and MM atoms obtained by expensive QM/MM calculations in a drastically reduced computational time. This model is applied on the acylation reaction in hydrated trypsin-BPTI complex to optimize the reaction path on the free energy surface by means of FEG and the nudged elastic band (NEB) method

The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit.

Science.gov (United States)

Cheng, Bingqing; Tribello, Gareth A; Ceriotti, Michele

2017-09-14

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fitted using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.

Free energy landscape and molecular pathways of gas hydrate nucleation

Energy Technology Data Exchange (ETDEWEB)

Bi, Yuanfei; Porras, Anna; Li, Tianshu, E-mail: tsli@gwu.edu [Department of Civil and Environmental Engineering, George Washington University, Washington DC 20052 (United States)

2016-12-07

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p{sub B} histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p{sub B} histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Free energy landscape and molecular pathways of gas hydrate nucleation

International Nuclear Information System (INIS)

Bi, Yuanfei; Porras, Anna; Li, Tianshu

2016-01-01

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Free energy landscape and molecular pathways of gas hydrate nucleation.

Science.gov (United States)

Bi, Yuanfei; Porras, Anna; Li, Tianshu

2016-12-07

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Comparative assessment of computational methods for the determination of solvation free energies in alcohol-based molecules.

Science.gov (United States)

Martins, Silvia A; Sousa, Sergio F

2013-06-05

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson-Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane-alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM-based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane-alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane-alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug-binding in computer-aided drug design. Copyright © 2013 Wiley Periodicals, Inc.

Trp-cage: Folding free energy landscape in explicit water

Science.gov (United States)

Zhou, Ruhong

2003-11-01

Trp-cage is a 20-residue miniprotein, which is believed to be the fastest folder known so far. In this study, the folding free energy landscape of Trp-cage has been explored in explicit solvent by using an OPLSAA force field with periodic boundary condition. A highly parallel replica exchange molecular dynamics method is used for the conformation space sampling, with the help of a recently developed efficient molecular dynamics algorithm P3ME/RESPA (particle-particle particle-mesh Ewald/reference system propagator algorithm). A two-step folding mechanism is proposed that involves an intermediate state where two correctly formed partial hydrophobic cores are separated by an essential salt-bridge between residues Asp-9 and Arg-16 near the center of the peptide. This metastable intermediate state provides an explanation for the superfast folding process. The free energy landscape is found to be rugged at low temperatures, and then becomes smooth and funnel-like above 340 K. The lowest free energy structure at 300 K is only 1.50 Å C-RMSD (C-rms deviation) from the NMR structures. The simulated nuclear Overhauser effect pair distances are in excellent agreement with the raw NMR data. The temperature dependence of the Trp-cage population, however, is found to be significantly different from experiment, with a much higher melting transition temperature above 400 K (experimental 315 K), indicating that the current force fields, parameterized at room temperature, need to be improved to correctly predict the temperature dependence.

Integrability and symmetries for the Helmholtz oscillator with friction

International Nuclear Information System (INIS)

Almendral, Juan A; Sanjuan, Miguel A F

2003-01-01

This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction

Kelvin-Helmholtz instability and kinetic internal kink modes in tokamaks

International Nuclear Information System (INIS)

Naitou, H.

2002-01-01

The m=1 and n=1 kinetic internal kink (KIK) mode with a nonuniform density profile is studied by the cylindrical version of the gyro-reduced-MHD code which is one of the extended MHD codes being able to treat the physics beyond resistive MHD. Electron inertia and electron finite temperature effects are crucial. The linear mode structure of KIK mode includes the sheared poloidal flow with m=1, which excites the vortexes due to the Kelvin-Helmholtz (K-H) instability. We have found that there is a strong coupling between the KIK mode and the K-H mode even in the early nonlinear stage of KIK instability in which the width of the m=1 magnetic island is sufficiently small. (author)

Two-Dimensional Free Energy Surfaces for Electron Transfer Reactions in Solution

Directory of Open Access Journals (Sweden)

Shigeo Murata

2008-01-01

Full Text Available Change in intermolecular distance between electron donor (D and acceptor (A can induce intermolecular electron transfer (ET even in nonpolar solvent, where solvent orientational polarization is absent. This was shown by making simple calculations of the energies of the initial and final states of ET. In the case of polar solvent, the free energies are functions of both D-A distance and solvent orientational polarization. On the basis of 2-dimensional free energy surfaces, the relation of Marcus ET and exciplex formation is discussed. The transient effect in fluorescence quenching was measured for several D-A pairs in a nonpolar solvent. The results were analyzed by assuming a distance dependence of the ET rate that is consistent with the above model.

Weighted density approximation for bonding in molecules: ring and cage polymers

CERN Document Server

Sweatman, M B

2003-01-01

The focus of this work is the bonded contribution to the intrinsic Helmholtz free energy of molecules. A weighted density approximation (WDA) for this contribution is presented within the interaction site model (ISM) for ring and cage polymers. The resulting density functional theory (ISM/WDA) for these systems is no more complex than theories for a pure simple fluid, and much less complex than density functional approaches that treat the bonding functional exactly. The ISM/WDA bonding functional is much more accurate than either the ISM/HNC or ISM/PY bonding functionals, which are related to the reference interaction-site model (RISM)/HNC and RISM/PY integral equations respectively, for ideal ring polymers. This means that the ISM/WDA functional should generally be more accurate for most 'real' ring or cage polymer systems when any reasonable approximation for the 'excess' contribution to the intrinsic Helmholtz free energy is employed.

Weighted density approximation for bonding in molecules: ring and cage polymers

International Nuclear Information System (INIS)

Sweatman, M B

2003-01-01

The focus of this work is the bonded contribution to the intrinsic Helmholtz free energy of molecules. A weighted density approximation (WDA) for this contribution is presented within the interaction site model (ISM) for ring and cage polymers. The resulting density functional theory (ISM/WDA) for these systems is no more complex than theories for a pure simple fluid, and much less complex than density functional approaches that treat the bonding functional exactly. The ISM/WDA bonding functional is much more accurate than either the ISM/HNC or ISM/PY bonding functionals, which are related to the reference interaction-site model (RISM)/HNC and RISM/PY integral equations respectively, for ideal ring polymers. This means that the ISM/WDA functional should generally be more accurate for most 'real' ring or cage polymer systems when any reasonable approximation for the 'excess' contribution to the intrinsic Helmholtz free energy is employed

Determination of partial molar volumes from free energy perturbation theory†

Science.gov (United States)

Vilseck, Jonah Z.; Tirado-Rives, Julian

2016-01-01

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood–Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm3 mol−1. The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute–solvent interactions. PMID:25589343

Determination of partial molar volumes from free energy perturbation theory.

Science.gov (United States)

Vilseck, Jonah Z; Tirado-Rives, Julian; Jorgensen, William L

2015-04-07

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase.

Science.gov (United States)

Nascimento, Érica C M; Oliva, Mónica; Andrés, Juan

2018-05-01

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase

Science.gov (United States)

Nascimento, Érica C. M.; Oliva, Mónica; Andrés, Juan

2018-05-01

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.

Novel approach to the Helmholtz integral equation solution by Fourier series expansion for acoustic radiation and scattering problems

CSIR Research Space (South Africa)

Shatalov, MY

2006-01-01

Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...

Calculation of the Local Free Energy Landscape in the Restricted Region by the Modified Tomographic Method.

Science.gov (United States)

Chen, Changjun

2016-03-31

The free energy landscape is the most important information in the study of the reaction mechanisms of the molecules. However, it is difficult to calculate. In a large collective variable space, a molecule must take a long time to obtain the sufficient sampling during the simulation. To save the calculation quantity, decreasing the sampling region and constructing the local free energy landscape is required in practice. However, the restricted region in the collective variable space may have an irregular shape. Simply restricting one or more collective variables of the molecule cannot satisfy the requirement. In this paper, we propose a modified tomographic method to perform the simulation. First, it divides the restricted region by some hyperplanes and connects the centers of hyperplanes together by a curve. Second, it forces the molecule to sample on the curve and the hyperplanes in the simulation and calculates the free energy data on them. Finally, all the free energy data are combined together to form the local free energy landscape. Without consideration of the area outside the restricted region, this free energy calculation can be more efficient. By this method, one can further optimize the path quickly in the collective variable space.

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

Science.gov (United States)

Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.; Mundy, Chistopher J.

2017-10-01

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

Towards a fossil free energy future. The next energy transition

Energy Technology Data Exchange (ETDEWEB)

Lazarus, M.; Greber, L.; Hall, J.; Bartels, C.; Bernow, S.; Hansen, E.; Raskin, P.; Von Hippel, D. (Stockholm Environment Institute, Boston, MA (United States))

1993-04-01

The report provides technical analysis and documentation as input to the Greenpeace project 'Towards a fossil free energy future'. It presents a main scenario and several variants for reducing greenhouse gas emissions, and the technical methods and assumptions used to develop them. The goal is to investigate the technical, economic and policy feasibility to phasing out fossil fuels over the next century as part of a strategy to avert unacceptably high levels or rates of global warming. 209 refs., 42 figs., 27 tabs.

Estimation of the Binding Free Energy of AC1NX476 to HIV-1 Protease Wild Type and Mutations Using Free Energy Perturbation Method.

Science.gov (United States)

Ngo, Son Tung; Mai, Binh Khanh; Hiep, Dinh Minh; Li, Mai Suan

2015-10-01

The binding mechanism of AC1NX476 to HIV-1 protease wild type and mutations was studied by the docking and molecular dynamics simulations. The binding free energy was calculated using the double-annihilation binding free energy method. It is shown that the binding affinity of AC1NX476 to wild type is higher than not only ritonavir but also darunavir, making AC1NX476 become attractive candidate for HIV treatment. Our theoretical results are in excellent agreement with the experimental data as the correlation coefficient between calculated and experimentally measured binding free energies R = 0.993. Residues Asp25-A, Asp29-A, Asp30-A, Ile47-A, Gly48-A, and Val50-A from chain A, and Asp25-B from chain B play a crucial role in the ligand binding. The mutations were found to reduce the receptor-ligand interaction by widening the binding cavity, and the binding propensity is mainly driven by the van der Waals interaction. Our finding may be useful for designing potential drugs to combat with HIV. © 2015 John Wiley & Sons A/S.

Can the regulated market help foster a free market for wind energy in Brazil?

International Nuclear Information System (INIS)

Dalbem, Marta Corrêa; Brandão, Luiz Eduardo Teixeira; Gomes, Leonardo Lima

2014-01-01

Wind energy has been negotiated in Brazil's regulated market through auctions organized by the government. Bilateral negotiations in the free market have been scarce. In 2011 wind farms were allowed to bid in ‘A minus 5 (A−5)' auctions, for energy with first delivery date 5 years ahead. This new design was expected to stimulate negotiations in the free market, as the 20-year contract in the regulated market eases financing while the 5-year grace period grants wind farms the option to sell whatever energy is generated beforehand in the free market. We modeled bidders' price decision in A−5 auctions as Real Options and concluded that given the low prices averaging USD 50/MW h, winners are tempted to defer investment, expecting more favorable equipment and energy prices, or a better knowledge of the wind site. Construction is likely to begin in 2–3 years, with little time left for the free market. Bidders that consider the option of eventually abandoning the project are more price competitive, increasing chances that some wind farms will never materialize. Therefore, this attempt to foster the free market may not pay-off and, moreover, it may have the unfavorable effect of turning Brazil's energy expansion planning a more difficult task. - Highlights: • Tight auction prices make winners exercise options to defer construction. • Investors that consider the option to abandon the project tend to win the auction. • High chances of default, when investors take abandonment options into account. • Auctioning wind farms for energy delivery 5 yr later will not foster a free market

Efficiency of free-energy calculations of spin lattices by spectral quantum algorithms

International Nuclear Information System (INIS)

Master, Cyrus P.; Yamaguchi, Fumiko; Yamamoto, Yoshihisa

2003-01-01

Ensemble quantum algorithms are well suited to calculate estimates of the energy spectra for spin-lattice systems. Based on the phase estimation algorithm, these algorithms efficiently estimate discrete Fourier coefficients of the density of states. Their efficiency in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Science.gov (United States)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Direct measurement of free-energy barrier to nucleation of crystallites in amorphous silicon thin films

Science.gov (United States)

Shi, Frank G.

1994-01-01

A method is introduced to measure the free-energy barrier W(sup *), the activation energy, and activation entropy to nucleation of crystallites in amorphous solids, independent of the energy barrier to growth. The method allows one to determine the temperature dependence of W(sup *), and the effect of the preparation conditions of the initial amorphous phase, the dopants, and the crystallization methds on W(sup *). The method is applied to determine the free-energy barrier to nucleation of crystallites in amorphous silicon (a-Si) thin films. For thermally induced nucleation in a-Si thin films with annealing temperatures in the range of from 824 to 983 K, the free-energy barrier W(sup *) to nucleation of silicon crystals is about 2.0 - 2.1 eV regardless of the preparation conditions of the films. The observation supports the idea that a-Si transforms into an intermediate amorphous state through the structural relaxation prior to the onset of nucleation of crystallites in a-Si. The observation also indicates that the activation entropy may be an insignificant part of the free-energy barrier for the nucleation of crystallites in a-Si. Compared with the free-energy barrier to nucleation of crystallites in undoped a-Si films, a significant reduction is observed in the free-energy barrier to nucleation in Cu-doped a-Si films. For a-Si under irradiation of Xe(2+) at 10(exp 5) eV, the free-energy barrier to ion-induced nucleation of crystallites is shown to be about half of the value associated with thermal-induced nucleation of crystallites in a-Si under the otherwise same conditions, which is much more significant than previously expected. The present method has a general kinetic basis; it thus should be equally applicable to nucleation of crystallites in any amorphous elemental semiconductors and semiconductor alloys, metallic and polymeric glasses, and to nucleation of crystallites in melts and solutions.

Designing molecular complexes using free-energy derivatives from liquid-state integral equation theory

International Nuclear Information System (INIS)

Mrugalla, Florian; Kast, Stefan M

2016-01-01

Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute–solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute–solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems. (paper)

SAAMBE: Webserver to Predict the Charge of Binding Free Energy Caused by Amino Acids Mutations.

Science.gov (United States)

Petukh, Marharyta; Dai, Luogeng; Alexov, Emil

2016-04-12

Predicting the effect of amino acid substitutions on protein-protein affinity (typically evaluated via the change of protein binding free energy) is important for both understanding the disease-causing mechanism of missense mutations and guiding protein engineering. In addition, researchers are also interested in understanding which energy components are mostly affected by the mutation and how the mutation affects the overall structure of the corresponding protein. Here we report a webserver, the Single Amino Acid Mutation based change in Binding free Energy (SAAMBE) webserver, which addresses the demand for tools for predicting the change of protein binding free energy. SAAMBE is an easy to use webserver, which only requires that a coordinate file be inputted and the user is provided with various, but easy to navigate, options. The user specifies the mutation position, wild type residue and type of mutation to be made. The server predicts the binding free energy change, the changes of the corresponding energy components and provides the energy minimized 3D structure of the wild type and mutant proteins for download. The SAAMBE protocol performance was tested by benchmarking the predictions against over 1300 experimentally determined changes of binding free energy and a Pearson correlation coefficient of 0.62 was obtained. How the predictions can be used for discriminating disease-causing from harmless mutations is discussed. The webserver can be accessed via http://compbio.clemson.edu/saambe_webserver/.

MESSENGER Orbital Observations of Large-Amplitude Kelvin-Helmholtz Waves at Mercury's Magnetopause

Science.gov (United States)

Sundberg, Torbjorn; Boardsen, Scott A.; Slavin, James A.; Anderson, Brian J.; Korth, Haje; Zurbuchen, Thomas H.; Raines, Jim M.; Solomon, Sean C.

2012-01-01

We present a survey of Kelvi\\ n-Helmholtz (KH) waves at Mercury's magnetopause during MESSENGER's first Mercury year in orb it. The waves were identified on the basis of the well-established sawtooth wave signatures that are associated with non-linear KH vortices at the magnetopause. MESSENGER frequently observed such KH waves in the dayside region of the magnetosphere where the magnetosheath flow velocity is still sub -sonic, which implies that instability growth rates at Mercury's magnetopau are much larger than at Earth. We attribute these greater rates to the limited wave energy dissipation in Mercury's highly resistive regolith. The wave amplitude was often on the order of ' 00 nT or more, and the wave periods were - 10- 20 s. A clear dawn-dusk asymmetry is present in the data, in that all of the observed wave events occurred in the post-noon and dusk-side sectors of the magnetopause. This asymmetry is like ly related to finite Larmor-radius effects and is in agreement with results from particle-in-cell simulations of the instability. The waves were observed almost exclusively during periods when the north-south component of the magnetosheath magnetic field was northward, a pattern similar to that for most terrestrial KH wave events. Accompanying plasma measurements show that the waves were associated with the transport of magnetosheath plasma into the magnetosphere.

Note on de Haas-van Alphen diamagnetism in thin, free-electron films

Directory of Open Access Journals (Sweden)

J. A. Grzesik

2012-03-01

Full Text Available We revisit the problem of de Haas-van Alphen (dHvA diamagnetic susceptibility oscillations in a thin, free-electron film trapped in a synthetic harmonic potential well. A treatment of this phenomenon at zero temperature was announced many years ago by Childers and Pincus (designated hereafter as CP, and we traverse initially much the same ground, but from a slightly different analytic perspective. That difference hinges around our use, in calculating the Helmholtz free energy F, of an inverse Laplace transform, Bromwich-type contour integral representation for the sharp distribution cutoff at Fermi level μ. The contour integral permits closed-form summation all at once over the discrete orbital Landau energy levels transverse to the magnetic field, and the energy associated with the in-plane canonical momenta ℏ k x and ℏ k z. Following such summation/integration, pole/residue pairs appear in the plane of complex transform variable s, a fourth-order pole at origin s = 0, and an infinite ladder, both up and down, of simple poles along the imaginary axis. The residue sum from the infinite pole ladder automatically engenders a Fourier series with period one in dimensionless variable μ/ ℏ ω (with effective angular frequency ω suitably defined, series which admits closed-form summation as a cubic polynomial within any given periodicity slot. Such periodicity corresponds to Landau levels slipping sequentially beneath Fermi level μ as the ambient magnetic field H declines in strength, and is manifested by the dHvA pulsations in diamagnetic susceptibility. The coëxisting steady contribution from the pole at origin has a similar cubic structure but is opposite in sign, inducing a competition whose outcome is a net magnetization that is merely quadratic in any given periodicity slot, modulated by a slow amplitude growth. Apart from some minor notes of passing discord, these simple algebraic structures confirm most of the CP formulae, and their

Free energy for protonation reaction in lithium-ion battery cathode materials

International Nuclear Information System (INIS)

Benedek, R.; Thackeray, M. M.; van de Walle, A.

2008-01-01

Calculations are performed of free energies for proton-for-lithium-ion exchange reactions in lithium-ion battery cathode materials. First-principles calculations are employed for the solid phases and tabulated ionization potential and hydration energy data for aqueous ions. Layered structures, spinel LiMn 2 O 4 , and olivine LiFePO 4 are considered. Protonation is most favorable energetically in layered systems, such as Li 2 MnO 3 and LiCoO 2 . Less favorable are ion-exchange in spinel LiMn 2 O 4 and LiV 3 O 8 . Unfavorable is the substitution of protons for Li in olivine LiFePO 4 , because of the large distortion of the Fe and P coordination polyhedra. The reaction free energy scales roughly linearly with the volume change in the reaction

Relationship between enamel bond fatigue durability and surface free-energy characteristics with universal adhesives.

Science.gov (United States)

Nagura, Yuko; Tsujimoto, Akimasa; Barkmeier, Wayne W; Watanabe, Hidehiko; Johnson, William W; Takamizawa, Toshiki; Latta, Mark A; Miyazaki, Masashi

2018-04-01

The relationship between enamel bond fatigue durability and surface free-energy characteristics with universal adhesives was investigated. The initial shear bond strengths and shear fatigue strengths of five universal adhesives to enamel were determined with and without phosphoric acid pre-etching. The surface free-energy characteristics of adhesive-treated enamel with and without pre-etching were also determined. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were higher than those to ground enamel. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were material dependent, unlike those to ground enamel. The surface free-energy of the solid (γ S ) and the hydrogen-bonding force (γSh) of universal adhesive-treated enamel were different depending on the adhesive, regardless of the presence or absence of pre-etching. The bond fatigue durability of universal adhesives was higher to pre-etched enamel than to ground enamel. In addition, the bond fatigue durability to pre-etched enamel was material dependent, unlike that to ground enamel. The surface free-energy characteristics of universal adhesive-treated enamel were influenced by the adhesive type, regardless of the presence or absence of pre-etching. The surface free-energy characteristics of universal adhesive-treated enamel were related to the results of the bond fatigue durability. © 2018 Eur J Oral Sci.

Analysis of Mechanical Energy Transport on Free-Falling Wedge during Water-Entry Phase

Directory of Open Access Journals (Sweden)

Wen-Hua Wang

2012-01-01

Full Text Available For better discussing and understanding the physical phenomena and body-fluid interaction of water-entry problem, here mechanical-energy transport (wedge, fluid, and each other of water-entry model for free falling wedge is studied by numerical method based on free surface capturing method and Cartesian cut cell mesh. In this method, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method. Then artificial compressibility method, dual-time stepping technique, and Roe's approximate Riemann solver are applied in the numerical scheme. Furthermore, the projection method of momentum equations and exact Riemann solution are used to calculate the fluid pressure on solid boundary. On this basis, during water-entry phase of the free-falling wedge, macroscopic energy conversion of overall body-fluid system and microscopic energy transformation in fluid field are analyzed and discussed. Finally, based on test cases, many useful conclusions about mechanical energy transport for water entry problem are made and presented.

Computation of Hydration Free Energies Using the Multiple Environment Single System Quantum Mechanical/Molecular Mechanical Method.

Science.gov (United States)

König, Gerhard; Mei, Ye; Pickard, Frank C; Simmonett, Andrew C; Miller, Benjamin T; Herbert, John M; Woodcock, H Lee; Brooks, Bernard R; Shao, Yihan

2016-01-12

A recently developed MESS-E-QM/MM method (multiple-environment single-system quantum mechanical molecular/mechanical calculations with a Roothaan-step extrapolation) is applied to the computation of hydration free energies for the blind SAMPL4 test set and for 12 small molecules. First, free energy simulations are performed with a classical molecular mechanics force field using fixed-geometry solute molecules and explicit TIP3P solvent, and then the non-Boltzmann-Bennett method is employed to compute the QM/MM correction (QM/MM-NBB) to the molecular mechanical hydration free energies. For the SAMPL4 set, MESS-E-QM/MM-NBB corrections to the hydration free energy can be obtained 2 or 3 orders of magnitude faster than fully converged QM/MM-NBB corrections, and, on average, the hydration free energies predicted with MESS-E-QM/MM-NBB fall within 0.10-0.20 kcal/mol of full-converged QM/MM-NBB results. Out of five density functionals (BLYP, B3LYP, PBE0, M06-2X, and ωB97X-D), the BLYP functional is found to be most compatible with the TIP3P solvent model and yields the most accurate hydration free energies against experimental values for solute molecules included in this study.

Efficient Construction of Free Energy Profiles of Breathing Metal-Organic Frameworks Using Advanced Molecular Dynamics Simulations.

Science.gov (United States)

Demuynck, Ruben; Rogge, Sven M J; Vanduyfhuys, Louis; Wieme, Jelle; Waroquier, Michel; Van Speybroeck, Veronique

2017-12-12

In order to reliably predict and understand the breathing behavior of highly flexible metal-organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials.

Efficient Construction of Free Energy Profiles of Breathing Metal–Organic Frameworks Using Advanced Molecular Dynamics Simulations

Science.gov (United States)

2017-01-01

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials. PMID:29131647

Free Energy-Based Virtual Screening and Optimization of RNase H Inhibitors of HIV-1 Reverse Transcriptase.

Science.gov (United States)

Zhang, Baofeng; D'Erasmo, Michael P; Murelli, Ryan P; Gallicchio, Emilio

2016-09-30

We report the results of a binding free energy-based virtual screening campaign of a library of 77 α-hydroxytropolone derivatives against the challenging RNase H active site of the reverse transcriptase (RT) enzyme of human immunodeficiency virus-1. Multiple protonation states, rotamer states, and binding modalities of each compound were individually evaluated. The work involved more than 300 individual absolute alchemical binding free energy parallel molecular dynamics calculations and over 1 million CPU hours on national computing clusters and a local campus computational grid. The thermodynamic and structural measures obtained in this work rationalize a series of characteristics of this system useful for guiding future synthetic and biochemical efforts. The free energy model identified key ligand-dependent entropic and conformational reorganization processes difficult to capture using standard docking and scoring approaches. Binding free energy-based optimization of the lead compounds emerging from the virtual screen has yielded four compounds with very favorable binding properties, which will be the subject of further experimental investigations. This work is one of the few reported applications of advanced-binding free energy models to large-scale virtual screening and optimization projects. It further demonstrates that, with suitable algorithms and automation, advanced-binding free energy models can have a useful role in early-stage drug-discovery programs.

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: From fluid to kinetic modeling

Czech Academy of Sciences Publication Activity Database

Henri, P.; Cerri, S.S.; Califano, F.; Pegoraro, F.; Rossi, C.; Faganello, M.; Šebek, Ondřej; Trávníček, Pavel M.; Hellinger, Petr; Frederiksen, J. T.; Nordlund, A.; Markidis, S.; Keppens, R.; Lapenta, G.

2013-01-01

Roč. 20, č. 10 (2013), 102118/1-102118/13 ISSN 1070-664X R&D Projects: GA MŠk(CZ) 7E11053 EU Projects: European Commission(XE) 263340 - SWIFF Grant - others:European Commission(XE) HPC-EUROPA2 - No. 228398; EU(XE) RI-283493; NASA (US) NNX11A1164G Institutional support: RVO:67985815 ; RVO:68378289 Keywords : Kelvin-Helmholtz instability * plasma kinetic theory * plasma magnetohydrodynamics Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics; BL - Plasma and Gas Discharge Physics (UFA-U) Impact factor: 2.249, year: 2013

Applying the Helmholtz Illusion to Fashion: Horizontal Stripes Won't Make You Look Fatter

Directory of Open Access Journals (Sweden)

Peter Thompson

2011-01-01

Full Text Available A square composed of horizontal lines appears taller and narrower than an identical square made up of vertical lines. Reporting this illusion, Hermann von Helmholtz noted that such illusions, in which filled space seems to be larger than unfilled space, were common in everyday life, adding the observation that ladies' frocks with horizontal stripes make the figure look taller. As this assertion runs counter to modern popular belief, we have investigated whether vertical or horizontal stripes on clothing should make the wearer appear taller or fatter. We find that a rectangle of vertical stripes needs to be extended by 7.1% vertically to match the height of a square of horizontal stripes and that a rectangle of horizontal stripes must be made 4.5% wider than a square of vertical stripes to match its perceived width. This illusion holds when the horizontal or vertical lines are on the dress of a line drawing of a woman. We have examined the claim that these effects apply only for 2-dimensional figures in an experiment with 3-D cylinders and find no support for the notion that horizontal lines would be ‘fattening’ on clothes. Significantly, the illusion persists when the horizontal or vertical lines are on pictures of a real half-body mannequin viewed stereoscopically. All the evidence supports Helmholtz's original assertion.

Possible Lead Free Nanocomposite Dielectrics for High Energy Storage Applications

Directory of Open Access Journals (Sweden)

Srinivas Kurpati

2017-03-01

Full Text Available There is an increasing demand to improve the energy density of dielectric capacitors for satisfying the next generation material systems. One effective approach is to embed high dielectric constant inclusions such as lead zirconia titanate in polymer matrix. However, with the increasing concerns on environmental safety and biocompatibility, the need to expel lead (Pb from modern electronics has been receiving more attention. Using high aspect ratio dielectric inclusions such as nanowires could lead to further enhancement of energy density. Therefore, the present brief review work focuses on the feasibility of development of a lead-free nanowire reinforced polymer matrix capacitor for energy storage application. It is expected that Lead-free sodium Niobate nanowires (NaNbO3 and Boron nitride will be a future candidate to be synthesized using simple hydrothermal method, followed by mixing them with polyvinylidene fluoride (PVDF/ divinyl tetramethyl disiloxanebis (benzocyclobutene matrix using a solution-casting method for Nanocomposites fabrication. The energy density of NaNbO3 and BN based composites are also be compared with that of lead-containing (PbTiO3/PVDF Nano composites to show the feasibility of replacing lead-containing materials from high-energy density dielectric capacitors. Further, this paper explores the feasibility of these materials for space applications because of high energy storage capacity, more flexibility and high operating temperatures. This paper is very much useful researchers who would like to work on polymer nanocomposites for high energy storage applications.

Free energy landscape and transition pathways from Watson–Crick to Hoogsteen base pairing in free duplex DNA

Science.gov (United States)

Yang, Changwon; Kim, Eunae; Pak, Youngshang

2015-01-01

Houghton (HG) base pairing plays a central role in the DNA binding of proteins and small ligands. Probing detailed transition mechanism from Watson–Crick (WC) to HG base pair (bp) formation in duplex DNAs is of fundamental importance in terms of revealing intrinsic functions of double helical DNAs beyond their sequence determined functions. We investigated a free energy landscape of a free B-DNA with an adenosine–thymine (A–T) rich sequence to probe its conformational transition pathways from WC to HG base pairing. The free energy landscape was computed with a state-of-art two-dimensional umbrella molecular dynamics simulation at the all-atom level. The present simulation showed that in an isolated duplex DNA, the spontaneous transition from WC to HG bp takes place via multiple pathways. Notably, base flipping into the major and minor grooves was found to play an important role in forming these multiple transition pathways. This finding suggests that naked B-DNA under normal conditions has an inherent ability to form HG bps via spontaneous base opening events. PMID:26250116

Polymer in a pore: Effect of confinement on the free energy barrier

Science.gov (United States)

Kumar, Sanjiv; Kumar, Sanjay

2018-06-01

We investigate the transfer of a polymer chain from cis- side to trans- side through two types of pores: cone-shaped channel and flat-channel. Using the exact enumeration technique, we obtain the free energy landscapes of a polymer chain for such systems. We have also calculated the free-energy barrier of a polymer chain attached to the edge of the pore. The model system allows us to calculate the force required to pull polymer from the pore and stall-force to confine polymer within the pore.

Exploring the free energy landscape: from dynamics to networks and back.

Directory of Open Access Journals (Sweden)

Diego Prada-Gracia

2009-06-01

Full Text Available Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.

A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations

KAUST Repository

Poulson, Jack

2013-05-02

A parallelization of a sweeping preconditioner for three-dimensional Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are shown to be O(γ2N4/3) and O(γN logN), where γ(ω) denotes the modestly frequency-dependent number of grid points per perfectly matched layer. Several computational and memory improvements are introduced relative to using black-box sparse-direct solvers for the auxiliary problems, and competitive runtimes and iteration counts are reported for high-frequency problems distributed over thousands of cores. Two open-source packages are released along with this paper: Parallel Sweeping Preconditioner (PSP) and the underlying distributed multifrontal solver, Clique. © 2013 Society for Industrial and Applied Mathematics.

Assessment of CO2 free energy options

International Nuclear Information System (INIS)

Cavlina, N.; Raseta, D.; Matutinovic, I.

2014-01-01

One of the European Union climate and energy targets is to significantly reduce CO 2 emissions, at least 20% by 2020, compared to 1990. In the power industry, most popular solution is use of solar and wind power. Since their production varies significantly during the day, for the purpose of base-load production they can be paired with gas-fired power plant. Other possible CO 2 -free solution is nuclear power plant. This article compared predicted cost of energy production for newly built nuclear power plant and newly built combination of wind or solar and gas-fired power plant. Comparison was done using Levelized Unit of Energy Cost (LUEC). Calculations were performed using the Monte Carlo method. For input parameters that have biggest uncertainty (gas cost, CO 2 emission fee) those uncertainties were addressed not only through probability distribution around predicted value, but also through different scenarios. Power plants were compared based on their economic lifetime. (authors)

Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.

Science.gov (United States)

Benet, Jorge; MacDowell, Luis G; Sanz, Eduardo

2015-04-07

In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup.

Free energy and plaquette expectation value for gluons on the lattice, in three dimensions

International Nuclear Information System (INIS)

Panagopoulos, H.; Skouroupathis, A.; Tsapalis, A.

2006-01-01

We calculate the perturbative value of the free energy in lattice QCD in three dimensions, up to three loops. Our calculation is performed using the Wilson formulation for gluons in SU(N) gauge theories. The free energy is directly related to the average plaquette. To carry out the calculation, we compute the coefficients involved in the perturbative expansion of the Free Energy up to three loops, using an automated set of procedures developed by us in Mathematica. The dependence on N is shown explicitly in our results. For purposes of comparison, we also present the individual contributions from every diagram. These have been obtained by means of two independent calculations, in order to cross check our results

Numerical modeling of isothermal compositional grading by convex splitting methods

KAUST Repository

Li, Yiteng

2017-04-09

In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.

The Free Energy in the Derrida-Retaux Recursive Model

Science.gov (United States)

Hu, Yueyun; Shi, Zhan

2018-05-01

We are interested in a simple max-type recursive model studied by Derrida and Retaux (J Stat Phys 156:268-290, 2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.

Effects of Energy Chirp on Echo-Enabled Harmonic Generation Free-Electron Lasers

International Nuclear Information System (INIS)

Huang, Z.

2009-01-01

We study effects of energy chirp on echo-enabled harmonic generation (EEHG). Analytical expressions are compared with numerical simulations for both harmonic and bunching factors. We also discuss the EEHG free-electron laser bandwidth increase due to an energy-modulated beam and its pulse length dependence on the electron energy chirp

Free Energy Landscapes of Alanine Oligopeptides in Rigid-Body and Hybrid Water Models.

Science.gov (United States)

Nayar, Divya; Chakravarty, Charusita

2015-08-27

Replica exchange molecular dynamics is used to study the effect of different rigid-body (mTIP3P, TIP4P, SPC/E) and hybrid (H1.56, H3.00) water models on the conformational free energy landscape of the alanine oligopeptides (acAnme and acA5nme), in conjunction with the CHARMM22 force field. The free energy landscape is mapped out as a function of the Ramachandran angles. In addition, various secondary structure metrics, solvation shell properties, and the number of peptide-solvent hydrogen bonds are monitored. Alanine dipeptide is found to have similar free energy landscapes in different solvent models, an insensitivity which may be due to the absence of possibilities for forming i-(i + 4) or i-(i + 3) intrapeptide hydrogen bonds. The pentapeptide, acA5nme, where there are three intrapeptide backbone hydrogen bonds, shows a conformational free energy landscape with a much greater degree of sensitivity to the choice of solvent model, though the three rigid-body water models differ only quantitatively. The pentapeptide prefers nonhelical, non-native PPII and β-sheet populations as the solvent is changed from SPC/E to the less tetrahedral liquid (H1.56) to an LJ-like liquid (H3.00). The pentapeptide conformational order metrics indicate a preference for open, solvent-exposed, non-native structures in hybrid solvent models at all temperatures of study. The possible correlations between the properties of solvent models and secondary structure preferences of alanine oligopeptides are discussed, and the competition between intrapeptide, peptide-solvent, and solvent-solvent hydrogen bonding is shown to be crucial in the relative free energies of different conformers.

Crystal–liquid interfacial free energy and thermophysical properties of pure liquid Ti using electrostatic levitation: Hypercooling limit, specific heat, total hemispherical emissivity, density, and interfacial free energy

International Nuclear Information System (INIS)

Lee, Geun Woo; Jeon, Sangho; Park, Cheolmin; Kang, Dong-Hee

2013-01-01

Highlights: • Thermophysical properties of liquid Ti are obtained by electrostatic levitation. • How to measure the thermophysical properties is shown with non-contact method. • Hypercooling limit of liquid Ti guarantying homogeneous nucleation is 341 K. • Accurate ratio C p /ε T of the liquid Ti is obtained with weak temperature dependence. • Interfacial free energy of Ti is estimated with the thermophysical parameters. -- Abstract: Thermophysical properties of liquid Ti are measured by a newly developed electrostatic levitation. In this study, we measure a hypercooling limit (ΔT hyp ), specific heat (C p ), total hemispherical emissivity (ε T ), and density (ρ) of liquid Ti. The ΔT hyp of the liquid Ti is 341 K. The C p of the liquid Ti shows very weak temperature dependence during supercooling. The ε T and ρ of the liquid Ti are given by 0.329 and ρ(T) (g/cm 3 ) = (4.16 − 2.36) · 10 −4 (T − T m ). Finally, the interfacial free energy is estimated with the measured thermophysical parameters. The interfacial free energy is 0.164 J/m 2 , and Turnbull’s coefficient is 0.48

Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA.

Science.gov (United States)

Berryman, Joshua T; Schilling, Tanja

2013-01-08

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their absolute free energies is a valuable strategy in certain important cases. We present calculations of absolute free energies of biomolecules, using a combination of the well-known Einstein molecule method (for treating the solute) with a conceptually related method of recent genesis for computing free energies of liquids (to treat the solvent and counterions). The approach is based on thermodynamic integration from a detailed atomistic model to one which is simplified but analytically solvable, thereby giving the absolute free energy as that of the tractable model plus a correction term found numerically. An example calculation giving the free energy with respect to salt concentration for the B- and Z-isomers of all-atom duplex DNA in explicit solvent and counterions is presented. The coexistence salt concentration is found with unprecedented accuracy.

Free radical production by high energy shock waves--comparison with ionizing irradiation.

Science.gov (United States)

Morgan, T R; Laudone, V P; Heston, W D; Zeitz, L; Fair, W R

1988-01-01

Fricke chemical dosimetry is used as an indirect measure of the free radical production of ionizing irradiation. We adapted the Fricke ferrous sulfate radiation dosimeter to examine the chemical effects of high energy shock waves. Significant free radical production was documented. The reaction was dose dependent, predictably increased by acoustic impedance, but curvilinear. A thousand shocks at 18 kilovolts induced the same free radical oxidation as 1100 rad cobalt-60 gamma ionizing irradiation, increasing to 2900 rad in the presence of an air-fluid zone of acoustic impedance. The biological effect of these free radicals was compared to that of cobalt-60 ionizing irradiation by measuring the affect on Chinese hamster cells by clonogenic assay. While cobalt-60 irradiation produced a marked decrease in clonogenic survivors, little effect was noted with high energy shock waves. This suggested that the chemical effects produced by shock waves were either absent or attenuated in the cells, or were inherently less toxic than those of ionizing irradiation.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods.

Science.gov (United States)

König, Gerhard; Miller, Benjamin T; Boresch, Stefan; Wu, Xiongwu; Brooks, Bernard R

2012-10-09

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

Free energy calculations along entropic pathways. III. Nucleation of capillary bridges and bubbles

Science.gov (United States)

Desgranges, Caroline; Delhommelle, Jerome

2017-05-01

Using molecular simulation, we analyze the capillary condensation and evaporation processes for argon confined in a cylindrical nanopore. For this purpose, we define the entropy of the adsorbed fluid as a reaction coordinate and determine the free energy associated with both processes along entropic pathways. For capillary condensation, we identify a complex free energy profile resulting from the multi-stage nature of this phenomenon. We find capillary condensation to proceed through the nucleation of a liquid bridge across the nanopore, followed by its expansion throughout the pore to give rise to the stable phase of high density. In the case of capillary evaporation, the free energy profile along the entropy pathway also exhibits different regimes, corresponding to the initial destabilization of the layered structure of the fluid followed by the formation, and subsequent expansion, of a bubble across the nanopore.

Monolithically integrated Helmholtz coils by 3-dimensional printing

Energy Technology Data Exchange (ETDEWEB)

Li, Longguang [Department of Electrical Engineering, University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Abedini-Nassab, Roozbeh; Yellen, Benjamin B., E-mail: yellen@duke.edu [Department of Electrical Engineering, University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)

2014-06-23

3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.

Monolithically integrated Helmholtz coils by 3-dimensional printing

International Nuclear Information System (INIS)

Li, Longguang; Abedini-Nassab, Roozbeh; Yellen, Benjamin B.

2014-01-01

3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.

Kelvin-Helmholtz instability in a bounded plasma flow

International Nuclear Information System (INIS)

Burinskaya, T. M.

2008-01-01

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfven velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth's magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfven velocity.

Free energy and structure of dislocation cores in two-dimensional crystals

NARCIS (Netherlands)

Bladon, P.B.; Frenkel, D.

2004-01-01

The nature of the melting transition in two dimensions is critically dependent on the core energy of dislocations. In this paper, we report calculations of the core free energy and the core size of dislocations in two-dimensional solids of systems interacting via square well, hard disk, and r-12

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2013-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...

Enzymatic versus Inorganic Oxygen Reduction Catalysts: Comparison of the Energy Levels in a Free-Energy Scheme

DEFF Research Database (Denmark)

Kjærgaard, Christian Hauge; Rossmeisl, Jan; Nørskov, Jens Kehlet

2010-01-01

In this paper, we present a method to directly compare the energy levels of intermediates in enzymatic and inorganic oxygen reduction catalysts. We initially describe how the energy levels of a Pt(111) catalyst, operating at pH = 0, are obtained. By a simple procedure, we then convert the energy...... levels of cytochrome c oxidase (CcO) models obtained at physiological pH = 7 to the energy levels at pH = 0, which allows for comparison. Furthermore, we illustrate how different bias voltages will affect the free-energy landscapes of the catalysts. This allows us to determine the so-called theoretical...

Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate.

Science.gov (United States)

Krivov, Sergei V

2018-06-06

Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for

Thermodynamics and elastic properties of Ir from first-principle calculations

International Nuclear Information System (INIS)

Li Qiang; Huang Duohui; Cao Qilong; Wang Fanhou

2013-01-01

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties, including phonon dispersion curves, equation of state, linear thermal expansion coefficient and temperature-dependent entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young's modulus of Ir have been studied using first-principles projector-augmented wave method. The results revealed that the predicted phonon dispersion curves of Ir are in agreement with the experimental measurements by neutron diffractions. Considering the thermal electronic contribution to Helmholtz free energy, the calculated entropy, enthalpy, heat capacity and linear thermal expansion co- efficient from the first-principle are consistent well with the experimental data. At 2600 K, the electronic heat capacity accounts for 17% of the total heat capacity at constant pressure, thus the thermal electronic contribution to Helmholtz free energy is very important. The predicted elastic constants, bulk modulus, shear modulus and Young's modulus at room temperature are also in agreement with the available measurements and increase with the increasing temperature. (authors)

ASTEM, Evaluation of Gibbs, Helmholtz and Saturation Line Function for Thermodynamics Calculation

International Nuclear Information System (INIS)

Moore, K.V.; Burgess, M.P.; Fuller, G.L.; Kaiser, A.H.; Jaeger, D.L.

1974-01-01

1 - Description of problem or function: ASTEM is a modular set of FORTRAN IV subroutines to evaluate the Gibbs, Helmholtz, and saturation line functions as published by the American Society of Mechanical Engineers (1967). Any thermodynamic quantity including derivative properties can be obtained from these routines by a user-supplied main program. PROPS is an auxiliary routine available for the IBM360 version which makes it easier to apply the ASTEM routines to power station models. 2 - Restrictions on the complexity of the problem: Unless re-dimensioned by the user, the highest derivative allowed is order 9. All arrays within ASTEM are one-dimensional to save storage area

No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

DEFF Research Database (Denmark)

Workman, Christopher; Krogh, Anders Stærmose

1999-01-01

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly diff...

The free energy of locking a ring: Changing a deoxyribonucleoside to a locked nucleic acid.

Science.gov (United States)

Xu, You; Villa, Alessandra; Nilsson, Lennart

2017-06-05

Locked nucleic acid (LNA), a modified nucleoside which contains a bridging group across the ribose ring, improves the stability of DNA/RNA duplexes significantly, and therefore is of interest in biotechnology and gene therapy applications. In this study, we investigate the free energy change between LNA and DNA nucleosides. The transformation requires the breaking of the bridging group across the ribose ring, a problematic transformation in free energy calculations. To address this, we have developed a 3-step (easy to implement) and a 1-step protocol (more efficient, but more complicated to setup), for single and dual topologies in classical molecular dynamics simulations, using the Bennett Acceptance Ratio method to calculate the free energy. We validate the approach on the solvation free energy difference for the nucleosides thymidine, cytosine, and 5-methyl-cytosine. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Numerical investigation on an array of Helmholtz resonators for the reduction of micro-pressure waves in modern and future high-speed rail tunnel systems

Science.gov (United States)

Tebbutt, J. A.; Vahdati, M.; Carolan, D.; Dear, J. P.

2017-07-01

Previous research has proposed that an array of Helmholtz resonators may be an effective method for suppressing the propagation of pressure and sound waves, generated by a high-speed train entering and moving in a tunnel. The array can be used to counteract environmental noise from tunnel portals and also the emergence of a shock wave in the tunnel. The implementation of an array of Helmholtz resonators in current and future high-speed train-tunnel systems is studied. Wave propagation in the tunnel is modelled using a quasi-one-dimensional formulation, accounting for non-linear effects, wall friction and the diffusivity of sound. A multi-objective genetic algorithm is then used to optimise the design of the array, subject to the geometric constraints of a demonstrative tunnel system and the incident wavefront in order to attenuate the propagation of pressure waves. It is shown that an array of Helmholtz resonators can be an effective countermeasure for various tunnel lengths. In addition, the array can be designed to function effectively over a wide operating envelope, ensuring it will still function effectively as train speeds increase into the future.

Ab initio calculation of the migration free energy of oxygen diffusion in pure and samarium-doped ceria