Gibbs free energy assisted passivation layers
Salihoglu, Omer; Tansel, T.; Hostut, M.; Ergun, Y.; Aydinli, A.
2016-05-01
Reduction of surface leakage is a major challenge in most photodetectors that requires the elimination of surface oxides on etched mesas during passivation. Engineering the passivation requires close attention to chemical reactions that take place at the interface during the process. In particular, removal of surface oxides may be controlled via Gibbs reactivity. We have compared electrical performance of type-II superlattice photodetectors, designed for MWIR operation, passivated by different passivation techniques. We have used ALD deposited Al2O3, HfO2, TiO2, ZnO, PECVD deposited SiO2, Si3N4 and sulphur containing octadecanethiol (ODT) selfassembled monolayers (SAM) passivation layers on InAs/GaSb p-i-n superlattice photodetectors with cutoff wavelength at 5.1 μm. In this work, we have compared the result of different passivation techniques which are done under same conditions, same epitaxial structure and same fabrication processes. We have found that ALD deposited passivation is directly related to the Gibbs free energy of the passivation material. Gibbs free energies of the passivation layer can directly be compared with native surface oxides to check the effectiveness of the passivation layer before the experimental study.
Inference with minimal Gibbs free energy in information field theory.
Ensslin, Torsten A; Weig, Cornelius
2010-11-01
Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.
Verotti Filho, C.; Costa, Glória Meyberg Nunes
1996-01-01
p. 351–355 Solubilities of several organic solids in four supercritical fluids are calculated with Soave and Peng-Robinson equations of state, incorporating excess Gibbs free energy into the mixing rules, with Heidemann-Kokal, Wong-Sandler and MHV2 procedures. Three excess Gibbs free energy models are used in the mixing rules: NRTL, UNiQUAC and UNIFAC. Furthermore, a comparison between these mixing rules and conventional two-binary-parameter form and modification of the excluded volume par...
ESTIMATION OF GIBBS FREE-ENERGIES OF FORMATION FOR POLYCHLORINATED-BIPHENYLS
HOLMES, DA; HARRISON, BK; DOLFING, J
1993-01-01
Gibbs free energies of formation for gas, subcooled liquid, and aqueous solution phases were estimated for all 209 polychlorinated biphenyl (PCB) congeners at 298.15 K and 100 000 Pa. A literature search was conducted to locate experimental data or predicted data for PCBs. Where other data were not
Estimates of Gibbs free energies of formation of chlorinated aliphatic compounds
Dolfing, Jan; Janssen, Dick B.
1994-01-01
The Gibbs free energy of formation of chlorinated aliphatic compounds was estimated with Mavrovouniotis' group contribution method. The group contribution of chlorine was estimated from the scarce data available on chlorinated aliphatics in the literature, and found to vary somewhat according to the
Experimental Determination of Third Derivative of the Gibbs Free Energy, G II
Koga, Yoshikata; Westh, Peter; Inaba, Akira
2010-01-01
We have been evaluating third derivative quantities of the Gibbs free energy, G, by graphically differentiating the second derivatives that are accessible experimentally, and demonstrated their power in elucidating the mixing schemes in aqueous solutions. Here we determine directly one of the third...
Electrochemical determination of Gibbs free energy of formation of magnesium ferrite
Ling Wang; Huizhu Zhou; Yanruo Hong; Girish M Kale
2007-01-01
The standard Gibbs free energy of formation of magnesium ferrite was determined by means of two types of solid state electrochemical cells: one using MgZr4(PO4)6 (MZP) as the solid electrolyte and the other using CaF2 as the solid electrolyte. The first cell was operated in the range of 950 to 1100 K. The second cell was operated in the range of 1125 to 1200 K. The reversibility of the cell EMFs was confirmed by microcoulometric titration. The Gibbs energy changes of magnesium ferrite relative to component oxides were calculated based on EMF measurements and are given by following expressions, respectively: △G(o)Ⅰ = -3579-15 T (J/mol) and △G(o)Ⅱ =6258-24.3 T (J/mol). The results obtained from two different cells are consistent with each other. The results also are in agreement with Rao's and Tretjakov's data in the measured temperature range. When the Gibbs free energies of formation of MgO and Fe2O3 were substituted in the reaction, the Gibbs free energies of formation of MgFe2O4 was obtained in two temperature ranges and the formations are shown as follows: △G(o)Ⅰ Formation = -1427394+360.5 T (J/mol) and △G(o)Ⅱ Formation = -1417557+351.2 T (J/mol).
The Gibbs-free-energy landscape for the solute association in nanoconfined aqueous solutions
赵亮; 王春雷; 方海平; 涂育松
2015-01-01
The theoretical model and the numerical analyses on the Gibbs-free-energy of the association states of am-phiphilic molecules in nanoconfined aqueous solutions are presented in detail. We exhibit the continuous change of the Gibbs-free-energy trend, which plays a critical role in the association states of the system transforming from the dispersion state, through the “reversible state”, and finally to the aggregation state in amphiphilic molecule solutions. Furthermore, for the“reversible state”, we present the difference in the free-energy bar-rier heights of the dispersion state and aggregation state, resulting from the competition between the entropy, which makes the solute molecules evenly disperse in the solution and the energy contribution driving the am-phiphilic molecules to aggregate into a larger cluster. These findings provide a comprehensive understanding of confinement effects on the solute association processes in aqueous solutions and may further improve the techniques of material fabrication.
Estimation of Gibbs Free Energy of Formation of Sialon （O‘—and X—Phases
WENHongjine; LIWenchao
1999-01-01
Based on introducing the quasi-parabolid rule,which indicates the relation of Gibbs free energy of formation of compounds and its compostitions,the Gibbs free energes of formation of Sialons (O'-and X-phases) were estimated.
Calculation of electric field effects on the Gibbs free energy of the Al-Li-Mg alloy
无
2007-01-01
Based on the Thomas-Fermi model the calculation methods of the monatomic Gibbs free energy were found.The interior potential boundary condition under electric field was defined. The calculation methods of Gibbs free energy for the monatomic, compound, and solid solution with electric field were set up. Under the influence of electric field, the Gibbs free energy of A1 is the most sensitive, followed by those of Li and Mg. At the solution temperature the Gibbs free energies of Al3Li and its elements under electric field are not symmetrical about the zero point of electric field, whereas at the aging temperature their values are symmetrical about the zero point of electric field. At the solution temperature near the zero point of electric field, the Gibbs free energy of Al3Li is higher than that of Al-2.14%Li. And at 460 K the Gibbs free energy of A13Li is lower than that of Al-2.14wt.%Li under electric field. The Gibbs free energy of 1420 alloy decreases from both sides of electric field to the zero point at the aging temperature.
Direct measurements of the Gibbs free energy of OH using a CW tunable laser
Killinger, D. K.; Wang, C. C.
1979-01-01
The paper describes an absorption measurement for determining the Gibbs free energy of OH generated in a mixture of water and oxygen vapor. These measurements afford a direct verification of the accuracy of thermochemical data of H2O at high temperatures and pressures. The results indicate that values for the heat capacity of H2O obtained through numerical computations are correct within an experimental uncertainty of 0.15 cal/mole K.
W. L. Silva; Ribeiro,J. C. T.; E. F.da Costa Jr; A. O. S.da Costa
2008-01-01
The reduction efficiency is an important variable during the black liquor burning process in the Kraft recovery boiler. This variable value is obtained by slow experimental routines and the delay of this measure disturbs the pulp and paper industry customary control. This paper describes an optimization approach for the reduction efficiency determination in the furnace bottom of the recovery boiler based on the minimization of the Gibbs free energy. The industrial data used in this study were...
Hellweg, Arnim
2016-01-01
The computational modelling of reactions is simple in theory but can be quite tricky in practice. This article aims at the purpose of providing an assistance to a proper way of describing reactions theoretically and provides rough guidelines to the computational methods involved. Reactions in liquid phase chemical equilibrium can be described theoretically in terms of the Gibbs free energy of reaction. This property can be divided into a sum of three disjunct terms, namely the gas phase reaction energy, the finite temperature contribution to the Gibbs free energy, and the Gibbs free energy of solvation. The three contributions to the Gibbs free energy of reaction can be computed separately, using different theoretico--chemical calculation methods. While some of these terms can be obtained reliably by computationally cheap methods, for others a high level of theory is required to obtain predictions of quantitative quality. In order to propose workflows which can strike the balance between accuracy and computat...
Felmy, A.R.
1990-04-01
This document is a user's manual and technical reference for the computerized chemical equilibrium model GMIN. GMIN calculates the chemical composition of systems composed of pure solid phases, solid-solution phases, gas phases, adsorbed phases, and the aqueous phase. In the aqueous phase model, the excess solution free energy is modeled by using the equations developed by PITZER and his coworkers, which are valid to high ionic strengths. The Davies equation can also be used. Activity coefficients for nonideal soild-solution phases are calculated using parameters of polynomial expansion in mole fraction of the excess free energy of mixing. The free energy of adsorbed phase species is described by the triple-layer site-binding model. The mathematical algorithm incorporated into GMIN is based upon a constrained minimization of the Gibbs free energy. This algorithm is numerically stable and reliably converges to a free energy minimum. The data base for GMIN contains all standard chemical potentials and Pitzer ion-interaction parameters necessary to model the system Na-K-Ca-Mg-H-Cl-SO{sub 4}-CO{sub 2}-B(OH){sub 4}-H{sub 2}0 at 25{degrees}C.
W. L. Silva
2008-09-01
Full Text Available The reduction efficiency is an important variable during the black liquor burning process in the Kraft recovery boiler. This variable value is obtained by slow experimental routines and the delay of this measure disturbs the pulp and paper industry customary control. This paper describes an optimization approach for the reduction efficiency determination in the furnace bottom of the recovery boiler based on the minimization of the Gibbs free energy. The industrial data used in this study were directly obtained from CENIBRA's data acquisition system. The resulting approach is able to predict the steady state behavior of the chemical composition of the furnace recovery boiler, - especially the reduction efficiency when different operational conditions are used. This result confirms the potential of this approach in the analysis of the daily operation of the recovery boiler.
Estimation of Gibbs free energy difference in Pd-based bulk metallic glasses
Cai Anhui; Xiong Xiang; Liu Yong; Tan JingYing; Zhou Yong; An Weike
2008-01-01
A new thermodynamic expression for Gibbs free energy difference 4G between the under-cooled Iiquid and the corresponding crystals of bulk metallic glasses was derived.The newly proposed expression always gives results in fairly good agreement with experimental values over entire temperature range between the fusion temperature Tm and the glass transition temperature Tg of Pd40Ni40P20,Pd40Cu30Ni10P20 and Pd43Cu27Ni10P20,which possess different heat capacities.However,the TS and KN expressions cannot always provide results in good agreement with the experimental values.In addition.the deviations between the experimental values and the △G calculated by the proposed expression at Tg are smaller than those given by other expressions for all the bulk metallic glasses studied.
Ulstrup, Jens
1999-01-01
We discuss a simple model for the environmental reorganisation Gibbs free energy, E-r, in electron transfer between a metalloprotein and a small reaction partner. The protein is represented as a dielectric globule with low dielectric constant, the metal centres as conducting spheres, all embedded...
Naumov, Sergej; von Sonntag, Clemens
2011-11-01
Free radicals are common intermediates in the chemistry of ozone in aqueous solution. Their reactions with ozone have been probed by calculating the standard Gibbs free energies of such reactions using density functional theory (Jaguar 7.6 program). O(2) reacts fast and irreversibly only with simple carbon-centered radicals. In contrast, ozone also reacts irreversibly with conjugated carbon-centered radicals such as bisallylic (hydroxycylohexadienyl) radicals, with conjugated carbon/oxygen-centered radicals such as phenoxyl radicals, and even with nitrogen- oxygen-, sulfur-, and halogen-centered radicals. In these reactions, further ozone-reactive radicals are generated. Chain reactions may destroy ozone without giving rise to products other than O(2). This may be of importance when ozonation is used in pollution control, and reactions of free radicals with ozone have to be taken into account in modeling such processes.
Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures
Castellanos-Suarez, Aly J., E-mail: acastell@ivic.gob.v [Centro de Estudios Interdisciplinarios de la Fisica (CEIF), Instituto Venezolano de Investigaciones Cientificas (IVIC), Apartado 21827, Caracas 1020A (Venezuela, Bolivarian Republic of); Garcia-Sucre, Maximo, E-mail: mgs@ivic.gob.v [Centro de Estudios Interdisciplinarios de la Fisica (CEIF), Instituto Venezolano de Investigaciones Cientificas (IVIC), Apartado 21827, Caracas 1020A (Venezuela, Bolivarian Republic of)
2011-03-15
A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.
Gary, Ronald K.
2004-01-01
The concentration dependence of (delta)S term in the Gibbs free energy function is described in relation to its application to reversible reactions in biochemistry. An intuitive and non-mathematical argument for the concentration dependence of the (delta)S term in the Gibbs free energy equation is derived and the applicability of the equation to…
Gibbs Free Energy and Activation Energy of ZrTiAlNiCuSn Bulk Glass Forming Alloys
Jianfei SUN; Jun SHEN; Zhenye ZHU; Gang WANG; Dawei XING; Yulai GAO; Bide ZHOU
2004-01-01
The Gibbs free energy differences between the supercooled liquid and the crystalline mixture for the (Zr52.5Ti5Al10- Ni14.6Cu17.9)(100-x)/100Snx ·(x=0, 1, 2, 3, 4 and 5) glass forming alloys are estimated by introducing the equation proposed by Thompson, Spaepen and Turnbull. It can be seen that the Gibbs free energy differences decrease first as the increases of Sn addition smaller than 3, then followed by a decrease due to the successive addition of Sn larger than 3, indicating that the thermal stabilities of these glass forming alloys increase first and then followed by a decrease owing to the excessive addition of Sn. Furthermore, the activation energy of Zr52.5Ti5Al10Ni14.6Cu17.9 and (Zr5 2.5Ti5 Al10 Ni14.6 Cu 17.9)0.97Sn3 was evaluated by Kissinger equation. It is noted that the Sn addition increases the activation energies for glass transition and crystallization, implying that the higher thermal stability can be obtained by appropriate addition of Sn.
Zhihua Wang
2017-05-01
Full Text Available Crude oil is generally produced with water, and the water cut produced by oil wells is increasingly common over their lifetime, so it is inevitable to create emulsions during oil production. However, the formation of emulsions presents a costly problem in surface process particularly, both in terms of transportation energy consumption and separation efficiency. To deal with the production and operational problems which are related to crude oil emulsions, especially to ensure the separation and transportation of crude oil-water systems, it is necessary to better understand the emulsification mechanism of crude oil under different conditions from the aspects of bulk and interfacial properties. The concept of shearing energy was introduced in this study to reveal the driving force for emulsification. The relationship between shearing stress in the flow field and interfacial tension (IFT was established, and the correlation between shearing energy and interfacial Gibbs free energy was developed. The potential of the developed correlation model was validated using the experimental and field data on emulsification behavior. It was also shown how droplet deformation could be predicted from a random deformation degree and orientation angle. The results indicated that shearing energy as the energy produced by shearing stress working in the flow field is the driving force activating the emulsification behavior. The deformation degree and orientation angle of dispersed phase droplet are associated with the interfacial properties, rheological properties and the experienced turbulence degree. The correlation between shearing stress and IFT can be quantified if droplet deformation degree vs. droplet orientation angle data is available. When the water cut is close to the inversion point of waxy crude oil emulsion, the interfacial Gibbs free energy change decreased and the shearing energy increased. This feature is also presented in the special regions where
Phadke, Sushil; Darshan Shrivastava, Bhakt; Ujle, S. K.; Mishra, Ashutosh; Dagaonkar, N.
2014-09-01
One of the potential driving forces behind a chemical reaction is favourable a new quantity known as the Gibbs free energy (G) of the system, which reflects the balance between these forces. Ultrasonic velocity and absorption measurements in liquids and liquid mixtures find extensive application to study the nature of intermolecular forces. Ultrasonic velocity measurements have been successfully employed to detect weak and strong molecular interactions present in binary and ternary liquid mixtures. After measuring the density and ultrasonic velocity of aqueous solution of 'Borassus Flabellifier' BF and Adansonia digitata And, we calculated Gibb's energy and intermolecular free length. The velocity of ultrasonic waves was measured, using a multi-frequency ultrasonic interferometer with a high degree of accuracy operating Model M-84 by M/s Mittal Enterprises, New Delhi, at a fixed frequency of 2MHz. Natural sample 'Borassus Flabellifier' BF fruit pulp and Adansonia digitata AnD powder was collected from Dhar, District of MP, India for this study.
Kharkats, Yurij I.; Ulstrup, Jens
1999-04-01
We discuss a simple model for the environmental reorganisation Gibbs free energy, Er, in electron transfer between a metalloprotein and a small reaction partner. The protein is represented as a dielectric globule with low dielectric constant, the metal centres as conducting spheres, all embedded in a continuous solvent with high dielectric constant. This model has previously reproduced thermodynamic metalloprotein properties. Er takes an analytic form expressed by a continuous image charge distribution, and depends weakly on the globular radius, indicating that repolarisation at the globule/solvent interface contributes less to these effects than to the work terms and driving force.
Gibbs free-energy difference between the glass and crystalline phases of a Ni-Zr alloy
Ohsaka, K.; Trinh, E. H.; Holzer, J. C.; Johnson, W. L.
1993-01-01
The heats of eutectic melting and devitrification, and the specific heats of the crystalline, glass, and liquid phases have been measured for a Ni24Zr76 alloy. The data are used to calculate the Gibbs free-energy difference, Delta G(AC), between the real glass and the crystal on an assumption that the liquid-glass transition is second order. The result shows that Delta G(AC) continuously increases as the temperature decreases in contrast to the ideal glass case where Delta G(AC) is assumed to be independent of temperature.
Gibbs free energy difference between the undercooled liquid and the beta phase of a Ti-Cr alloy
Ohsaka, K.; Trinh, E. H.; Holzer, J. C.; Johnson, W. L.
1992-01-01
The heat of fusion and the specific heats of the solid and liquid have been experimentally determined for a Ti60Cr40 alloy. The data are used to evaluate the Gibbs free energy difference, delta-G, between the liquid and the beta phase as a function of temperature to verify a reported spontaneous vitrification (SV) of the beta phase in Ti-Cr alloys. The results show that SV of an undistorted beta phase in the Ti60Cr40 alloy at 873 K is not feasible because delta-G is positive at the temperature. However, delta-G may become negative with additional excess free energy to the beta phase in the form of defects.
Dreier, Jens P.; Isele, Thomas; Reiffurth, Clemens; Offenhauser, Nikolas; Kirov, Sergei A.; Dahlem, Markus A.; Herreras, Oscar
2012-01-01
In the evolution of the cerebral cortex, the sophisticated organization in a steady state far away from thermodynamic equilibrium has produced the side effect of two fundamental pathological network events: ictal epileptic activity and spreading depolarization. Ictal epileptic activity describes the partial disruption, and spreading depolarization describes the near-complete disruption of the physiological double Gibbs–Donnan steady state. The occurrence of ictal epileptic activity in patients has been known for decades. Recently, unequivocal electrophysiological evidence has been found in patients that spreading depolarizations occur abundantly in stroke and brain trauma. The authors propose that the ion changes can be taken to estimate relative changes in Gibbs free energy from state to state. The calculations suggest that in transitions from the physiological state to ictal epileptic activity to spreading depolarization to death, the cortex releases Gibbs free energy in a stepwise fashion. Spreading depolarization thus appears as a twilight state close to death. Consistently, electrocorticographic recordings in the core of focal ischemia or after cardiac arrest display a smooth transition from the initial spreading depolarization component to the later ultraslow negative potential, which is assumed to reflect processes in cellular death. PMID:22829393
Albite feldspar dissolution kinetics as a function of the Gibbs free energy at high pCO_2
Hellmann, Roland; Tisserand, Delphine; Renard, François
2008-01-01
We are currently measuring the dissolution kinetics of albite feldspar at 100 deg C in the presence of high levels of dissolved CO_2 (pCO_2 = 9 MPa) as a function of the saturation state of the feldspar (Gibbs free energy of reaction, \\Delta G). The experiments are conducted using a flow through reactor, thereby allowing the dissolution reactions to occur at a fixed pH and at constant, but variable saturation states. Preliminary results indicate that at far-from-equilibrium conditions, the dissolution kinetics of albite are defined by a rate plateau, with R \\approx 5.0 x 10^{-10} mol m^{-2} s^{-1} at -70 -40 kJ mol^{-1}, the rates decrease sharply, revealing a strong inverse relation between the dissolution rate and free energy. Based on the experiments carried out to date, the dissolution rate-free energy data correspond to a highly non-linear and sigmoidal relation, in accord with recent studies.
DOLFING, J; HARRISON, BK
1992-01-01
The Gibbs free energies of formation of various classes of halogenated aromatic compounds were estimated with Benson's method. The data were used to evaluate the potential of these compounds to serve as electron acceptors in anaerobic environments. The results indicate that for (chloro) benzenes, be
DOLFING, J; HARRISON, BK
1992-01-01
The Gibbs free energies of formation of various classes of halogenated aromatic compounds were estimated with Benson's method. The data were used to evaluate the potential of these compounds to serve as electron acceptors in anaerobic environments. The results indicate that for (chloro) benzenes,
Tiago Campos Pereira
2007-01-01
Full Text Available The RNA interference (RNAi technique is a recent technology that uses double-stranded RNA molecules to promote potent and specific gene silencing. The application of this technique to molecular biology has increased considerably, from gene function identification to disease treatment. However, not all small interfering RNAs (siRNAs are equally efficient, making target selection an essential procedure. Here we present Strand Analysis (SA, a free online software tool able to identify and classify the best RNAi targets based on Gibbs free energy (deltaG. Furthermore, particular features of the software, such as the free energy landscape and deltaG gradient, may be used to shed light on RNA-induced silencing complex (RISC activity and RNAi mechanisms, which makes the SA software a distinct and innovative tool.
Isham, M. A.
1992-01-01
Silicon carbide and silicon nitride are considered for application as structural materials and coating in advanced propulsion systems including nuclear thermal. Three-dimensional Gibbs free energy were constructed for reactions involving these materials in H2 and H2/H2O. Free energy plots are functions of temperature and pressure. Calculations used the definition of Gibbs free energy where the spontaneity of reactions is calculated as a function of temperature and pressure. Silicon carbide decomposes to Si and CH4 in pure H2 and forms a SiO2 scale in a wet atmosphere. Silicon nitride remains stable under all conditions. There was no apparent difference in reaction thermodynamics between ideal and Van der Waals treatment of gaseous species.
HYOUNGJU YOON
2013-02-01
Full Text Available It is required that the pH of the sump solution should be above 7.0 to retain iodine in a liquid phase and be within the material compatibility constraints under LOCA condition of PWR. The pH of the sump solution can be determined by conventional chemical equilibrium constants or by the minimization of Gibbs free energy. The latter method developed as a computer code called SOLGASMIX-PV is more convenient than the former since various chemical components can be easily treated under LOCA conditions. In this study, SOLGASMIX-PV code was modified to accommodate the acidic and basic materials produced by radiolysis reactions and to calculate the pH of the sump solution. When the computed pH was compared with measured by the ORNL experiment to verify the reliability of the modified code, the error between two values was within 0.3 pH. Finally, two cases of calculation were performed for the SKN 3&4 and UCN 1&2. As results, pH of the sump solution for the SKN 3&4 was between 7.02 and 7.45, and for the UCN 1&2 plant between 8.07 and 9.41. Furthermore, it was found that the radiolysis reactions have insignificant effects on pH because the relative concentrations of HCl, HNO3, and Cs are very low.
Yoon, Hyoung Ju [Dept. of Nuclear Engineering, University of Kyunghee, Seoul (Korea, Republic of)
2013-02-15
It is required that the pH of the sump solution should be above 7.0 to retain iodine in a liquid phase and be within the material compatibility constraints under LOCA condition of PWR. The pH of the sump solution can be determined by conventional chemical equilibrium constants or by the minimization of Gibbs free energy. The latter method developed as a computer code called SOLGASMIX-PV is more convenient than the former since various chemical components can be easily treated under LOCA conditions. In this study, SOLGASMIX-PV code was modified to accommodate the acidic and basic materials produced by radiolysis reactions and to calculate the pH of the sump solution. When the computed pH was compared with measured by the ORNL experiment to verify the reliability of the modified code, the error between two values was within 0.3 pH. Finally, two cases of calculation were performed for the SKN 3 and 4 and UCN 1 and 2. As results, pH of the sump solution for the SKN 3 and 4 was between 7.02 and 7.45, and for the UCN 1 and 2 plant between 8.07 and 9.41. Furthermore, it was found that the radiolysis reactions have insignificant effects on pH because the relative concentrations of HCl, HNO3, and Cs are very low.
Size fluctuations of near critical and Gibbs free energy for nucleation of BDA on Cu(001)
Schwarz, Daniel; van Gastel, Raoul; Zandvliet, Henricus J.W.; Poelsema, Bene
2012-01-01
We present a low-energy electron microscopy study of nucleation and growth of BDA on Cu(001) at low supersaturation. At sufficiently high coverage, a dilute BDA phase coexists with c(8×8) crystallites. The real-time microscopic information allows a direct visualization of near-critical nuclei,
The combination of transformed and constrained Gibbs energies.
Blomberg, Peter B A; Koukkari, Pertti S
2009-08-01
Gibbs free energy is the thermodynamic potential representing the fundamental equation at constant temperature, pressure, and molar amounts. Transformed Gibbs energies are important for biochemical systems because the local concentrations within cell compartments cannot yet be determined accurately. The method of Constrained Gibbs Energies adds kinetic reaction extent limitations to the internal constraints of the system thus extending the range of applicability of equilibrium thermodynamics from predefined constraints to dynamic constraints, e.g., adding time-dependent constraints of irreversible chemical change. In this article, the implementation and use of Transformed Gibbs Energies in the Gibbs energy minimization framework is demonstrated with educational examples. The combined method has the advantage of being able to calculate transient thermodynamic properties during dynamic simulation.
Enzyme Catalysis and the Gibbs Energy
Ault, Addison
2009-01-01
Gibbs-energy profiles are often introduced during the first semester of organic chemistry, but are less often presented in connection with enzyme-catalyzed reactions. In this article I show how the Gibbs-energy profile corresponds to the characteristic kinetics of a simple enzyme-catalyzed reaction. (Contains 1 figure and 1 note.)
Enzyme Catalysis and the Gibbs Energy
Ault, Addison
2009-01-01
Gibbs-energy profiles are often introduced during the first semester of organic chemistry, but are less often presented in connection with enzyme-catalyzed reactions. In this article I show how the Gibbs-energy profile corresponds to the characteristic kinetics of a simple enzyme-catalyzed reaction. (Contains 1 figure and 1 note.)
Silvério, Sara C.; Rodríguez, Oscar; Teixeira, J. A.; Macedo, Eugénia
2010-01-01
The Gibbs free energy of transfer of a suitable hydrophobic probe can be regarded as a measure of the relative hydrophobicity of the different phases. The methylene group (CH2) can be considered hydrophobic, and thus be a suitable probe for hydrophobicity. In this work, the partition coefficients of a series of five dinitrophenylated-amino acids were experimentally determined, at 23 °C, in three different tie-lines of the biphasic systems: (UCON + K2HPO4), (UCON + potassium phosph...
Dolfing, Jan; Novak, Igor
2015-02-01
The sequence of redox reactions in the natural environment generally follows the electron affinity of the electron acceptors present and can be rationalized by the redox potentials of the appropriate half-reactions. Answering the question how halogenated aromatics fit into this sequence requires information on their Gibbs free energy of formation values. In 1992 Gibbs free energy data for various classes of halogenated aromatic compounds were systematically explored for the first time based on Benson's group contribution method. Since then more accurate quantum chemical calculation methods have become available. Here we use these methods to estimate enthalpy and Gibbs free energy of formation values of all chlorinated and brominated phenols. These data and similar state-of-the-art datasets for halogenated benzenes and benzoates were then used to calculate two-electron redox potentials of halogenated aromatics for standard conditions and for pH 7. The results underline the need to take speciation into consideration when evaluating redox potentials at pH 7 and highlight the fact that halogenated aromatics are excellent electron acceptors in aqueous environments.
Li, Hui-Yu; Guo, Xing-Min
2015-02-01
Aiming to fill the thermodynamic blank in CaO-FeO-Fe2O3 system, the determination of the Gibbs free energy of formation from elements for ternary Ca4Fe9O17 was carried out using a solid-state galvanic cell with air and calcium zirconate material, respectively, as the reference electrode and electrolyte. The ternary system Ca2Fe2O5-CaFe2O4-Ca4Fe9O17 was selected as the measuring electrode and its equilibrium was confirmed. The essential thermodynamic data of Ca2Fe2O5 and CaFe2O4 were cited from the reassessed data from a previous investigation. The reversible electromotive forces of the cell were determined from 1273 K to 1473 K (1000 °C to 1200 °C). The Gibbs free energy of formation from elements for Ca4Fe9O17 was derived and given by: The increment of enthalpy and entropy of formation from elements for Ca4Fe9O17 at 298 K (25 °C) are calculated to be and . The Ellingham diagram was developed in temperature range 1273 K to 1473 K (1000 °C to 1200 °C). The oxygen potential of Ca4Fe9O17 was found to be slightly higher than CaFe2O4 and much higher than Ca2Fe2O5.
Lomzov, Alexander A; Vorobjev, Yury N; Pyshnyi, Dmitrii V
2015-12-10
A molecular dynamics simulation approach was applied for the prediction of the thermal stability of oligonucleotide duplexes. It was shown that the enthalpy of the DNA/DNA complex formation could be calculated using this approach. We have studied the influence of various simulation parameters on the secondary structure and the hybridization enthalpy value of Dickerson-Drew dodecamer. The optimal simulation parameters for the most reliable prediction of the enthalpy values were determined. The thermodynamic parameters (enthalpy and entropy changes) of a duplex formation were obtained experimentally for 305 oligonucleotides of various lengths and GC-content. The resulting database was studied with molecular dynamics (MD) simulation using the optimized simulation parameters. Gibbs free energy changes and the melting temperatures were evaluated using the experimental correlation between enthalpy and entropy changes of the duplex formation and the enthalpy values calculated by the MD simulation. The average errors in the predictions of enthalpy, the Gibbs free energy change, and the melting temperature of oligonucleotide complexes were 11%, 10%, and 4.4 °C, respectively. We have shown that the molecular dynamics simulation gives a possibility to calculate the thermal stability of native DNA/DNA complexes a priori with an unexpectedly high accuracy.
Maggi, F.; Riley, W. J.
2016-12-01
We propose a mathematical framework to introduce the concept of differential free energy of activation in enzymatically catalyzed reactions, and apply it to N uptake by microalgae and bacteria. This framework extends the thermodynamic capabilities of the classical transition-state theory in and harmonizes the consolidated definitions of kinetic parameters with their thermodynamic and physical meaning. Here, the activation energy is assumed to be a necessary energetic level for equilibrium complexation between reactants and activated complex; however, an additional energy contribution is required for the equilibrium activated complex to release reaction products. We call this "differential free energy of activation"; it can be described by a Boltzmann distribution, and corresponds to a free energy level different from that of complexation. Whether this level is above or below the free energy of activation depends on the reaction, and defines energy domains that correspond to "superactivated", "activated", and "subactivated" complexes. The activated complex reaching one of those states will eventually release the products from an energy level different than that of activation. The concept of differential free energy of activation was tested on 57 independent experiments of NH4+ and NO3- uptake by various microalgae and bacteria at temperatures ranging between 1 and 45oC. Results showed that the complexation equilibrium always favored the activated complex, but the differential energy of activation led to an apparent energy barrier consistent with observations. Temperature affected all energy levels within this framework but did not alter substantially these thermodynamic features. Overall the approach: (1) provides a thermodynamic and mathematical link between Michaelis-Menten and rate constants; (2) shows that both kinetic parameters can be described or approximated by Arrhenius' like equations; (3) describes the likelihood of formation of sub-, super-, and
Illustrating Enzyme Inhibition Using Gibbs Energy Profiles
Bearne, Stephen L.
2012-01-01
Gibbs energy profiles have great utility as teaching and learning tools because they present students with a visual representation of the energy changes that occur during enzyme catalysis. Unfortunately, most textbooks divorce discussions of traditional kinetic topics, such as enzyme inhibition, from discussions of these same topics in terms of…
Sobolev, S. L., E-mail: sobolev@icp.ac.ru [Russian Academy of Sciences, Institute of Problems of Chemical Physics (Russian Federation)
2017-03-15
An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V{sub D}, where V{sub D} is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V{sub D}, the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.
Lima da Silva, Aline; Müller, Iduvirges Lourdes
Solid oxide fuel cells (SOFCs) are very flexible, unlike other fuel cells. In principle, SOFCs can operate on almost any fuel. Currently much effort is invested in the development of SOFCs for portable applications operating directly on liquid fuels such as methanol and ethanol rather than hydrogen. However, there are very few publications dealing with the direct use of glycerol in SOFCs for portable systems. A recently published study shows that the performance achieved for an SOFC fueled by pure glycerol is quite interesting even when there is a thick electrolyte membrane, indicating that glycerol is a promising fuel for portable applications. For this reason a thermodynamic analysis for SOFCs operating directly on glycerol fuel is performed in the present study. The Gibbs energy minimization method computes the equilibrium compositions of the anode gas mixture, carbon deposition boundaries and electromotive forces (EMFs) as a function of fuel utilization and temperature. Moreover, the minimum amounts of H 2O, CO 2 (direct internal reforming case) and air (partial oxidation case) to be added to glycerol in the feedstock to avoid carbon deposition at the open circuit voltage (OCV) are calculated. Finally, a thermodynamic analysis is performed, taking into account the experimental conditions employed in a previous study. Experimental observations concerning carbon deposition in an SOFC operating on glycerol can be explained by the theoretical analysis developed in the present study. Additionally, the effect of mixed electronic-ionic conduction of the electrolyte on carbon deposition at the anode is discussed based on the thermodynamic analysis of the C-O system.
Marjolin, Aude; Gourlaouen, Christophe; Clavaguéra, Carine; Ren, Pengyu Y; Piquemal, Jean-Philip; Dognon, Jean-Pierre
2014-10-01
The hydration free energies, structures, and dynamics of open- and closed-shell trivalent lanthanide and actinide metal cations are studied using molecular dynamics simulations (MD) based on a polarizable force field. Parameters for the metal cations are derived from an ab initio bottom-up strategy. MD simulations of six cations solvated in bulk water are subsequently performed with the AMOEBA polarizable force field. The calculated first-and second shell hydration numbers, water residence times, and free energies of hydration are consistent with experimental/theoretical values leading to a predictive modeling of f-elements compounds.
Kleeman, W P; Bailey, L C
1988-06-01
An in vitro method utilizing high-performance liquid chromatography (HPLC) was developed in order to investigate the adsorptive process between activated charcoal and various drugs and toxic chemicals by measuring their Gibbs free energy of adsorption from various acetonitrile:water mobile phases. This report details the derivation and validation of the equation for calculating the Gibbs free energy of liquid-solid adsorption via HPLC. The derived equation incorporates the following experimental parameters: specific surface area of the adsorbent, specific retention volume of the solute, molar volume of the mobile phase, and surface concentration of the solute in a predefined standard state. This equation was validated by means of a closed thermodynamic cycle composed of three segments. Each segment represents a different physical process: gas-solid adsorption of methyl iodide on activated charcoal, gas-liquid solution of methyl iodide in n-hexadecane, and liquid-solid adsorption of methyl iodide on activated charcoal from n-hexadecane. The Gibbs free energy for each of these thermodynamic processes was determined by the appropriate chromatographic technique. Since the cycle did not balance because it did not account for the interaction of n-hexadecane and activated charcoal, it was altered to include a gas-liquid-solid chromatographic technique. When the Gibbs free energies of solution and gas-solid adsorption determined by this chromatographic technique were incorporated into the cycle, the resulting imbalance was only 0.213 kJ/mol (1.1%), thereby validating the derived equation.
Silverio, Sara C. [LSRE - Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n. 4200-465 Porto (Portugal); IBB - Institute for Biotechnology and Bioengineering, Centre for Biological Engineering, University of Minho, Campus de Gualtar, 4710-057 Braga (Portugal); Rodriguez, Oscar [LSRE - Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n. 4200-465 Porto. Portugal (Portugal); Teixeira, Jose A. [IBB - Institute for Biotechnology and Bioengineering, Centre for Biological Engineering, University of Minho, Campus de Gualtar, 4710-057 Braga (Portugal); Macedo, Eugenia A., E-mail: eamacedo@fe.up.p [LSRE - Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n. 4200-465 Porto (Portugal)
2010-08-15
The Gibbs free energy of transfer of a suitable hydrophobic probe can be regarded as a measure of the relative hydrophobicity of the different phases. The methylene group (CH{sub 2}) can be considered hydrophobic, and thus be a suitable probe for hydrophobicity. In this work, the partition coefficients of a series of five dinitrophenylated-amino acids were experimentally determined, at 23 {sup o}C, in three different tie-lines of the biphasic systems: (UCON + K{sub 2}HPO{sub 4}), (UCON + potassium phosphate buffer, pH 7), (UCON + KH{sub 2}PO{sub 4}), (UCON + Na{sub 2}HPO{sub 4}), (UCON + sodium phosphate buffer, pH 7), and (UCON + NaH{sub 2}PO{sub 4}). The Gibbs free energy of transfer of CH{sub 2} units were calculated from the partition coefficients and used to compare the relative hydrophobicity of the equilibrium phases. The largest relative hydrophobicity was found for the ATPS formed by dihydrogen phosphate salts.
Gibbs energy of formation of cobalt divanadium tetroxide
Jacob, K. T.; Pandit, S. Shashidhara
1985-11-01
The Gibbs energy of formation of V 2O 3-saturated spinel CoV 2O 4 has been measured in the temperature range 900-1700 K using a solid state galvanic cell, which can be represented as Pt, Co + CoV 2O 4 + {V2O3}/{(CaO)}{ZrO2}/{Co} + CoO, Pt. The standard free energy of formation of cobalt vanadite from component oxides can be represented as CoO (rs) + V 2O 3 (cor) → CoV 2O 4 (sp), ΔG° = -30,125 - 5.06 T (± 150) J mole -1. Cation mixing on crystallographically nonequivalent sites of the spinel is responsible for the decrease in free energy with increasing temperature. A correlation between "second law" entropies of formation of cubic 2-3 spinels from component oxides with rock salt and corundum structures and cation distribution is presented. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that copper vanadite is unstable.
First-Year University Chemistry Textbooks' Misrepresentation of Gibbs Energy
Quilez, Juan
2012-01-01
This study analyzes the misrepresentation of Gibbs energy by college chemistry textbooks. The article reports the way first-year university chemistry textbooks handle the concepts of spontaneity and equilibrium. Problems with terminology are found; confusion arises in the meaning given to [delta]G, [delta][subscript r]G, [delta]G[degrees], and…
First-Year University Chemistry Textbooks' Misrepresentation of Gibbs Energy
Quilez, Juan
2012-01-01
This study analyzes the misrepresentation of Gibbs energy by college chemistry textbooks. The article reports the way first-year university chemistry textbooks handle the concepts of spontaneity and equilibrium. Problems with terminology are found; confusion arises in the meaning given to [delta]G, [delta][subscript r]G, [delta]G[degrees], and…
Consistent estimation of Gibbs energy using component contributions.
Noor, Elad; Haraldsdóttir, Hulda S; Milo, Ron; Fleming, Ronan M T
2013-01-01
Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.
Consistent estimation of Gibbs energy using component contributions.
Elad Noor
Full Text Available Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.
Pimentel-Filho, Natan de Jesus; Martins, Mayra Carla de Freitas; Nogueira, Guilherme Bicalho; Mantovani, Hilário Cuquetto; Vanetti, Maria Cristina Dantas
2014-11-03
Staphylococcus aureus is an opportunistic pathogen often multidrug-resistant that not only causes a variety of human diseases, but also is able to survive on biotic and abiotic surfaces through biofilm communities. The best way to inhibit biofilm establishment is to prevent cell adhesion. In the present study, subinhibitory concentrations of the bacteriocins bovicin HC5 and nisin were tested for their capability to interfere with the adhesion of S. aureus to polystyrene. Subinhibitory dosages of the bacteriocins reduced cell adhesion and this occurred probably due to changes in the hydrophobicity of the bacterial cell and polystyrene surfaces. After treatment with bovicin HC5 and nisin, the surfaces became more hydrophilic and the free energy of adhesion (∆G(adhesion)) between bacteria and the polystyrene surface was unfavorable. The transcriptional level of selected genes was assessed by RT-qPCR approach, revealing that the bacteriocins affected the expression of some important biofilm associated genes (icaD, fnbA, and clfB) and rnaIII, which is involved in the quorum sensing mechanism. The conditioning of food-contact surfaces with bacteriocins can be an innovative and powerful strategy to prevent biofilms in the food industry. The results are relevant for food safety as they indicate that bovicin HC5 and nisin can inhibit bacterial adhesion and consequent biofilm establishment, since cell adhesion precedes biofilm formation.
Holmes, Richard D.; O'Neill, Hugh St. C.; Arculus, Richard J.
1986-11-01
Galvanic cells with oxygen-specific solid electrolytes made of calcia-stabilized zirconia have been used to make equilibrium measurements of the standard Gibbs free energy of formation, ΔfG0m,( T), for copper (I) oxide (Cu 2O), nickel (II) oxide (NiO), cobalt (II) oxide (CoO), and wüstite (Fe xO) over the temperature range from 900-1400 K. The measured values of ΔfG0m at 1300 K are -73950, -123555, -142150, and -179459 J · mol -1 for Cu 2O, NiO, CoO, and Fe 0.947O, respectively. The precision of these measurements is ± 30-60 J · mol -1, and their absolute accuracy is estimated to be ± 100-200 J·mol -1. Using values of -76.557, -94.895, -79.551, and -71.291 J · K -1 · mol -1 for the entropies of formation, ΔfSm0, (298.15 K), the calculated enthalpies of formation, ΔfHm0, (298.15 K), are -170508, -240110, -237390, and -266458 J · mol -1 for Cu 2O, NiO, CoO, and Fe 0.947O, respectively. These values of ΔfSm0 (298.15 K) and ΔfHm0 (298.15 K) are in good agreement with the best available calorimetric measurements.
From slump loss to Gibbs' free energy
Jensen, Ole Mejlhede; Diamond, Sidney
2006-01-01
In its classical form, the science of construction materials is a descriptive, empirical discipline related to certain types of materials, e.g. the study of the properties of wood, steel, concrete and plastics. This traditional division of the science into the separate study of the different mate...
Illustrating the Effect of pH on Enzyme Activity Using Gibbs Energy Profiles
Bearne, Stephen L.
2014-01-01
Gibbs energy profiles provide students with a visual representation of the energy changes that occur during enzyme catalysis, making such profiles useful as teaching and learning tools. Traditional kinetic topics, such as the effect of pH on enzyme activity, are often not discussed in terms of Gibbs energy profiles. Herein, the symbolism of Gibbs…
Illustrating the Effect of pH on Enzyme Activity Using Gibbs Energy Profiles
Bearne, Stephen L.
2014-01-01
Gibbs energy profiles provide students with a visual representation of the energy changes that occur during enzyme catalysis, making such profiles useful as teaching and learning tools. Traditional kinetic topics, such as the effect of pH on enzyme activity, are often not discussed in terms of Gibbs energy profiles. Herein, the symbolism of Gibbs…
Bozlee, Brian J.
2007-01-01
The impact of raising Gibbs energy of the enzyme-substrate complex (G[subscript 3]) and the reformulation of the Michaelis-Menten equation are discussed. The maximum velocity of the reaction (v[subscript m]) and characteristic constant for the enzyme (K[subscript M]) will increase with increase in Gibbs energy, indicating that the rate of reaction…
李春喜; 王子镐; 宋红艳
2001-01-01
Based on the thermodynamic definition of surface tension and UNIQUAC Gibbs free energy model,a two-parameter surface tension equation is derived. σm=∑ixiσi-RT∑i(xiqi)/(∑jθjτji)∑jθj(τji)/(A)T,P,x In this equation,the first term represents pure component contribution to the surface tension of a mixture,and the second term represents the excess surface tension due to the molecular interaction difference between different components. For ideal solution,the excess surface tension term disappeared,and the surface tension is equivalent to that of pure component averaged with mole fraction.The feasibility of the new equation has been tested for 90 binary and 15 multicomponent systems and the AAD is found to be 0.44% and 1.57%, respectively. Results showed good precision by using the developed equation with simplicity and reliability for practical uses.%根据表面张力的热力学定义以及UNIQUAC过量Gibbs自由能表达式,推导出了一个新的两参数表面张力方程，σm=∑ixiσi-RT∑i(xiqi)/(∑jθjτji)∑jθj(τji)/(A)T,P,x该方程第一项为纯组分对液体混合物表面张力的贡献，第二项为不同组分间作用力的差异引起的过量表面张力。对于理想溶液，过量表面张力项为零，因此，混合物的表面张力等于各个纯组分表面张力的摩尔分数平均值。通过90个二元体系和15个多元体系表面张力的计算，对新方程的性能进行了测试，发现其对二元体系和多元体系计算的总平均相对偏差分别为0.44%和1.57%。结果表明，该模型计算精度高，公式简单实用，而且对各种体系具有广泛的适应性。
Determination of Gibbs energies of formation in aqueous solution using chemical engineering tools.
Toure, Oumar; Dussap, Claude-Gilles
2016-08-01
Standard Gibbs energies of formation are of primary importance in the field of biothermodynamics. In the absence of any directly measured values, thermodynamic calculations are required to determine the missing data. For several biochemical species, this study shows that the knowledge of the standard Gibbs energy of formation of the pure compounds (in the gaseous, solid or liquid states) enables to determine the corresponding standard Gibbs energies of formation in aqueous solutions. To do so, using chemical engineering tools (thermodynamic tables and a model enabling to predict activity coefficients, solvation Gibbs energies and pKa data), it becomes possible to determine the partial chemical potential of neutral and charged components in real metabolic conditions, even in concentrated mixtures.
Guodong Liu
2014-01-01
Full Text Available Soil drought, that can be enhanced by global warming increases ammonia (NH_{3} volatilization. This laboratory study was conducted with two soils: Krome Gravelly Loam (KGL from Florida and Warden Silt Loam (WSL from Washington State and two fertilizers: Ammonium sulfate [(NH_{4}_{2}SO_{4}] or ammonium nitrate (NH_{4}NO_{3}. Two water regimes including 20 and 80% Field Capacity (FC were used at 20°C which is the average temperature in the potato growing season in Washington State. The data demonstrated that variation in NH_{3} volatilization subject to different soil water regimes can be explained by changes in Gibbs free energy of Nitrogen (N fertilization in soils with varying water contents. The absolute values of Gibbs free energy of (NH_{4}_{2}SO_{4} or NH_{4}NO_{3} applied to soil at 20% FC soil water regime were 5-fold greater than at 80% FC. Accordingly, the equilibrium constant (K of deprotonation of ammonium ions in soil solutions at 20% FC was 3,000- or 50-fold greater than that at 80% FC for (NH_{4}_{2}SO_{4} or NH_{4}NO_{3}, respectively. Nitrogen loss via NH_{3} volatilization was 4-to 7-fold greater at 20% FC than that at 80% FC. This study suggests potential acceleration of NH_{3} volatilization from soils under drought. Therefore, optimal water management is critical to mitigate NH_{3} volatilization from agricultural soils.
Tuck, Adrian F
2017-08-24
There is no widely agreed definition of entropy, and consequently Gibbs energy, in open systems far from equilibrium. One recent approach has sought to formulate an entropy and Gibbs energy based on observed scale invariances in geophysical variables, particularly in atmospheric quantities, including the molecules constituting stratospheric chemistry. The Hamiltonian flux dynamics of energy in macroscopic open nonequilibrium systems maps to energy in equilibrium statistical thermodynamics, and corresponding equivalences of scale invariant variables with other relevant statistical mechanical variables such as entropy, Gibbs energy, and 1/(kBoltzmannT), are not just formally analogous but are also mappings. Three proof-of-concept representative examples from available adequate stratospheric chemistry observations-temperature, wind speed and ozone-are calculated, with the aim of applying these mappings and equivalences. Potential applications of the approach to scale invariant observations from the literature, involving scales from molecular through laboratory to astronomical, are considered. Theoretical support for the approach from the literature is discussed.
A Reaction Method for Estimating Gibbs Energy and Enthalpy of Formation of Complex Minerals
Li, Ruibing; Zhang, Tingan; Liu, Yan; Kuang, Shibo
2017-04-01
New and updated thermodynamic data for simple binary compounds are readily available from both experimental measurements and theoretical calculations. Based on these available data, an approach is proposed to predict Gibbs energies and enthalpies of formation for complex minerals of metallurgical, chemical, and other industrial importance. The approach assumes that complex minerals are formed from binary composite oxides, which in turn, are formed from individual pure oxides. The validity of this approach is examined by comparing the calculated values of Gibbs energies and enthalpies against the experimentally measured ones reported in literature. The results show that for typical complex minerals with available experimental data, the calculated results exhibit an average residual of 0.51 pct for Gibbs energies and 0.52 pct for enthalpies, compared to the experimental results. This new approach thus correlates well with experimental approaches and can be applied to most of the complex minerals.
Gibbs energies of formation of the intermetallic compounds of U-Sn system
Pattanaik, Ashit K.; Kandan, R. [Fuel Chemistry Group, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India); Nagarajan, K., E-mail: knag@igcar.gov.in [Fuel Chemistry Group, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India); Vasudeva Rao, P.R. [Fuel Chemistry Group, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India)
2013-02-25
Highlights: Black-Right-Pointing-Pointer Gibbs energies of formation of the intermetallic compounds, USn{sub 3}, U{sub 3}Sn{sub 7}, USn{sub 2} and USn were determined by using high temperature molten salt galvanic cell electromotive force method. Black-Right-Pointing-Pointer The Gibbs energies of formation of USn{sub 3}, U{sub 3}Sn{sub 7}, USn{sub 2} and USn with respect to {alpha}-U and liquid Sn, in the temperature range 682-905 K were determined to be -172.8 + 0.061 T, -527.8 + 0.200 T, -174.9 + 0.073 T and -176.9 + 0.064 T kJ mol{sup -1}, respectively. Black-Right-Pointing-Pointer Gibbs energy formation of the U{sub 3}Sn{sub 7}, USn{sub 2} and USn are being reported for the first time. - Abstract: Gibbs energies of formation of the intermetallic compounds, USn{sub 3}, U{sub 3}Sn{sub 7}, USn{sub 2}, and USn were determined by using high temperature molten salt galvanic cells: U(s)//UCl{sub 3} in LiCl-KCl (eutectic)//U-Sn alloy, where pure uranium was used as one of the electrodes and a two phase alloy of uranium and tin as the other. The two phase alloys used in cells I, II, III and IV as the electrodes were Left-Pointing-Angle-Bracket USn{sub 3} Right-Pointing-Angle-Bracket + {l_brace}Sn{r_brace}, Left-Pointing-Angle-Bracket U{sub 3}Sn{sub 7} + USn{sub 3} Right-Pointing-Angle-Bracket , Left-Pointing-Angle-Bracket USn{sub 2} + U{sub 3}Sn{sub 7} Right-Pointing-Angle-Bracket and Left-Pointing-Angle-Bracket USn + USn{sub 2} Right-Pointing-Angle-Bracket , respectively. The Gibbs energies of formation ({Delta}{sub f}G{sup 0}) of USn{sub 3}, U{sub 3}Sn{sub 7}, USn{sub 2} and USn with respect to {alpha}-U and liquid Sn, in the temperature range 682-905 K, were determined to be given by (table) The Gibbs energy of formation for U{sub 3}Sn{sub 7}, USn{sub 2} and USn have been obtained for the first time.
Hanson, Robert M.; Riley, Patrick; Schwinefus, Jeff; Fischer, Paul J.
2008-01-01
The use of qualitative graphs of Gibbs energy versus temperature is described in the context of chemical demonstrations involving phase changes and colligative properties at the general chemistry level. (Contains 5 figures and 1 note.)
Perturbative Interpretation of Adaptive Thouless-Anderson-Palmer Free Energy
Yasuda, Muneki; Takahashi, Chako; Tanaka, Kazuyuki
2016-07-01
In conventional well-known derivation methods for the adaptive Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are difficult to mathematically justify except in some mean-field models, must be made. Here, we present a new adaptive TAP free energy derivation method. Using this derivation technique, without any special assumptions, the adaptive TAP free energy can be simply obtained as a high-temperature expansion of the Gibbs free energy.
A Short Essay on the Uses of Free Energy
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…
Plyasunov, Andrey V.; Shock, Everett L.
2000-08-01
Experimental results of phase equilibria studies at elevated temperatures for more than twenty hydrocarbon-water systems were uniformly correlated within the framework of the Peng-Robinson-Stryjek-Vera equation of state in combination with simple mixing rules. This treatment allows evaluation of the Gibbs energy of hydration for many alkanes, 1-alkenes, cycloalkanes (derivatives of cyclohexane) and alkylbenzenes up to 623 K at saturated water vapor pressure and up to 573 K at 50 MPa. Results for homologous series show regular changes with increasing carbon number, and confirm the applicability of the group contribution approach to the Gibbs energy of hydration of hydrocarbons at elevated temperatures. The temperature dependence of group contributions to the Gibbs energy of hydration were determined for CH 3, CH 2, and CH in aliphatic hydrocarbons; C=C and H for alkenes; c-CH 2 and c-CH in cycloalkanes; and CH ar and C ar in alkylbenzenes (or aromatic hydrocarbons). Close agreement between calculated and experimental results suggests that this approach provides reasonable estimates of Gibbs energy of hydration for many alkanes, 1-alkenes, alkyl cyclohexanes and alkylbenzenes at temperatures up to 623 K and pressures up to 50 MPa.
Luetich, J J
2001-01-01
A comparison of three methods to write the Gibbs energy: the algebraic procedure to obtain the transformed composition variables introduced by Barbosa and Doherty, the classical non-stoichiometric formulation discussed by Smith and Missen, and the use of Legendre transformations suggested by Alberty. This paper is the second member of a tetralogy conceived to give insight into the concept of microscopic reversibility.
A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace
Kruskopf, Ari; Visuri, Ville-Valtteri
2017-08-01
In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.
Force Field Benchmark of Organic Liquids. 2. Gibbs Energy of Solvation.
Zhang, Jin; Tuguldur, Badamkhatan; van der Spoel, David
2015-06-22
Quantitative prediction of physical properties of liquids is a longstanding goal of molecular simulation. Here, we evaluate the predictive power of the Generalized Amber Force Field (Wang et al. J. Comput. Chem. 2004, 25, 1157-1174) for the Gibbs energy of solvation of organic molecules in organic solvents using the thermodynamics integration (TI) method. The results are compared to experimental data, to a model based on quantitative structure property relations (QSPR), and to the conductor-like screening models for realistic solvation (COSMO-RS) model. Although the TI calculations yield slightly better correlation to experimental results than the other models, in all fairness we should conclude that the difference between the models is minor since both QSPR and COSMO-RS yield a slightly lower RMSD from that of the experiment (<3.5 kJ/mol). By analyzing which molecules (either as solvents or solutes) are outliers in the TI calculations, we can pinpoint where additional parametrization efforts are needed. For the force field based TI calculations, deviations from the experiment occur in particular when compounds containing nitro or ester groups are solvated into other liquids, suggesting that the interaction between these groups and solvents may be too strong. In the COSMO-RS calculations, outliers mainly occur when compounds containing (in particular aromatic) rings are solvated despite using a ring correction term in the calculations.
Free energies of the Potts model on a Cayley tree
Rozikov, U. A.; Rakhmatullaev, M. M.
2017-01-01
For the Potts model on the Cayley tree, we obtain some explicit formulas for the free energies and entropies in the case of vector-valued boundary conditions. These formulas include translation-invariant, periodic, and Dobrushin-like boundary conditions and also those corresponding to weakly periodic Gibbs measures.
Gibbs Paradox and Similarity Principle
Lin, Shu-Kun
2008-01-01
Adding -lnN! term to the accepted entropy formula will immediately make the entropy function nonadditive and sometimes negative. As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: the thermodynamic entropy of mixing is always zero and the Gibbs free energy change is also always zero during the formation of any ideal mixture of gases, liquids, solids or solutions, whether their components are different or identical. However, information loss is observed and must be the exclusive driving force of these spontaneous processes. Information is defined and calculated as the amount of the compressed data. Information losses due to dynamic motion and static symmetric structure formation are defined as two kinds of entropies-dynamic entropy and static entropy, respectively. Entropy is defined and calculated as the logarithm of the symmetry number. There are three laws of information theory, where the first and the second laws are analogs of the two thermod...
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
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
Harvey, J.-P.; Gheribi, A. E.; Chartrand, P.
2011-08-01
The design of multicomponent alloys used in different applications based on specific thermo-physical properties determined experimentally or predicted from theoretical calculations is of major importance in many engineering applications. A procedure based on Monte Carlo simulations (MCS) and the thermodynamic integration (TI) method to improve the quality of the predicted thermodynamic properties calculated from classical thermodynamic calculations is presented in this study. The Gibbs energy function of the liquid phase of the Cu-Zr system at 1800 K has been determined based on this approach. The internal structure of Cu-Zr melts and amorphous alloys at different temperatures, as well as other physical properties were also obtained from MCS in which the phase trajectory was modeled by the modified embedded atom model formalism. A rigorous comparison between available experimental data and simulated thermo-physical properties obtained from our MCS is presented in this work. The modified quasichemical model in the pair approximation was parameterized using the internal structure data obtained from our MCS and the precise Gibbs energy function calculated at 1800 K from the TI method. The predicted activity of copper in Cu-Zr melts at 1499 K obtained from our thermodynamic optimization was corroborated by experimental data found in the literature. The validity of the amplitude of the entropy of mixing obtained from the in silico procedure presented in this work was analyzed based on the thermodynamic description of hard sphere mixtures.
Fluctuation Bounds For Interface Free Energies in Spin Glasses
Arguin, L.-P.; Newman, C. M.; Stein, D. L.; Wehr, J.
2014-07-01
We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.
Behzad Nematollahi; Mehran Rezaei; Ebrahim Nemati Lay; Majid Khajenoori
2012-01-01
Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon for-mation.The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure (1-25 atm),temperature (600-1300 K),carbon dioxide to methane ratio (0-2) and oxygen to methane ratio (0-1).The thermodynamic results were compared with the results obtained over a Ru supported catalyst.The results revealed that by increasing the reaction pressure methane conversion decreased.Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane.The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.
Aspiala, M., E-mail: markus.aspiala@aalto.fi; Sukhomlinov, D., E-mail: dmitry.sukhomlinov@aalto.fi; Taskinen, P., E-mail: pekka.taskinen@aalto.fi
2013-12-10
Highlights: • An improved experimental apparatus and new data analysis method have been applied. • Galvanic cells including solid zirconia electrolyte were measured accurately. • Δ{sub f}G° values for TeO{sub 2} have been determined in wide temperature range. • Third law plots for S{sub 298}{sup °} and ΔH{sub 298}{sup °} of TeO{sub 2} were produced using the experimentally observed values. - Abstract: The standard Gibbs energy of formation of TeO{sub 2} in the temperature range 369–795 °C was measured by the EMF method involving solid-oxide electrolyte galvanic cells of the type: (−)Pt, Ir, Te(s, l), TeO{sub 2}(s, l)|YSZ|O{sub 2}, Pt(+), where YSZ denotes stabilized zirconia with 8.5 mass percent of yttrium oxide. The standard Gibbs energies of formation obtained from the above cells are linear functions of temperature as: Δ{sub f}G° (kJ/mol) = −317.09 + 0.180 T (K) ± 0.307 (642–722.15 K) both phasess are solid. Δ{sub f}G° (kJ/mol) = −318.01 + 0.181 T (K) ± 0.308 (722.15–1005.8 K) Te – liquid; TeO{sub 2} – solid. Δ{sub f}G° (kJ/mol) = −256.26 + 0.120 T (K) ± 0.226 (1005.8–1068 K) both phases are liquid.
A Short Essay on the Uses of Free Energy
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...
Free Energy in Introductory Physics
Prentis, Jeffrey J.; Obsniuk, Michael J.
2016-02-01
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 and maximize entropy. There are many pedagogical articles on energy and entropy. Here we present a simple model to illustrate the concept of free energy and the principle of minimum free energy.
Yamamoto, Hiroaki; Morishita, Masao; Yamamoto, Takeo; Furukawa, Kazuma
2011-02-01
The standard Gibbs energies of formation of Mo2B, αMoB, Mo2B5, and MoB4 in the molybdenum-boron binary system were determined by measuring electromotive forces of galvanic cells using an Y2O3-stabilized ZrO2 solid oxide electrolyte. The results are as follows: begin{aligned} Updelta_{{f}} {{G}}^circ ( {{{Mo}}2 {{B}}} )/{{J}} {{mol}}^{ - 1} & = - 193100 + 44.10T ± 700( {1198{{ K to }}1323{{ K}}( {925^circ {{C to }}1050^circ {{C}}} )} ) \\ Updelta_{{f}} {{G}}^circ (α {{MoB}})/{{J}} {{mol}}^{ - 1} & = - 164000 + 26.45T ± 700( {1213{{ K to }}1328{{ K}}( {940^circ {{C to }}1055^circ {{C}}} )} ) \\ Updelta_{{f}} {{G}}^circ ( {{{Mo}}2 {{B}}5 } )/{{J}} {{mol}}^{ - 1} & = - 622500 + 117.0T ± 3000( {1205{{ K to }}1294{{ K}}( {932^circ {{C to }}1021^circ {{C}}} )} ) \\ Updelta_{{f}} {{G}}^circ ( {{{MoB}}4 } )/{{J}} {{mol}}^{ - 1} & = - 387300 + 93.53T ± 3000( {959{{ K to }}1153{{ K}}( {686^circ {{C to }}880^circ {{C}}} )} ) \\ where the standard pressure is 1 bar (100 kPa).
Free Energies of Formation Measurements on Solid-State Electrochemical Cells
Rollino, J. A.; Aronson, S.
1972-01-01
A simple experiment is proposed that can provide the student with some insight into the chemical properties of solids. It also demonstrates the relationship between the Gibbs free energy of formation of an ionic solid and the emf of an electrochemical cell. (DF)
Black hole free energy during charged collapse: a numerical study
Beauchesne, Hugues
2012-01-01
We perform a numerical investigation of the thermodynamics during the collapse of a charged (complex) scalar field to a Reissner-Nordstr\\"om (RN) black hole in isotropic coordinates. Numerical work on gravitational collapse in isotropic coordinates has recently shown that the negative of the total Lagrangian approaches the Helmholtz free energy F= E-TS of a Schwarzschild black hole at late times of the collapse (where E is the black hole mass, T the temperature and S the entropy). The relevant thermodynamic potential for the RN black hole is the Gibbs free energy G=E-TS-$\\Phi_H$ Q where Q is the charge and $\\Phi_H$ the electrostatic potential at the outer horizon. In charged collapse, there is a large outgoing matter wave which prevents the exterior from settling quickly to a static state. However, the interior region is not affected significantly by the wave. We find numerically that the interior contribution to the Gibbs free energy is entirely gravitational and accumulates in a thin shell just inside the h...
Free Energy in Introductory Physics
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…
Yamamoto, Hiroaki; Morishita, Masao; Miyake, Yuta; Hiramatsu, Shusuke
2017-06-01
The thermodynamic properties for the tungsten-boron binary system were determined by measuring electromotive forces of galvanic cells using an Y2O3-stabilized ZrO2 solid oxide electrolyte. Assuming that W2B and αWB are the stoichiometric compounds, and W2B5- x and W1- x B3 are the nonstoichiometric compounds having solubility widths of 0.670 ≤ X B ≤ 0.690 and 0.805 ≤ X B ≤ 0.822, respectively, they were treated as the intermediate phases of W0.667B0.333, αW0.50B0.50, W0.330B0.670 W0.310B0.690, and W0.195B0.805 W0.178B0.822. The Gibbs energies of mixing, ∆mix G, determined in the present study are listed as follows: Δ_{{mix}} G({W}_{0.667} {B}_{0.333} )/{{J}} {{mol}}^{ - 1} = {-}78070 + 26.01T ± 70 [1305{-}1422{{ K}}(1032{-}1149°C)], Δ_{{mix}} G(α {W}_{0.50} {B}_{0.50} )/{{J}} {{mol}}^{ - 1} = {-}86140 + 20.19T ± 200 [1310{-}1399{{ K }}(1037{-}1126°C)], Δ_{{mix}} G({W}_{0.330} {B}_{0.670} )/{{J}} {{mol}}^{ - 1} = {-}78910 + 18.11T ± 200 [1228{-}1410{{ K }}(955{-}1137°C)], ; Δ_{{mix}} G({W}_{0.310} {B}_{0.690} )/{{J}} {{mol}}^{ - 1} = {-}77350 + 17.52T ± 500 [1228{-}1410{{ K }}(955{-}1137°C)], Δ_{{mix}} G({W}_{0.195} {B}_{0.805} )/{{J}} {{mol}}^{ - 1} = {-}63920 + 12.08T ± 500 [1170{-}1340{{ K }}(897{-}1067°C)], Δ_{{mix}} G({W}_{0.178} {B}_{0.822} )/{{J}} {{mol}}^{ - 1} = {-}60090 + 11.15T ± 200 [1170{-}1340{{ K }}(897{-}1067°C)]. Using the thermodynamic properties determined in the present study, the composition-oxygen partial pressure diagram of the tungsten-boron-oxygen system was constructed under the conditions at 1273 K (1000 °C) and a total pressure of 1 bar (100 kPa). It is useful to understand the oxidation property of tungsten-boron binary alloys.
Pissarra, P.D.; Nielsen, Jens Bredal
1997-01-01
) is an intermediate. It is found that the L-lysine pathway in P. chrysogenum is thermodynamically feasible and that the calculated standard Gibbs free energy values of the two enzymes controlling the pathway flux indicate that they operate far from equilibrium. It is therefore proposed that the regulation of alpha......-aminoadipate reductase by lysine is important to maintain a high concentration of alpha-aminoadipate in order to direct the carbon flux to penicillin production. Secondly the changes in Gibbs free energy in the penicillin biosynthetic pathway during fed-batch cultivation were studied. The analysis showed that all...
Smedbäck, Mikael
2011-01-01
The free energy of ABJM theory has previously been computed in the strong and weak coupling limits. In this note, we report on results for the computation of the first non-vanishing quantum correction to the free energy, from the field theory side. The correction can be expressed in terms of a thermal mass for the scalar fields. This mass vanishes to 1-loop order, but there is a non-vanishing result to 2-loop order. Hence, the leading correction to the free energy is non-analytic in the 't Hooft coupling constant lambda. The reason is that the infrared divergences necessitate a resummation of ring diagrams and a related reorganization of perturbation theory, in which already the leading correction receives contributions from all orders in lambda. These results suggest that the free energy interpolates smoothly between weak and strong coupling.
SOCIAL EQUIVALENT OF FREE ENERGY
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.
Free Energy, Value, and Attractors
Karl Friston
2012-01-01
Full Text Available It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable states they expect to encounter.
Free Energy, Value, and Attractors
Friston, Karl; Ao, Ping
2012-01-01
It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable) states they expect to encounter. PMID:22229042
A Modified Gibbs Free Energy Minimisation Model for Fluid Bed Coal Gasification
Ściążko Marek
2015-03-01
Full Text Available A modified approach to equilibrium modelling of coal gasification is presented, based on global thermodynamic analysis of both homogeneous and heterogeneous reactions occurring during a gasification process conducted in a circulating fluid bed reactor. The model is based on large-scale experiments (ca. 200 kg/h with air used as a gasification agent and introduces empirical modifications governing the quasi-equilibrium state of two reactions: water-gas shift and Boudouard reaction. The model predicts the formation of the eight key gaseous species: CO, CO2, H2O, H2, H2S, N2, COS and CH4, volatile hydrocarbons represented by propane and benzene, tar represented by naphthalene, and char containing the five elements C, H, O, N, S and inorganic matter.
Tang, Ying [State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083 (China); Du, Yong, E-mail: yongducalphad@gmail.com [State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083 (China); Zhang, Lijun [State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083 (China); Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universitaet Bochum, Stiepeler Str. 129, 44801 Bochum (Germany); Yuan, Xiaoming [State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083 (China); Kaptay, George [Department of Nanotechnology, University of Miskolc, H-3515 Miskolc, Egyetemvaros E/7 - 606 (Hungary); Department of Nano-materials, BAY-LOGI Research Institute, H-3515 Miskolc, Egyetemvaros E/7 - 606 (Hungary)
2012-01-10
Highlights: Black-Right-Pointing-Pointer An exponential formulation to describe ternary excess Gibbs energy is proposed. Black-Right-Pointing-Pointer Theoretical analysis is performed to verify stability of phase using new formulation. Black-Right-Pointing-Pointer Al-Mg-Si system and its boundary binaries have been assessed by the new formulation. Black-Right-Pointing-Pointer Present calculations for Al-Mg-Si system are more reasonable than previous ones. - Abstract: An exponential formulation was proposed to replace the linear interaction parameter in the Redlich-Kister (R-K) polynomial for the excess Gibbs energy of ternary solution phase. The theoretical analysis indicates that the proposed new exponential formulation can not only avoid the artificial miscibility gap at high temperatures but also describe the ternary system well. A thermodynamic description for the Al-Mg-Si system and its boundary binaries was then performed by using both R-K linear and exponential formulations. The inverted miscibility gaps occurring in the Mg-Si and the Al-Mg-Si systems at high temperatures due to the use of R-K linear polynomials are avoided by using the new formulation. Besides, the thermodynamic properties predicted with the new formulation confirm the general thermodynamic belief that the solution phase approaches to the ideal solution at infinite temperatures, which cannot be described with the traditional R-K linear polynomials.
Gibbs-Thomson effect in nanocrystalline Fe-Ge
Sarkar, S.; Bansal, C.; Chatterjee, Ashok
2000-08-01
We studied the phase transformation behavior of chemically disordered bcc (α) phase Fe1-xGex alloys near the Fe3Ge stoichiometry synthesized in the nanocrystalline state by mechanical alloying of the elemental constituents. The evolution of the equilibrium L12 ordered (ɛ') phase was seen to occur via a metastable DO3-ordered (α1) phase, but a significant α1-->ɛ' phase transformation took place only after the growth of the grains. This behavior is understood with the help of a capillary effect or the Gibbs-Thomson effect wherein the grain boundary energy of the nanosize grains raises the Gibbs free energy of the ɛ' phase relative to the α1 phase for small sizes and the ɛ' phase grows only after a certain grain size is reached.
Dick, Thomas J.; Wierzbicki, Andrzej; Madura, Jeffry D.
Free energy perturbation Monte Carlo (FEP/MC) simulations are performed for both the liquid and solid phases of water to determine the melting temperature of several popular three and four-site water models. Gibbs free energy vs. temperature plots are constructed from the simulations to determine the melting temperature. For the liquid phase, standard FEP/MC simulations are used to calculate the free energy relative to the gas phase at multiple temperatures. The free energy of the solid phase relative to the gas phase is calculated at multiple temperatures using the lattice-coupling method. The intersection of the free energy regression lines determines the estimate of the melting temperature. Additionally, simulations were carried out for simple salt solutions to determine the freezing point depressions (FPD). The simulations reproduce the FPD as a function of salt concentration for solutions of NaCl, KCl, CaCl2, and MgCl2.
Harvey, J.-P.; Gheribi, A. E.; Chartrand, P.
2012-12-01
In this work, an in silico procedure to generate a fully coherent set of thermodynamic properties obtained from classical molecular dynamics (MD) and Monte Carlo (MC) simulations is proposed. The procedure is applied to the Al-Zr system because of its importance in the development of high strength Al-Li alloys and of bulk metallic glasses. Cohesive energies of the studied condensed phases of the Al-Zr system (the liquid phase, the fcc solid solution, and various orthorhombic stoichiometric compounds) are calculated using the modified embedded atom model (MEAM) in the second-nearest-neighbor formalism (2NN). The Al-Zr MEAM-2NN potential is parameterized in this work using ab initio and experimental data found in the literature for the AlZr3-L12 structure, while its predictive ability is confirmed for several other solid structures and for the liquid phase. The thermodynamic integration (TI) method is implemented in a general MC algorithm in order to evaluate the absolute Gibbs energy of the liquid and the fcc solutions. The entropy of mixing calculated from the TI method, combined to the enthalpy of mixing and the heat capacity data generated from MD/MC simulations performed in the isobaric-isothermal/canonical (NPT/NVT) ensembles are used to parameterize the Gibbs energy function of all the condensed phases in the Al-rich side of the Al-Zr system in a CALculation of PHAse Diagrams (CALPHAD) approach. The modified quasichemical model in the pair approximation (MQMPA) and the cluster variation method (CVM) in the tetrahedron approximation are used to define the Gibbs energy of the liquid and the fcc solid solution respectively for their entire range of composition. Thermodynamic and structural data generated from our MD/MC simulations are used as input data to parameterize these thermodynamic models. A detailed analysis of the validity and transferability of the Al-Zr MEAM-2NN potential is presented throughout our work by comparing the predicted properties obtained
Eigenstate Gibbs ensemble in integrable quantum systems
Nandy, Sourav; Sen, Arnab; Das, Arnab; Dhar, Abhishek
2016-12-01
The eigenstate thermalization hypothesis conjectures that for a thermodynamically large system in one of its energy eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of relevant conserved quantities. In a chaotic quantum system, only the energy is expected to play that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and therefore the reduced density matrix requires specification of all the corresponding parameters (generalized Gibbs ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e., requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately truncated generalized Gibbs ensembles. We further show that the presence of these rare eigenstates differentiates the model from the chaotic case and leads to the system being described by a generalized Gibbs ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a typical (Gibbs-like) eigenstate of the prequench Hamiltonian.
The free energy method and the Wright-Fisher model with 2 alleles.
Tran, Tat Dat; Hofrichter, Julian; Jost, Jürgen
2015-12-01
We systematically investigate the Wright-Fisher model of population genetics with the free energy functional formalism of statistical mechanics and in the light of recent mathematical work on the connection between Fokker-Planck equations and free energy functionals. In statistical physics, entropy increases, or equivalently, free energy decreases, and the asymptotic state is given by a Gibbs-type distribution. This also works for the Wright-Fisher model when rewritten in divergence to identify the correct free energy functional. We not only recover the known results about the stationary distribution, that is, the asymptotic equilibrium state of the model, in the presence of positive mutation rates and possibly also selection, but can also provide detailed formulae for the rate of convergence towards that stationary distribution. In the present paper, the method is illustrated for the simplest case only, that of two alleles.
Eigenstate Gibbs Ensemble in Integrable Quantum Systems
Nandy, Sourav; Das, Arnab; Dhar, Abhishek
2016-01-01
The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\\it relevant} conserved quantities. In a generic system, only the energy plays that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and hence the reduced density matrix requires specification of an infinite number of parameters (Generalized Gibbs Ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density, that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e. requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then s...
Predicting binding free energies in solution
Jensen, Jan H
2015-01-01
Recent predictions of absolute binding free energies of host-guest complexes in aqueous solution using electronic structure theory have been encouraging for some systems, while other systems remain problematic for others. In paper I summarize some of the many factors that could easily contribute 1-3 kcal/mol errors at 298 K: three-body dispersion effects, molecular symmetry, anharmonicity, spurious imaginary frequencies, insufficient conformational sampling, wrong or changing ionization states, errors in the solvation free energy of ions, and explicit solvent (and ion) effects that are not well-represented by continuum models. While the paper is primarily a synthesis of previously published work there are two new results: the adaptation of Legendre transformed free energies to electronic structure theory and a use of water clusters that maximizes error cancellation in binding free energies computed using explicit solvent molecules. While I focus on binding free energies in aqueous solution the approach also a...
Mechanism of active transport: free energy dissipation and free energy transduction.
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 ...
Linear embedding of free energy minimization
Moussa, Jonathan E
2016-01-01
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to attain. Such properties include the preservation of convexity, lower bounds on free energy, and applicability to systems without subsystem structure. We satisfy all of these properties by embedding free energy minimization into a linear program over energy-resolved expectation values. Numerical results on small systems are encouraging, but a lack of size consistency necessitates further development for large systems.
Inagaki, Taichi; Ishida, Toyokazu
2016-10-01
We propose a method for computing a melting point on the basis of the Gibbs free energy difference between the solid and liquid phases. The free energy difference is calculated from the average pressure obtained by performing a standard NVT simulation with a solid-liquid two-phase configuration. The method is validated by the melting point calculations of argon and benzene systems. In addition, the method is applied to a mannitol system, and the more reliable melting point than the previous estimate is successfully predicted. These results demonstrate that this method is very simple and useful to calculate melting points.
Graph representation of protein free energy landscape.
Li, Minghai; Duan, Mojie; Fan, Jue; Han, Li; Huo, Shuanghong
2013-11-14
The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.
Configurational space continuity and free energy calculations
Tian, Pu
2016-01-01
Free energy is arguably the most importance function(al) for understanding of molecular systems. A number of rigorous and approximate free energy calculation/estimation methods have been developed over many decades. One important issue, the continuity of an interested macrostate (or path) in configurational space, has not been well articulated, however. As a matter of fact, some important special cases have been intensively discussed. In this perspective, I discuss the relevance of configurational space continuity in development of more efficient and reliable next generation free energy methodologies.
Free Energy and Internal Combustion Engine Cycles
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.
Accurate free energy calculation along optimized paths.
Chen, Changjun; Xiao, Yi
2010-05-01
The path-based methods of free energy calculation, such as thermodynamic integration and free energy perturbation, are simple in theory, but difficult in practice because in most cases smooth paths do not exist, especially for large molecules. In this article, we present a novel method to build the transition path of a peptide. We use harmonic potentials to restrain its nonhydrogen atom dihedrals in the initial state and set the equilibrium angles of the potentials as those in the final state. Through a series of steps of geometrical optimization, we can construct a smooth and short path from the initial state to the final state. This path can be used to calculate free energy difference. To validate this method, we apply it to a small 10-ALA peptide and find that the calculated free energy changes in helix-helix and helix-hairpin transitions are both self-convergent and cross-convergent. We also calculate the free energy differences between different stable states of beta-hairpin trpzip2, and the results show that this method is more efficient than the conventional molecular dynamics method in accurate free energy calculation.
The Role of the Concentration Scale in the Definition of Transfer Free Energies
Moeser, Beate
2014-01-01
The Gibbs free energy of transferring a solute at infinite dilution between two solvents quantifies differences in solute-solvent interactions $-$ if the transfer takes place at constant molarity of the solute. Yet, many calculation formulae and measuring instructions that are commonly used to quantify solute-solvent interactions correspond to transfer processes in which not the molarity of the solute but its concentration measured in another concentration scale is constant. Here, we demonstrate that in this case, not only the change in solute-solvent interactions is quantified but also the entropic effect of a volume change during the transfer. Consequently, the "phenomenon" which is known as "concentration-scale dependence" of transfer free energies is simply explained by a volume-entropy effect. Our explanations are of high importance for the study of cosolvent effects on protein stability.
Escape rates for Gibbs measures
Ferguson, Andrew
2010-01-01
We study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of Hausdorff dimension of the survivor set.
Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics
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 TDSÃ‚Â° of the Gibbs standard free energy relation DGÃ‚Â°= DHÃ‚Â°-TDSÃ‚Â° serves to account for differences or changes in nonthermal energies that do not contribute to DGÃ‚Â° and that, since DHÃ‚Â° serves to account for differences or changes in total energy, complete enthalpy-entropy (DHÃ‚Â° - TDSÃ‚Â° compensation must invariably occur in isothermal processes for which TDSÃ‚Â° 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
Photosynthetic free energy transduction. Modelling electrochemical events.
Kooten, van O.
1988-01-01
This thesis is concerned with a particular part of the photosynthesis process. This part consists of the light-induced transmembrane electric potential gradient, the electrochemical pH gradient and the subsequent transformation of the energy contained in these gradients into chemical free energy of
Gibbs Sampling for the Uninitiated
2010-04-01
CS-TR-4956 UMIACS-TR-2010-04 LAMP-TR-153 April 2010 GIBBS SAMPLING FOR THE UNINITIATED Philip Resnik Eric Hardisty Department of Linguistics...Institute for Advanced Computer Studies University of Maryland College Park, MD 20742-3275 resnik AT umd.edu Department of Computer Science Institute for...Prescribed by ANSI Std Z39-18 Gibbs Sampling for the Uninitiated Philip Resnik Department of Linguistics and Institute for Advanced Computer Studies
Good Practices in Free-energy Calculations
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.
Free energy cascade in gyrokinetic turbulence
Navarro, A Bañón; Albrecht-Marc, M; Merz, F; Görler, T; Jenko, F; Carati, D
2010-01-01
In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a forward (from large to small scales), extremely local, and self-similar cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large eddy simulation techniques for gyrokinetics.
Garrido, Nuno M; Queimada, António J; Jorge, Miguel; Macedo, Eugénia A; Economou, Ioannis G
2009-09-08
The 1-octanol/water partition coefficient is an important thermodynamic variable usually employed to understand and quantify the partitioning of solutes between aqueous and organic phases. It finds widespread use in many empirical correlations to evaluate the environmental fate of pollutants as well as in the design of pharmaceuticals. The experimental evaluation of 1-octanol/water partition coefficients is an expensive and time-consuming procedure, and thus, theoretical estimation methods are needed, particularly when a physical sample of the solute may not yet be available, such as in pharmaceutical screening. 1-Octanol/water partition coefficients can be obtained from Gibbs free energies of solvation of the solute in both the aqueous and the octanol phases. The accurate evaluation of free energy differences remains today a challenging problem in computational chemistry. In order to study the absolute solvation Gibbs free energies in 1-octanol, a solvent that can mimic many properties of important biological systems, free energy calculations for n-alkanes in the range C1-C8 were performed using molecular simulation techniques, following the thermodynamic integration approach. In the first part of this paper, we test different force fields by evaluating their performance in reproducing pure 1-octanol properties. It is concluded that all-atom force fields can provide good accuracy but at the cost of a higher computational time compared to that of the united-atom force fields. Recent versions of united-atom force fields, such as Gromos and TraPPE, provide satisfactory results and are, thus, useful alternatives to the more expensive all-atom models. In the second part of the paper, the Gibbs free energy of solvation in 1-octanol is calculated for several n-alkanes using three force fields to describe the solutes, namely Gromos, TraPPE, and OPLS-AA. Generally, the results obtained are in excellent agreement with the available experimental data and are of similar
The Gibbs Thomson effect in magnetron-sputtered austenitic stainless steel films
Cusenza, S.; Borchers, C.; Carpene, E.; Schaaf, P.
2007-03-01
Magnetron sputtering of austenitic stainless steel AISI 316, which has a face-centred cubic structure (γ), leads to films exhibiting a body-centred cubic (α) structure or a mixture of α- and γ-phases. The microstructure of the deposited films was studied by Mössbauer spectroscopy, x-ray diffraction and transmission electron microscopy. With increasing deposition temperature a phase transformation from α- to γ-phase was observed in these films. Instantaneous recording of the electromotive force shows that nickel content and deposition temperature are crucial factors for phase stability and phase formation. In room temperature deposited stainless steel films, the phase transformation after vacuum annealing can be described by the Johnson-Mehl-Avrami kinetic model. These phase transformations in stainless steel films during annealing can be explained with the Gibbs-Thomson effect, where the grain boundary energy raises the Gibbs free energy.
The Gibbs-Thomson effect in magnetron-sputtered austenitic stainless steel films
Cusenza, S [Universitaet Goettingen, II Physikalisches Institut, Friedrich-Hund-Platz 1, 37077 Goettingen (Germany); Borchers, C [Universitaet Goettingen, II Physikalisches Institut, Friedrich-Hund-Platz 1, 37077 Goettingen (Germany); Carpene, E [Politecnico di Milano, Dipartimento di Fisica, Piazza Leonardo da Vinci 32, 20133 Milan (Italy); Schaaf, P [Universitaet Goettingen, II Physikalisches Institut, Friedrich-Hund-Platz 1, 37077 Goettingen (Germany)
2007-03-14
Magnetron sputtering of austenitic stainless steel AISI 316, which has a face-centred cubic structure ({gamma}), leads to films exhibiting a body-centred cubic ({alpha}) structure or a mixture of {alpha}- and {gamma}-phases. The microstructure of the deposited films was studied by Moessbauer spectroscopy, x-ray diffraction and transmission electron microscopy. With increasing deposition temperature a phase transformation from {alpha}- to {gamma}-phase was observed in these films. Instantaneous recording of the electromotive force shows that nickel content and deposition temperature are crucial factors for phase stability and phase formation. In room temperature deposited stainless steel films, the phase transformation after vacuum annealing can be described by the Johnson-Mehl-Avrami kinetic model. These phase transformations in stainless steel films during annealing can be explained with the Gibbs-Thomson effect, where the grain boundary energy raises the Gibbs free energy.
On the free energy of ionic hydration
Hummer, G; García, A E; Hummer, Gerhard; Pratt, Lawrence R.; Garcia, Angel E.
1995-01-01
The hydration free energies of ions exhibit an approximately quadratic dependence on the ionic charge, as predicted by the Born model. We analyze this behavior using second-order perturbation theory. This provides effective methods to calculating free energies from equilibrium computer simulations. The average and the fluctuation of the electrostatic potential at charge sites appear as the first coefficients in a Taylor expansion of the free energy of charging. Combining the data from different charge states allows calculation of free-energy profiles as a function of the ionic charge. The first two Taylor coefficients of the free-energy profiles can be computed accurately from equi- librium simulations; but they are affected by a strong system-size dependence. We apply corrections for these finite-size effects by using Ewald lattice sum- mation and adding the self-interactions consistently. Results are presented for a model ion with methane-like Lennard-Jones parameters in SPC water. We find two very closely ...
Free energy analysis of cell spreading.
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
Energy policy and free trade in Canada
Uslaner, E.M. (Maryland Univ., College Park, MD (USA))
1989-08-01
Canada and the USA signed a free trade agreement that went into effect on 1 January 1989. The USA saw the accord as having the potential to open markets in both countries for the mutual advantage of each. Americans have become more protectionist in recent years, but the object of such protectionism has been Japan rather than Canada. Canadians worried that the accord might lead to further economic and cultural domination by the USA. Many Canadians view their energy resources as a national birthright that can play a key role in fostering a sense of nationalism. Other Canadians consider energy resources to be provincial birthrights and worry that the federal government will interfere in free trade with other countries (especially the USA) to impose a feeling of nationalism on Canada. The debate over free trade thus mirrors that on energy in Canada. (author).
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata
2016-01-01
We analytically 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. 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.
Free energy balance in gyrokinetic turbulence
Bañón Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Görler, T.; Jenko, F.
2011-09-01
Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Atamas, Alexander A; Cuppen, Herma M; Koudriachova, Marina V; de Leeuw, Simon W
2013-01-31
The thermodynamics of binary sII hydrogen clathrates with secondary guest molecules is studied with Monte Carlo simulations. The small cages of the sII unit cell are occupied by one H(2) guest molecule. Different promoter molecules entrapped in the large cages are considered. Simulations are conducted at a pressure of 1000 atm in a temperature range of 233-293 K. To determine the stabilizing effect of different promoter molecules on the clathrate, the Gibbs free energy of fully and partially occupied sII hydrogen clathrates are calculated. Our aim is to predict what would be an efficient promoter molecule using properties such as size, dipole moment, and hydrogen bonding capability. The gas clathrate configurational and free energies are compared. The entropy makes a considerable contribution to the free energy and should be taken into account in determining stability conditions of binary sII hydrogen clathrates.
Applications for Energy Recovering Free Electron Lasers
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.
Potential Fluctuation Equality for Free Energy Evaluation
Ngo, Van
2011-01-01
Jarzynski's equality [1] allows us to investigate free energy landscapes (FELs) by constructing distributions of work performed on a system from an initial ensemble of states to final states. This work is experimentally measured by extension-versus-force (EVF) curves. We proposed a new approach that enables us to reconstruct such FELs without necessity of measuring EVF curves. We proved that any free energy changes could be computed by measuring the fluctuations of a harmonic external potential in final states. The main assumption of our proof is that one should probably treat a potential's minimum {\\lambda} (thought to be control parameter) and time in separate and independent manners. We recovered Jarzynski's equality from the introduction of a double Heaviside function. We then applied the approach in molecular dynamics (MD) simulations to compute the free energy barrier of breaking DNA base pairs (bps). The free energy barrier for breaking a CG bp in our simulations is identified as 1.7 +/- 0.2 kcal/mol t...
Free energy and dendritic self-organisation
Stefan J Kiebel
2011-10-01
Full Text Available In this paper, we pursue recent observations that, through selective dendritic filtering, single neurons respond to specific sequences of presynaptic inputs. We try to provide a principled and mechanistic account of this selectivity by applying the free energy principle to a dendrite that is immersed in its neuropil or environment. We assume that neurons self-organize to minimise a free energy bound on the self-information or surprise of presynaptic inputs that are sampled. We model this as a selective pruning of dendritic spines that are expressed on a dendritic branch. This pruning occurs when the optimized postsynaptic gain falls below a threshold. Crucially, postsynaptic gain is itself optimized with respect to free energy. Pruning suppresses free energy as the dendrite selects presynaptic signals that conform to its expectations, specified by a generative model implicit in its intracellular kinetics. Not only does this provide a principled account of how neurons organize and selectively sample the myriad of potential presynaptic inputs they are exposed to, but it also connects the optimization of elemental neuronal (dendritic processing to generic (surprise or evidence-based schemes in statistics and machine learning, such as Bayesian model selection and automatic relevance determination.
Calculating Free Energies Using Average Force
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.
Analysis of the Bogoliubov free energy functional
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...
Gibbs Ensembles of Nonintersecting Paths
Borodin, Alexei
2008-01-01
We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures on lozenge and domino tilings of the plane, some of which are non-translation-invariant. The correlation kernels of our processes can be viewed as extensions of the discrete sine kernel, and we show that the Gibbs property is a consequence of simple linear relations satisfied by these kernels. The processes depend on infinitely many parameters, which are closely related to parametrization of totally positive Toeplitz matrices.
Hiemstra, Tjisse
2015-06-01
Ferrihydrite (Fh) is an excellent model for understanding nanoparticle behavior in general. Moreover, Fh is one of the most important Fe (hydr) oxides in nature. Fh particles can be extremely small leading to a very high reactive surface area that changes its chemical potential, strongly affecting the solubility, nucleation, and stability. These characteristics can be coupled to the interfacial Gibbs free energy, being γ = 0.186 ± 0.01 J m-2 for Fh. The surface free energy has a relatively large contribution of surface entropy (-TSsurf = +0.079 ± 0.01 J m-2). The surface entropy is primarily related to the formation of surface groups by chemisorption of water (-17.1 J mol-1 K-1), for Fh equivalent with +0.064 ± 0.002 J m-2 at a surface loading NH2O = 12.6 μmol m-2. The entropy contribution of physisorbed water has been estimated by analyzing, as model, the surface enthalpy, entropy, and Gibbs free energy of the principal interfaces of H2O, i.e. ice-water-gas. It is about 20% of the contribution of chemisorbed water. The surface enthalpy of Fh is exceptionally low (Hsurf = +0.107 ± 0.01 J m-2), which can be explained by surface depletion (SD) of relatively unstable Fe polyhedra, or similarly, by additional surface loading of the non-depleted mineral core with specific Fe polyhedra for stabilization. The experimental enthalpy of Fh formation varies linearly with the surface area and correctly predicts the enthalpy value for the mineral core (-405.2 ± 1.2 kJ mol FeO3/2), being similar to the literature value for Fh as virtual bulk material (-406.7 ± 1.5 kJ mol FeO3/2) obtained with MO/DFT computations. The thermochemical quantities of the mineral core and surface are essentially the same for the entire range of Fh samples, in line with the SD model. The solubility of Fh suspensions as a whole may differ from the behavior of individual particles due to polydispersity. For 2-line Fh, the overall solubility is log Kso ∼ -38.5 ± 0.1 and for prolongedly aged 6
Lu, Shih-I
2009-11-15
In this article, we examined the Gibbs energy of activation for the Z/E thermal isomerization reaction of (1Z)-acetaldehyde hydrazone and (1Z)-acetaldehyde N,N-dimethylhydrazone, at 298.15 K in the solvent of cyclohexane. We carried out computations employing both the Gaussian-4 (G4) theory and the coupled cluster method using both single and double substitutions and triple excitations noniteratively, CCSD(T). The CCSD(T) energy is extrapolated to the complete basis set (CBS). We compared the calculated results to the available experimental observation. It appeared that both G4 and CCSD(T)/CBS computations overestimated the experimental value by as much as about 6 and 12 kcal/mol in the present two cases. We discussed possible sources of error and proposed the experimental kinetic data could be questionable.
The Magnetic Free Energy in Active Regions
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.
Friston, Karl J; Stephan, Klaas E
2007-12-01
If one formulates Helmholtz's ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory input and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organisation and responses.In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure.
Holographic free energy and thermodynamic geometry
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.)
Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation
Doremus, R. H.
1982-01-01
It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.
VARIATIONAL PRINCIPLE FOR FUZZY GIBBS MEASURES
Verbitskiy, Evgeny
2010-01-01
In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden M
Steele, W. V.; Chirico, R. D.
1989-06-01
Ideal-gas thermodynamic properties for indoline and 2-methylindole based on accurate calorimetric measurements (between 300 to 500 K and 300 to 700 K, respectively) were determined; well into the range of typical chemical process temperatures. The calorimetrically derived values provide a firm basis for the prediction of thermodynamic properties for a large family of structures including many substituted indoles and indolines. Critical-temperature/density measurements obtained using a differential scanning calorimeter (DSC) are reported for 2-methylindole. A critical pressure and acentric factor are derived for 2-methylindole. Group-additivity estimation methods are employed to estimate the Gibbs energies of formation for the reactants, intermediates, and products in a reaction scheme for the hydrodenitrogenation (HDN) of indole. Thermodynamic equilibria calculations on the indole/indoline/hydrogen system are compared with experimental batch-reaction measurements reported in the literature. The interplay between thermodynamics and kinetics in the HDN of indole is discussed. 41 refs., 11 figs., 23 tabs.
Hassein-bey-Larouci, A., E-mail: hasseinbey@yahoo.fr [Laboratoire Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, Université des Sciences et de la Technologie Houari Boumediene, B.P. 32, El-Alia, 16111 Bab-Ezzouar, Alger (Algeria); Igoujilen, O.; Aitkaci, A. [Laboratoire Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, Université des Sciences et de la Technologie Houari Boumediene, B.P. 32, El-Alia, 16111 Bab-Ezzouar, Alger (Algeria); Segovia, J.J.; Villamañán, M.A. [TERMOCAL Research Group, Escuela de Ingenierías Industriales, Universidad de Valladolid, Paseo del Cauce, 59, 47011 Valladolid (Spain)
2014-08-10
Highlights: • Many engineering applications require quantitative thermodynamic data of the fluids. • Excess properties of mixtures are important in the understanding of mixing process. • The results are used to explain the molecular interaction in the mixtures. - Abstract: Dynamic and kinematic viscosities, and densities of the ternary mixture {x_1 propanol + x_2 DMF + x_3 chloroform} and of the three corresponding binary systems have been measured at 293.15, 303.15, 313.15 and 323.15 K and atmospheric pressure. The thermophysical properties, viscosity deviations (Δη), kinematic viscosity (γ), excess Gibbs energies of activation of viscous flow (G*{sup E}) and excess molar volumes (V{sup E}) have been calculated from experimental values of dynamic viscosity, η, and density, ρ. The different results have been correlated by the Redlich–Kister equation for the binary mixtures and the Cibulka equation for equation for the ternary ones.
Gershanov, V. Yu.; Garmashov, S. I.
2015-01-01
We prove the existence of an effect inverse to the Gibbs-Thomson effect for mass transfer in systems consisting of a solid phase and the solution of the solid phase material in a certain solvent. The effect involves a change in the shape of the interface due to a variation of the equilibrium concentrations under it, which is induced by external conditions, and exists in the presence of a negative feedback for mass transfer associated with capillary effects.
Analysis of the Bogoliubov free energy functional
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...... of a phase transition to Bose{Einstein condensation, and establish the phase diagram. We also give a calculation of the critical temperature assuming the gas is dilute, and nd that it agrees with earlier numerical studies. The thesis contains an introduction, a physical review paper outlining the main...
Free energy of a Lovelock holographic superconductor
Aranguiz, Ligeia
2014-01-01
We study black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories with [d/2] gravitational coupling constants and two arbitrary functions that govern the matter interaction is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is exact, analytic and it includes the effects of back reaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, and classify holographic superconductors in terms of the parameter...
Kittaka, Shigeharu; Ishimaru, Shinji; Kuranishi, Miki; Matsuda, Tomoko; Yamaguchi, Toshio
2006-07-21
The effect of confinement on the solid-liquid phase transitions of water was studied by using DSC and FT-IR measurements. Enthalpy changes upon melting of frozen water in MCM-41 and SBA-15 were determined as a function of pore size and found to decrease with decreasing pore size. The melting point also decreased almost monotonically with a decrease in pore size. Analysis of the Gibbs-Thomson relation on the basis of the thermodynamic data showed that there were two stages of interfacial free energy change after the constant region, i.e., below a pore size of 6.0 nm: a gradual decrease down to 3.4 nm and another decrease after a small jump upward. This fact demonstrates that the simple Gibbs-Thomson relation, i.e., a linear relation between the melting point change and the inverse pore size, is limited to the range not far from the melting point of bulk water. FT-IR measurements suggest that the decrease in enthalpy change and interfacial free energy change with decreasing pore size reflect the similarity of the structures of both liquid and solid phases of water in smaller pores at lower temperatures.
Battley, Edwin H
2013-06-01
Microbial growth is a biological process that has been previously treated as a chemical reaction operating in accord with the Gibbs free energy equation, Delta G = Delta H-T Delta S. The heat of yeast growth was the first to be measured, in 1856, by direct calorimetry of a large wine vat. Until then there was a tendency for biologists to continue with the old notion that the energy change accompanying the growth of microorganisms was reflected in the amount of heat that was produced during this process. The application of chemical thermodynamics to systems involving microbial growth did not occur until much later. The full application of the Gibbs equation to microbial growth did not take place until the experimental measurement of yeast cell entropy was made in 1997 Further investigations then showed that the quantity of thermal energy for solid substances represented by TS was twice that of the quantity of thermal energy represented by Qab that is experimentally necessary to raise T of a substance from 0/K to T/K. Since there can only be one value for this, the use of the equation Delta X = Delta H-Delta Qab was investigated with respect to microbial growth, and is described in this review.
Effective Floquet-Gibbs states for dissipative quantum systems
Shirai, Tatsuhiko; Thingna, Juzar; Mori, Takashi; Denisov, Sergey; Hänggi, Peter; Miyashita, Seiji
2016-05-01
A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.
The Limit of Free Magnetic Energy in Active Regions
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.
Effective Free Energy for Individual Dynamics
Grauwin, Sebastian; Bertin, Eric; Jensen, Pablo; 10.1142/S0219525911003128
2011-01-01
Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.
Analytic example of a free energy functional
Tutschka; Kahl
2000-09-01
We use the ideas of Percus for the construction of classical density functionals for two model interactions: simple hard spheres and adhesive hard spheres (AHSs). The required input, the properties of the uniform fluid, is taken from the analytic mean spherical solution for these two systems. For hard spheres we derive-via a bilinear decomposition of the direct correlation functions-a set of basis functions, which is the same as the one presented by Rosenfeld in his fundamental measure theory framework. For AHSs additional basis functions have to be considered to ensure the bilinear decomposition of the direct correlation functions; we present an expression for the free energy functional for the one-component case.
Free Magnetic Energy and Coronal Heating
Winebarger, Amy; Moore, Ron; Falconer, David
2012-01-01
Previous work has shown that the coronal X-ray luminosity of an active region increases roughly in direct proportion to the total photospheric flux of the active region's magnetic field (Fisher et al. 1998). It is also observed, however, that the coronal luminosity of active regions of nearly the same flux content can differ by an order of magnitude. In this presentation, we analyze 10 active regions with roughly the same total magnetic flux. We first determine several coronal properties, such as X-ray luminosity (calculated using Hinode XRT), peak temperature (calculated using Hinode EIS), and total Fe XVIII emission (calculated using SDO AIA). We present the dependence of these properties on a proxy of the free magnetic energy of the active region
Mora Osorio, Camilo Andrés; González Barrios, Andrés Fernando
2016-12-07
Calculation of the Gibbs free energy changes of biological molecules at the oil-water interface is commonly performed with Molecular Dynamics simulations (MD). It is a process that could be performed repeatedly in order to find some molecules of high stability in this medium. Here, an alternative method of calculation has been proposed: a group contribution method (GCM) for peptides based on MD of the twenty classic amino acids to obtain free energy change during the insertion of any peptide chain in water-dodecane interfaces. Multiple MD of the twenty classic amino acids located at the interface of rectangular simulation boxes with a dodecane-water medium were performed. A GCM to calculate the free energy of entire peptides is then proposed. The method uses the summation of the Gibbs free energy of each amino acid adjusted in function of its presence or absence in the chain as well as its hydrophobic characteristics. Validation of the equation was performed with twenty-one peptides all simulated using MD in dodecane-water rectangular boxes in previous work, obtaining an average relative error of 16%.
Energy flow and energy dissipation in a free surface.
Goldburg, Walter; Cressman, John
2005-11-01
Turbulent flows on a free surface are strongly compressible [1] and do not conserve energy in the absence of viscosity as bulk fluids do. Despite violation of assumptions essential to Kolmogorov's theory of 1941 (K41) [2, 3], surface flows show strong agreement with Kolmogorov scaling, though intermittency is larger there. Steady state turbulence is generated in a tank of water, and the spatially averaged energy flux is measured from the four-fifth's law at each instant of time. Likewise, the energy dissipation rate as measured from velocity gradients is also a random variable in this experiment. The energy flux - dissipation rate cross-correlation is measured to be correlated in incompressible bulk flows, but strongly anti-correlated on the surface. We argue that the reason for this discrepancy between surface and bulk flows is due to compressible effects present on the surface. [1] J. R. Cressman, J. Davoudi, W. I. Goldburg, and J. Schumacher, New Journal of Physics, 6, 53, 2004. [2] U. Frisch. Turbulence: The legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, 1995. [3] A. N. Kolmogorov, Doklady Akad. Nauk SSSR, 32, 16, 1941.
Linden, H. R.; Singer, S. F.
2001-12-01
It is generally agreed that hydrogen is an ideal energy source, both for transportation and for the generation of electric power. Through the use of fuel cells, hydrogen becomes a high-efficiency carbon-free power source for electromotive transport; with the help of regenerative braking, cars should be able to reach triple the current mileage. Many have visualized a distributed electric supply network with decentralized generation based on fuel cells. Fuel cells can provide high generation efficiencies by overcoming the fundamental thermodynamic limitation imposed by the Carnot cycle. Further, by using the heat energy of the high-temperature fuel cell in co-generation, one can achieve total thermal efficiencies approaching 100 percent, as compared to present-day average power-plant efficiencies of around 35 percent. In addition to reducing CO2 emissions, distributed generation based on fuel cells also eliminates the tremendous release of waste heat into the environment, the need for cooling water, and related limitations on siting. Manufacture of hydrogen remains a key problem, but there are many technical solutions that come into play whenever the cost equations permit . One can visualize both central and local hydrogen production. Initially, reforming of abundant natural gas into mixtures of 80% H2 and 20% CO2 provides a relatively low-emission source of hydrogen. Conventional fossil-fuel plants and nuclear plants can become hydrogen factories using both high-temperature topping cycles and electrolysis of water. Hydro-electric plants can manufacture hydrogen by electrolysis. Later, photovoltaic and wind farms could be set up at favorable locations around the world as hydrogen factories. If perfected, photovoltaic hydrogen production through catalysis would use solar photons most efficiently . For both wind and PV, hydrogen production solves some crucial problems: intermittency of wind and of solar radiation, storage of energy, and use of locations that are not
Cuendet, Michel A; Tuckerman, Mark E
2012-10-09
Alchemical free energy simulations are commonly used to calculate relative binding or solvation free energies in molecular systems. The convergence of alchemical free energy calculations is often hampered by inefficient sampling of the conformational degrees of freedom, which remain trapped in metastable substates. Here, we show that thermodynamic integration (TI) or free energy perturbation (FEP) can be combined with the recent driven adiabatic free energy dynamics (dAFED) method, in order to enhance conformational sampling along a set of chosen collective variables. The resulting TI-dAFED or FEP-dAFED methods are validated on a two-dimensional analytical problem. The ability of these methods to provide accurate free energy differences for realistic molecular systems is demonstrated by calculating the enantiomerization free energy of the alanine dipeptide in explicit solvent.
Dynamical Gibbs-non-Gibbs transitions : a study via coupling and large deviations
Wang, Feijia
2012-01-01
In this thesis we use both the two-layer and the large-deviation approach to study the conservation and loss of the Gibbs property for both lattice and mean-field spin systems. Chapter 1 gives general backgrounds on Gibbs and non-Gibbs measures and outlines the the two-layer and the large-deviation
Transportation inequalities: From Poisson to Gibbs measures
Ma, Yutao; Wang, Xinyu; Wu, Liming; 10.3150/00-BEJ268
2011-01-01
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on $\\mathbb{N}^{\\Lambda}$ or the continuum Gibbs measure on the configuration space.
DYNAMIC FREE ENERGY HYSTERESIS MODEL IN MAGNETOSTRICTIVE ACTUATORS
无
2006-01-01
A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure, numerical implementation method of the dynamic model is provided. The resistor parameter in the dynamic model changes according to different frequency ranges. This makes numerical implementation results reasonable in the discussed operating frequency range. The validity of the dynamic free energy model is illustrated by comparison with experimental data.
Absolute Free Energies for Biomolecules in Implicit or Explicit Solvent
Berryman, Joshua T.; Schilling, Tanja
Methods for absolute free energy calculation by alchemical transformation of a quantitative model to an analytically tractable one are discussed. These absolute free energy methods are placed in the context of other methods, and an attempt is made to describe the best practice for such calculations given the current state of the art. Calculations of the equilibria between the four free energy basins of the dialanine molecule and the two right- and left-twisted basins of DNA are discussed as examples.
Yoshida, Koh; Baluja, Shipra; Inaba, Akira; Koga, Yoshikata
2011-06-01
Using a differential pressure perturbation calorimetry developed by us recently [K. Yoshida, S. Baluja, A. Inaba, K. Tozaki, and Y. Koga, "Experimental determination of third derivative of G (III): Differential pressure perturbation calorimetry (II)," J. Solution Chem. (in press)], we experimentally determined the partial molar S-V cross fluctuation density of solute B, SVδB, in binary aqueous solutions for B = 1-propanol (1P) and glycerol (Gly). This third derivative of G provides information about the effect of solute B on the S-V cross fluctuation density, SVδ, in aqueous solution as the concentration of B varies. Having determined SVδB by better than 1% uncertainty, we evaluated for the first time the fourth derivative quantity SVδB-B = N(∂SVδB /∂nB) for B = 1P and Gly graphically without resorting to any fitting functions within several percent. This model-free quantity gives information about the acceleration of the effect of solute B on SVδ. By comparing fourth derivative quantities, SVδB-B, among B = 1P, Gly, and 2-butoxyethanol obtained previously, the distinction of the effect of solute on H2O becomes clearer than before when only the third derivative quantities were available.
Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices.
Dechant, Andreas; Kessler, David A; Barkai, Eli
2015-10-23
We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∝H(x,p)(-1/D), where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution.
Ferrando, Nicolas; Gedik, Ibrahim; Lachet, Véronique; Pigeon, Laurent; Lugo, Rafael
2013-06-13
In this work, a new transferable united-atom force field has been developed to predict phase equilibrium and hydration free energy of carboxylic acids. To take advantage of the transferability of the AUA4 force field, all Lennard-Jones parameters of groups involved in the carboxylic acid chemical function are reused from previous parametrizations of this force field. Only a unique set of partial electrostatic charges is proposed to reproduce the experimental gas phase dipole moment, saturated liquid densities and vapor pressures. Phase equilibrium properties of various pure carboxylic acids (acetic acid, propanoic acid, butanoic acid, pentanoic acid, hexanoic acid) and one diacid (1,5-pentanedioic) are studied through Monte Carlo simulations in the Gibbs ensemble. A good accuracy is obtained for pure compound saturated liquid densities and vapor pressures (average deviation of 2% and 6%, respectively), as well as for critical points. The vaporization enthalpy is, however, poorly predicted for short acids, probably due to a limitation of the force field to correctly describe the significant dimerization in the vapor phase. Pressure-composition diagrams for two binary mixtures (acetic acid + n-butane and propanoic acid + pentanoic acid) are also computed with a good accuracy, showing the transferability of the proposed force field to mixtures. Hydration free energies are calculated for three carboxylic acids using thermodynamic integration. A systematic overestimation of around 10 kJ/mol is observed compared to experimental data. This new force field parametrized only on saturated equilibrium properties appears insufficient to reach an acceptable precision for this property, and only relative hydration free energies between two carboxylic acids can be correctly predicted. This highlights the limitation of the transferability feature of force fields to properties not included in the parametrization database.
Free-Energy Calculations. A Mathematical Perspective
Pohorille, Andrzej
2015-01-01
conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.
Christov, Christomir. E-mail: hhristov@chem.ucsd.edu
2003-11-01
Gibbs free energy of formation) of the solid phases (simple salts, six sulfate - M{sub 2}SO{sub 4} {center_dot} M{sup '}SO{sub 4} {center_dot} 6H{sub 2}O, and five selenate - M{sub 2}SeO{sub 4} {center_dot} M{sup '}SeO{sub 4} {center_dot} 6H{sub 2}O - double salts) crystallizing in the systems under consideration are determined.
Accurate estimation of solvation free energy using polynomial fitting techniques.
Shyu, Conrad; Ytreberg, F Marty
2011-01-15
This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem, 2009, 30, 2297). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and nonequidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest that these polynomial techniques, especially with use of nonequidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. Copyright © 2010 Wiley Periodicals, Inc.
Diabat Interpolation for Polymorph Free-Energy Differences.
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.
Amadei, A; Apol, MEF; DiNola, A; Berendsen, HJC
1996-01-01
A new theory is presented for calculating the Helmholtz free energy based on the potential energy distribution function. The usual expressions of free energy, internal energy and entropy involving the partition function are rephrased in terms of the potential energy distribution function, which must
Amadei, A; Apol, MEF; DiNola, A; Berendsen, HJC
1996-01-01
A new theory is presented for calculating the Helmholtz free energy based on the potential energy distribution function. The usual expressions of free energy, internal energy and entropy involving the partition function are rephrased in terms of the potential energy distribution function, which must
The MgO-Al2O3-SiO2 system - Free energy of pyrope and Al2O3-enstatite. [in earth mantle formation
Saxena, S. K.
1981-01-01
The model of fictive ideal components is used to determine Gibbs free energies of formation of pyrope and Al2O3-enstatite from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range 1200-1600 K. It is noted that Al2O3 forms an ideal solution with MgSiO3. These thermochemical data are found to be consistent with the Al2O3 isopleths that could be drawn using most recent experimental data and with the reversed experimental data on the garnet-spinel field boundary.
Free energy of topologically massive gravity and flat space holography
Grumiller, Daniel
2015-01-01
We calculate the free energy from the on-shell action for topologically massive gravity with negative and vanishing cosmological constant, thereby providing a first principles derivation of the free energy of BTZ black holes and flat space cosmologies. We summarize related recent checks of flat space holography.
CALCULATION OF RELATIVE FREE-ENERGY VIA INDIRECT PATHWAYS
MARK, AE; VANGUNSTEREN, WF; BERENDSEN, HJC
1991-01-01
A general method is presented to reduce the simulation time required to compute the relative free energy between two states X and Y of a molecular system by computer simulation. Although the free energy difference DELTA-A(x-->y) is, in principle, independent of the pathway chosen to change X into Y,
Free energy changes on freezing and melting ductile metals
Lynden-Bell, R.M.; Duijneveldt, J.S. van; Frenkel, D.
1993-01-01
The variation in Landau free energy while melting platinum was investigated at a number of temperatures using computer simulation with a model potential. The technique used was to apply a biasing potential in a Monte Carlo simulation with umbrella sampling. From the Landau free energy curves one can
Accelerated weight histogram method for exploring free energy landscapes
Lindahl, Viveca; Hess, Berk
2014-01-01
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 an...
Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State
Regnier, Stephane; Priest, Eric
2007-01-01
To understand the physics of solar flares, including the local reorganisation 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...
A Gibbs distribution that learns from GA dynamics
Kitagata, Manabu
2010-01-01
A general procedure of average-case performance evaluation for population dynamics such as genetic algorithms (GAs) is proposed and its validity is numerically examined. We introduce a learning algorithm of Gibbs distributions from training sets which are gene configurations (strings) generated by GA in order to figure out the statistical properties of GA from the view point of thermodynamics. The learning algorithm is constructed by means of minimization of the Kullback-Leibler information between a parametric Gibbs distribution and the empirical distribution of gene configurations. The formulation is applied to the solvable probabilistic models having multi-valley energy landscapes, namely, the spin glass chain and the Sherrington-Kirkpatrick model. By using computer simulations, we discuss the asymptotic behaviour of the effective temperature scheduling and the residual energy induced by the GA dynamics.
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.
Guidelines for the analysis of free energy calculations.
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.
Surface free energy for systems with integrable boundary conditions
Goehmann, Frank [Fachbereich C-Physik, Bergische Universitaet Wuppertal, 42097 Wuppertal (Germany); Bortz, Michael [Department of Theoretical Physics, Australian National University, Canberra ACT 0200 (Australia); Frahm, Holger [Institut fuer Theoretische Physik, Universitaet Hannover, 30167 Hannover (Germany)
2005-12-16
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.
Regeneralized London free energy for high-Tc vortex lattices
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 .
Study on Surface Free Energy of Thermochromic Wood
无
2010-01-01
Thermochromic wood is a kind of new functional materials. It is significant for thermochromic wood development to study surface free energy. Samples of Chinese white poplar were colored using thermochromic agent though the method of ultrasonic impregnation and its surface free energy was investigated in the experiment. The results showed that the surface free energy for untreated, black-red, orange-yellow and blue thermochromic wood was 40.25, 29.85, 28.30 and 21.05 mN/m, respectively. The FTIR results show...
Sabyasachi Haldar
2014-07-01
Full Text Available New Free Electrons Wire will enable the use of electrical energy and also energy in various other forms, in a loss free way, at room temperature. Free Electrons confined in vacuum at the order of 10-4 torr or more, at the core of the wire, can move a distance as long as about, to a few kilometers without any collision. The vacuum is maintained in a tube made up of alternate layers of Teflon and Silicon Oxynitride. The columbic repulsion between these free electrons will actually conduct energy without any loss. The free electrons trapped in vacuum tube, should be at a particular density of around 2.02 x 108 electrons per unit area. A metal encapsulation(s over the wire is there to keep the electromagnetic field remain confined within the free electron wire, to make it harmless to the health of living creatures. Apart from loss free energy transportation, the free electron wire is also capable of generating very high electromagnetic field due to the free electrons, simply by removing the metal encapsulation(s, which can be used for various purposes. The materials and techniques adopted will make New Free Electron Wire producible commercially, at the cost of general copper wires.
Energy model for the Zr-based metallic glass alloy melt with clusters
2007-01-01
An energy model for the melt of bulk metallic glass (BMG) with clusters was estab- lished, the Gibbs free energy and interfacial energy for the Zr-Al-Ni ternary alloy melt with Zr2Ni clusters were calculated, and the effects of the clusters on the Gibbs free energy, interfacial energy and nucleation rate were analyzed. The results showed that the existence of the clusters in the Zr-Al-Ni ternary alloy melt enables the Gibbs free energy to decrease in the composition range where bulk metallic glass forms easily, makes the interfacial energy increase and changes the distribu- tion of the interfacial energy with the alloy composition. Because of the clusters in the melt, the Gibbs free energy of the Zr66Al8Ni26 alloy melt decreases about 0.3-1 kJ/mol and the interfacial energy between the melt and crystal nucleus increases about 0.016 J/m2. The nucleation rate of the undercooled Zr66Al8Ni26 alloy melt de- creases evidently under the influence of the clusters on Gibbs free energy and the interfacial energy, and the maximum of the nucleation rate in the melt with the Zr2Ni clusters is only about 107 mol1s1.
Energy model for the Zr-based metallic glass alloy melt with clusters
YANG YuanSheng; LI HuiQiang; TONG WenHui
2007-01-01
An energy model for the melt of bulk metallic glass (BMG) with clusters was established, the Gibbs free energy and interfacial energy for the Zr-Al-Ni ternary alloy melt with Zr2Ni clusters were calculated, and the effects of the clusters on the Gibbs free energy, interfacial energy and nucleation rate were analyzed. The results showed that the existence of the clusters in the Zr-Al-Ni ternary alloy melt enables the Gibbs free energy to decrease in the composition range where bulk metallic glass forms easily, makes the interfacial energy increase and changes the distribution of the interfacial energy with the alloy composition. Because of the clusters in the melt, the Gibbs free energy of the Zr66Al8Ni26 alloy melt decreases about 0.3-1 kJ/mol and the interfacial energy between the melt and crystal nucleus increases about 0.016 J/m2. The nucleation rate of the undercooled Zr66Al8Ni26 alloy melt decreases evidently under the influence of the clusters on Gibbs free energy and the interfacial energy, and the maximum of the nucleation rate in the melt with the Zr2Ni clusters is only about 107 mol-1·s-1.
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.
Bcc crystal-fluid interfacial free energy in Yukawa systems.
Heinonen, V; Mijailović, A; Achim, C V; Ala-Nissila, T; Rozas, R E; Horbach, J; Löwen, H
2013-01-28
We determine the orientation-resolved interfacial free energy between a body-centered-cubic (bcc) crystal and the coexisting fluid for a many-particle system interacting via a Yukawa pair potential. For two different screening strengths, we compare results from molecular dynamics computer simulations, density functional theory, and a phase-field-crystal approach. Simulations predict an almost orientationally isotropic interfacial free energy of 0.12k(B)T/a(2) (with k(B)T denoting the thermal energy and a the mean interparticle spacing), which is independent of the screening strength. This value is in reasonable agreement with our Ramakrishnan-Yussouff density functional calculations, while a high-order fitted phase-field-crystal approach gives about 2-3 times higher interfacial free energies for the Yukawa system. Both field theory approaches also give a considerable anisotropy of the interfacial free energy. Our result implies that, in the Yukawa system, bcc crystal-fluid free energies are a factor of about 3 smaller than face-centered-cubic crystal-fluid free energies.
Near-equilibrium measurements of nonequilibrium free energy
Crooks, Gavin
2012-04-09
A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a nonequilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.
The free-energy principle: a unified brain theory?
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 computations employing Jarzynski identity and Wang - Landau algorithm
Kalyan, M. Suman; Murthy, K. P. N.; Sastry, V. S. S.
2016-05-01
We introduce a simple method to compute free energy differences employing Jarzynski identity in conjunction with Wang - Landau algorithm. We demonstrate this method on Ising spin system by comparing the results with those obtained from canonical sampling.
Standard free energy of formation of iron iodide
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.
Practical Aspects of Free-Energy Calculations: A Review.
Hansen, Niels; van Gunsteren, Wilfred F
2014-07-08
Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.
Free energy surfaces in the superconducting mixed state
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.
Accelerated weight histogram method for exploring free energy landscapes
Lindahl, V.; Lidmar, J.; Hess, B.
2014-07-01
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.
Accelerated weight histogram method for exploring free energy landscapes
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.
Variational description of Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model
Fernandez, R.; den Hollander, F.; Martinez, J.
2013-01-01
We perform a detailed study of Gibbs-non-Gibbs transitions for the Curie- Weiss model subject to independent spin-flip dynamics (“infinite-temperature” dynamics). We show that, in this setup, the program outlined in van Enter et al. (Moscow Math J 10:687–711, 2010) can be fully completed, namely, Gi
Surface free energy of copper-zinc alloy for energy-saving of boiler
WANG Man; LIANG Jinsheng; TANG Qingguo; MING Xing; MENG Junping; DING Yan
2006-01-01
Cu-Zn, Cu-Zn-Sn, Cu-Zn-Ni alloys were melted by vacuum smelter. The effect factors to the surface free energy of the alloys such as chemical composition, crystal structure and surface crystal lattice distortion etc. were investigated by OCA30 automatic contact angle test instrument, metallography microscope and XRD instrument etc. Results suggests: adding alloy element to Cu may increase its surface free energy, and the more kinds of alloy elements are added, the more surface free energy increases; the alloy element Sn an increase the surface free energy of Cu-Zn alloy; Cu-Zn alloy with fir-tree crystal structure, great phase discrepancy and obvious composition aliquation has greater surface free energy; Cu-Zn alloy with compounds and serious surface crystal lattice distortion has greater surface free energy.
Basic ingredients of free energy calculations: a review.
Christ, Clara D; Mark, Alan E; van Gunsteren, Wilfred F
2010-06-01
Methods to compute free energy differences between different states of a molecular system are reviewed with the aim of identifying their basic ingredients and their utility when applied in practice to biomolecular systems. A free energy calculation is comprised of three basic components: (i) a suitable model or Hamiltonian, (ii) a sampling protocol with which one can generate a representative ensemble of molecular configurations, and (iii) an estimator of the free energy difference itself. Alternative sampling protocols can be distinguished according to whether one or more states are to be sampled. In cases where only a single state is considered, six alternative techniques could be distinguished: (i) changing the dynamics, (ii) deforming the energy surface, (iii) extending the dimensionality, (iv) perturbing the forces, (v) reducing the number of degrees of freedom, and (vi) multi-copy approaches. In cases where multiple states are to be sampled, the three primary techniques are staging, importance sampling, and adiabatic decoupling. Estimators of the free energy can be classified as global methods that either count the number of times a given state is sampled or use energy differences. Or, they can be classified as local methods that either make use of the force or are based on transition probabilities. Finally, this overview of the available techniques and how they can be best used in a practical context is aimed at helping the reader choose the most appropriate combination of approaches for the biomolecular system, Hamiltonian and free energy difference of interest.
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.
Free energy of the Lennard-Jones solid
Hoef, van der Martin A.
2000-01-01
We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around 0.94–1.
Free energy of the Lennard-Jones solid
van der Hoef, Martin Anton
2000-01-01
We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around
Energy buildup in sheared force-free magnetic fields
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.
Free energy estimation of short DNA duplex hybridizations
Leger Serge
2010-02-01
Full Text Available Abstract Background Estimation of DNA duplex hybridization free energy is widely used for predicting cross-hybridizations in DNA computing and microarray experiments. A number of software programs based on different methods and parametrizations are available for the theoretical estimation of duplex free energies. However, significant differences in free energy values are sometimes observed among estimations obtained with various methods, thus being difficult to decide what value is the accurate one. Results We present in this study a quantitative comparison of the similarities and differences among four published DNA/DNA duplex free energy calculation methods and an extended Nearest-Neighbour Model for perfect matches based on triplet interactions. The comparison was performed on a benchmark data set with 695 pairs of short oligos that we collected and manually curated from 29 publications. Sequence lengths range from 4 to 30 nucleotides and span a large GC-content percentage range. For perfect matches, we propose an extension of the Nearest-Neighbour Model that matches or exceeds the performance of the existing ones, both in terms of correlations and root mean squared errors. The proposed model was trained on experimental data with temperature, sodium and sequence concentration characteristics that span a wide range of values, thus conferring the model a higher power of generalization when used for free energy estimations of DNA duplexes under non-standard experimental conditions. Conclusions Based on our preliminary results, we conclude that no statistically significant differences exist among free energy approximations obtained with 4 publicly available and widely used programs, when benchmarked against a collection of 695 pairs of short oligos collected and curated by the authors of this work based on 29 publications. The extended Nearest-Neighbour Model based on triplet interactions presented in this work is capable of performing accurate
Importance of configurational contributions to the free energy of nanoclusters
M. Posselt
2013-07-01
Full Text Available An effective simulation method based on the Wang-Landau Monte Carlo algorithm is used in order to demonstrate the significance of the configurational contributions to the free energy of embedded nanoclusters. Starting from the most stable cluster configuration the simulation provides all geometrically different, but simply connected and sufficiently compact configurations of a nanocluster of a given size and the respective formation energies. The knowledge of these data allows the calculation of the free formation and free binding energy of the cluster at T ≠ 0. The method is applied to coherent Cu clusters in bcc-Fe. It is shown that even at moderate temperatures the configurational contributions to the free formation and binding energy must not be neglected. The dependence of the monomer free binding energy on clusters size is found to change significantly with increasing temperature which has a considerable effect on the pathway of cluster evolution. Therefore, present investigations provide an essential contribution to the improvement of the input parameters for object kinetic Monte Carlo simulations and rate theory used in multi-scale simulations of the nanostructure evolution. The calculation scheme developed in this work is rather general and applicable to many types of embedded nanoclusters. Compared to the method of overlapping distributions hitherto used in some cases to determine the configurational part of the free energy the new method has major advantages. Various tests are performed in order verify the presented approach and to compare with the results of the other calculation procedure. A roadmap is proposed to include the vibrational contributions to the free energy of the clusters within the framework of the method employed in this work.
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.
Canadian energy development under the Free Trade Agreement
McRae, R.N. (Calgary Univ., AB (CA). Dept. of Economics)
1991-06-01
The Free Trade Agreements between Canada and the USA endorses the status quo as far as energy trade is concerned; but it provides an important guarantee of future access, as far as Canada is concerned. This is especially critical for natural gas and electricity exports, since they are expected to increase. This article will demonstrate that an increase in energy exports benefits not only the energy sector but also provides favourable macroeconomic responses. (author).
Casimir free energy and pressure for magnetic metal films
Klimchitskaya, G. L.; Mostepanenko, V. M.
2016-07-01
We examine the Casimir free energy and pressure of magnetic metal films, which are free standing in vacuum, sandwiched between two dielectric plates and deposited on either nonmagnetic or magnetic metallic plates. All calculations are performed using both the Drude and plasma model approaches to the Lifshitz theory. According to our results, the Casimir free energies and pressures calculated using both theoretical approaches are significantly different in the magnitude and sign even for thin films of several tens of nanometers thickness. Thus, for the Ni film of 47 nm thickness deposited on a Fe plate the obtained magnitudes of the Casimir free energy differ by the factor of 5866. We show that the Casimir free energy and pressure of a magnetic film calculated using the plasma model approach do not possess the classical limit but exponentially fast drop to zero with increasing film thickness. If the Drude model approach is used, the classical limit is reached for magnetic films of about 150 nm thickness, but the Casimir free energy remains nonzero in the limit of ideal metal, contrary to expectations. For the plasma model approach the Casimir free energy of a film vanishes in this case. Numerical computations are performed for the magnetic films made of Ni, nonmagnetic plates made of Cu and Al, and magnetic plates made of Fe using the tabulated optical data for the complex indexes of refraction of all metals. The obtained results can be used for a discrimination between the plasma and Drude model approaches in the Casimir physics and in the investigation of stability of thin films.
A psychovisual quality metric in free-energy principle.
Zhai, Guangtao; Wu, Xiaolin; Yang, Xiaokang; Lin, Weisi; Zhang, Wenjun
2012-01-01
In this paper, we propose a new psychovisual quality metric of images based on recent developments in brain theory and neuroscience, particularly the free-energy principle. The perception and understanding of an image is modeled as an active inference process, in which the brain tries to explain the scene using an internal generative model. The psychovisual quality is thus closely related to how accurately visual sensory data can be explained by the generative model, and the upper bound of the discrepancy between the image signal and its best internal description is given by the free energy of the cognition process. Therefore, the perceptual quality of an image can be quantified using the free energy. Constructively, we develop a reduced-reference free-energy-based distortion metric (FEDM) and a no-reference free-energy-based quality metric (NFEQM). The FEDM and the NFEQM are nearly invariant to many global systematic deviations in geometry and illumination that hardly affect visual quality, for which existing image quality metrics wrongly predict severe quality degradation. Although with very limited or even without information on the reference image, the FEDM and the NFEQM are highly competitive compared with the full-reference SSIM image quality metric on images in the popular LIVE database. Moreover, FEDM and NFEQM can measure correctly the visual quality of some model-based image processing algorithms, for which the competing metrics often contradict with viewers' opinions.
Determination of Free-Energy Relationships Using Gas Chromatography
Snow, Nicholas H.
1996-06-01
By performing a few straightforward analyses on a gas chromatograph, it is possible to calculate the free energy, enthalpy, and entropy changes that occur when a compound transfers between the mobile and stationary phases. The partition theory of chromatography allows this transfer to be expressed as a chemical equlibrium. By calculating the equilibrium constant for this reaction from chromatographic retention times, the standard free energy change may be determined, and from this, the standard enthalpy and entropy changes. Also, by calculating these values at several temperatures for structurally related compounds, it is possible to explore the relationship between chromatographic retention, standard free energy, and the structure of a compound. These calculations were performed for groups of homologous alcohols, acetates, and hydrocarbons on packed and capillary column gas chromatographs, using both polar and non-polar columns, and on computer simulation software. It is seen that for homologous compounds, the relationship between standard free energy change in partitioning and hydrocarbon chain length for this reaction is linear. It is also seen that gas chromatography represents a useful tool for the calculation and comparison of thermodynamic properties of compounds and that straightforward exercise of this type allows training of students in chromatographic analysis, basic partition theory, thermodynamic relationships, and linear free energy relationships.
PhyloGibbs-MP: module prediction and discriminative motif-finding by Gibbs sampling.
Siddharthan, Rahul
2008-08-29
PhyloGibbs, our recent Gibbs-sampling motif-finder, takes phylogeny into account in detecting binding sites for transcription factors in DNA and assigns posterior probabilities to its predictions obtained by sampling the entire configuration space. Here, in an extension called PhyloGibbs-MP, we widen the scope of the program, addressing two major problems in computational regulatory genomics. First, PhyloGibbs-MP can localise predictions to small, undetermined regions of a large input sequence, thus effectively predicting cis-regulatory modules (CRMs) ab initio while simultaneously predicting binding sites in those modules-tasks that are usually done by two separate programs. PhyloGibbs-MP's performance at such ab initio CRM prediction is comparable with or superior to dedicated module-prediction software that use prior knowledge of previously characterised transcription factors. Second, PhyloGibbs-MP can predict motifs that differentiate between two (or more) different groups of regulatory regions, that is, motifs that occur preferentially in one group over the others. While other "discriminative motif-finders" have been published in the literature, PhyloGibbs-MP's implementation has some unique features and flexibility. Benchmarks on synthetic and actual genomic data show that this algorithm is successful at enhancing predictions of differentiating sites and suppressing predictions of common sites and compares with or outperforms other discriminative motif-finders on actual genomic data. Additional enhancements include significant performance and speed improvements, the ability to use "informative priors" on known transcription factors, and the ability to output annotations in a format that can be visualised with the Generic Genome Browser. In stand-alone motif-finding, PhyloGibbs-MP remains competitive, outperforming PhyloGibbs-1.0 and other programs on benchmark data.
PhyloGibbs-MP: module prediction and discriminative motif-finding by Gibbs sampling.
Rahul Siddharthan
Full Text Available PhyloGibbs, our recent Gibbs-sampling motif-finder, takes phylogeny into account in detecting binding sites for transcription factors in DNA and assigns posterior probabilities to its predictions obtained by sampling the entire configuration space. Here, in an extension called PhyloGibbs-MP, we widen the scope of the program, addressing two major problems in computational regulatory genomics. First, PhyloGibbs-MP can localise predictions to small, undetermined regions of a large input sequence, thus effectively predicting cis-regulatory modules (CRMs ab initio while simultaneously predicting binding sites in those modules-tasks that are usually done by two separate programs. PhyloGibbs-MP's performance at such ab initio CRM prediction is comparable with or superior to dedicated module-prediction software that use prior knowledge of previously characterised transcription factors. Second, PhyloGibbs-MP can predict motifs that differentiate between two (or more different groups of regulatory regions, that is, motifs that occur preferentially in one group over the others. While other "discriminative motif-finders" have been published in the literature, PhyloGibbs-MP's implementation has some unique features and flexibility. Benchmarks on synthetic and actual genomic data show that this algorithm is successful at enhancing predictions of differentiating sites and suppressing predictions of common sites and compares with or outperforms other discriminative motif-finders on actual genomic data. Additional enhancements include significant performance and speed improvements, the ability to use "informative priors" on known transcription factors, and the ability to output annotations in a format that can be visualised with the Generic Genome Browser. In stand-alone motif-finding, PhyloGibbs-MP remains competitive, outperforming PhyloGibbs-1.0 and other programs on benchmark data.
Generalization of Gibbs Entropy and Thermodynamic Relation
Park, Jun Chul
2010-01-01
In this paper, we extend Gibbs's approach of quasi-equilibrium thermodynamic processes, and calculate the microscopic expression of entropy for general non-equilibrium thermodynamic processes. Also, we analyze the formal structure of thermodynamic relation in non-equilibrium thermodynamic processes.
Variational Approach to Enhanced Sampling and Free Energy Calculations
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.
A Variational Approach to Enhanced Sampling and Free Energy Calculations
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.
Generalized Ensemble Sampling of Enzyme Reaction Free Energy Pathways
Wu, Dongsheng; Fajer, Mikolai I.; Cao, Liaoran; Cheng, Xiaolin; Yang, Wei
2016-01-01
Free energy path sampling plays an essential role in computational understanding of chemical reactions, particularly those occurring in enzymatic environments. Among a variety of molecular dynamics simulation approaches, the generalized ensemble sampling strategy is uniquely attractive for the fact that it not only can enhance the sampling of rare chemical events but also can naturally ensure consistent exploration of environmental degrees of freedom. In this review, we plan to provide a tutorial-like tour on an emerging topic: generalized ensemble sampling of enzyme reaction free energy path. The discussion is largely focused on our own studies, particularly ones based on the metadynamics free energy sampling method and the on-the-path random walk path sampling method. We hope that this mini presentation will provide interested practitioners some meaningful guidance for future algorithm formulation and application study. PMID:27498634
Free energy barrier in the growth of sulfuric acid-ammonia and sulfuric acid-dimethylamine clusters
Olenius, T.; Kupiainen-Määttä, O.; Ortega, I. K.; Kurtén, T.; Vehkamäki, H.
2013-08-01
The first step in atmospheric new particle formation involves the aggregation of gas phase molecules into small molecular clusters that can grow by colliding with gas molecules and each other. In this work we used first principles quantum chemistry combined with a dynamic model to study the steady-state kinetics of sets of small clusters consisting of sulfuric acid and ammonia or sulfuric acid and dimethylamine molecules. Both sets were studied with and without electrically charged clusters. We show the main clustering pathways in the simulated systems together with the quantum chemical Gibbs free energies of formation of the growing clusters. In the sulfuric acid-ammonia system, the major growth pathways exhibit free energy barriers, whereas in the acid-dimethylamine system the growth occurs mainly via barrierless condensation. When ions are present, charged clusters contribute significantly to the growth in the acid-ammonia system. For dimethylamine the role of ions is minor, except at very low acid concentration, and the growing clusters are electrically neutral.
Elm, Jonas; Bilde, Merete; Mikkelsen, Kurt V
2012-06-12
This work assesses different computational strategies for predicting structures and Gibb's free energies of reaction of atmospheric prenucleation clusters. The performance of 22 Density Functional Theory functionals in predicting equilibrium structures of molecules and water prenucleation clusters of atmospheric relevance is evaluated against experimental data using a test set of eight molecules and prenucleation clusters: SO2, H2SO4, CO2·H2O, CS2·H2O, OCS·H2O, SO2·H2O, SO3·H2O, and H2SO4·H2O. Furthermore, the functionals are tested and compared for their ability to predict the free energy of reaction for the formation of five benchmark atmospheric prenucleation clusters: H2SO4·H2O, H2SO4·(H2O)2, H2SO4·NH3, HSO4(-)·H2O, and HSO4(-)·(H2O)2. The performance is evaluated against experimental data, coupled cluster, and complete basis set extrapolation procedure methods. Our investigation shows that the utilization of the M06-2X functional with the 6-311++G(3df,3pd) basis set represents an improved approach compared to the conventionally used PW91 functional, yielding mean absolute errors of 0.48 kcal/mol and maximum errors of 0.67 kcal/mol compared to experimental results.
Liu, Guoyu; Gu, Daming; Liu, Haiyan; Ding, Wei; Luan, Huoxin; Lou, Yanmin
2012-06-01
In this article, the validity and accuracy of the free energy perturbation (FEP) model used in a previous article for ionic liquid-type Gemini imidazolium surfactants (ILGISs) is further evaluated by using it to model the Enthalpy-entropy compensation of Sulfobetaine-type Zwitterionic Gemini Surfactants (SZGSs), with different carbon atoms of the hydrophobic group or the spacer chain length, in aqueous solutions. In the FEP model, the Gibbs free energy contributions to the driving force for micelle formation are computed using hydration data obtained from molecular dynamics simulations. According to the pseudo-phase separation model, the thermodynamic properties of micellization in aqueous solutions for SZGS were discussed. The results show that the micellization of SZGS in aqueous solutions is a spontaneous and entropy-driven process. It is linearly Enthalpy-entropy compensated and different from the micelle formation of ILGIS but similar to anionic surfactants. The compensation temperature was found to be (302±3)K which was lower than ILGIS. As the temperature rises, the micellization is easy initially but then becomes difficult with the unusual changes of enthalpy values from positive to negative. The contribution of entropy change to the micellization tends to decrease but the contribution of enthalpy change tends to increase. In particular, as the number carbon atoms in the alkyl chains and spacer chains are increased, the thermodynamic favorability and stability of the micelles both increase.
Sampling saddle points on a free energy surface.
Samanta, Amit; Chen, Ming; Yu, Tang-Qing; Tuckerman, Mark; E, Weinan
2014-04-28
Many problems in biology, chemistry, and materials science require knowledge of saddle points on free energy surfaces. These saddle points act as transition states and are the bottlenecks for transitions of the system between different metastable states. For simple systems in which the free energy depends on a few variables, the free energy surface can be precomputed, and saddle points can then be found using existing techniques. For complex systems, where the free energy depends on many degrees of freedom, this is not feasible. In this paper, we develop an algorithm for finding the saddle points on a high-dimensional free energy surface "on-the-fly" without requiring a priori knowledge the free energy function itself. This is done by using the general strategy of the heterogeneous multi-scale method by applying a macro-scale solver, here the gentlest ascent dynamics algorithm, with the needed force and Hessian values computed on-the-fly using a micro-scale model such as molecular dynamics. The algorithm is capable of dealing with problems involving many coarse-grained variables. The utility of the algorithm is illustrated by studying the saddle points associated with (a) the isomerization transition of the alanine dipeptide using two coarse-grained variables, specifically the Ramachandran dihedral angles, and (b) the beta-hairpin structure of the alanine decamer using 20 coarse-grained variables, specifically the full set of Ramachandran angle pairs associated with each residue. For the alanine decamer, we obtain a detailed network showing the connectivity of the minima obtained and the saddle-point structures that connect them, which provides a way to visualize the gross features of the high-dimensional surface.
Gibbs free energy and conditions of spinel (MgO-Al{sub 2}O{sub 3}) formation in liquid steel
Itoh, H. [Kuzuu Works, Yoshizawa Lime Industry, Kuzuu-machi (Japan); Fujii, K. [Aishin AW Co. Ltd., Anjo (Japan); Nagasaka, T.; Hino, M. [Dept. of Metallurgy, Graduate School of Engineering, Tohoku Univ., Sendai (Japan)
2003-02-01
The formation conditions of spinel non-metallic inclusion during deoxidation with aluminum in secondary refining furnace with MgO lining were discussed in the present work. The thermodynamic data of deoxidation equilibrium with magnesium, calcium and aluminum in liquid iron were determined by the authors. The activities of oxygen and dissolved deoxidizer were evaluated in the thermodynamic description by the first and second order interaction parameters including the cross product terms. (orig.)
On the Free Energy That Drove Primordial Anabolism
Michael Kaufmann
2009-04-01
Full Text Available A key problem in understanding the origin of life is to explain the mechanism(s that led to the spontaneous assembly of molecular building blocks that ultimately resulted in the appearance of macromolecular structures as they are known in modern biochemistry today. An indispensable thermodynamic prerequisite for such a primordial anabolism is the mechanistic coupling to processes that supplied the free energy required. Here I review different sources of free energy and discuss the potential of each form having been involved in the very first anabolic reactions that were fundamental to increase molecular complexity and thus were essential for life.
Interface free energies in p-spin glass models.
Moore, M A
2006-04-07
The replica method is used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has one-step replica symmetry breaking (1RSB). In any finite dimension the interface free energy is exponentially small for a large system. This result implies that, in finite dimensions, the 1RSB state does not exist, as it is destroyed by thermal excitation of arbitrarily large droplets. The implications of this for the theory of structural glasses are discussed.
Interface free energies in p-spin glass models
2006-01-01
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has one-step replica symmetry breaking (1RSB). In any finite dimension the interface free energy is exponentially small for a large system. This result implies that in finite dimensions, the 1RSB state does not exist, as it is destroyed by thermal excitation of arbi...
Mesoscopic Model for Free Energy Landscape Analysis of DNA sequences
Tapia-Rojo, R; Mazo, J J; Falo, F; 10.1103/PhysRevE.86.021908
2012-01-01
A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites within genome sequences.
Stabilizing Perturbative Yang-Mills Free Energy with Gribov Quantization
Fukushima, Kenji
2013-01-01
We evaluate the free energy of the Yang-Mills theory using the Gribov quantization that copes with non-perturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=T_c~2T_c major uncertainty in our results comes from the non-perturbative running coupling that is adopted from the lattice simulation, while the convergence above 2T_c is impressively robust.
CALCULATION OF CONFORMATIONAL ENTROPY AND FREE ENERGY OF POLYSILANE CHAIN
Meng-bo Luo; Ying-cai Chen; Jian-hua Huang; Jian-min Xu
2001-01-01
The conformational entropy S and free energy F were calculated by exact enumeration of polysilane chain up to 23 segments with excluded volume (EV) and long-range van der Waals (VW) interaction. A nonlinear relation between SEV+VW and chain length n was found though SEV was found to vary linearly with n. We found that the second-order transition temperature of polysilane chain with VW interaction increases with the increase of chain length, while that of polysilane chain without VW interaction is chain length independent. Moreover, the free energies FEV+VW and FEV are both linearly related with n, and FEV+VW＜FEV for all temperatures.``
Relationship between wave energy and free energy from pickup ions in the Comet Halley environment
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.
Free energy functionals for polarization fluctuations: Pekar factor revisited
Dinpajooh, Mohammadhasan; Newton, Marshall D.; Matyushov, Dmitry V.
2017-02-01
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. 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).
Locating landmarks on high-dimensional free energy surfaces.
Chen, Ming; Yu, Tang-Qing; Tuckerman, Mark E
2015-03-17
Coarse graining of complex systems possessing many degrees of freedom can often be a useful approach for analyzing and understanding key features of these systems in terms of just a few variables. The relevant energy landscape in a coarse-grained description is the free energy surface as a function of the coarse-grained variables, which, despite the dimensional reduction, can still be an object of high dimension. Consequently, navigating and exploring this high-dimensional free energy surface is a nontrivial task. In this paper, we use techniques from multiscale modeling, stochastic optimization, and machine learning to devise a strategy for locating minima and saddle points (termed "landmarks") on a high-dimensional free energy surface "on the fly" and without requiring prior knowledge of or an explicit form for the surface. In addition, we propose a compact graph representation of the landmarks and connections between them, and we show that the graph nodes can be subsequently analyzed and clustered based on key attributes that elucidate important properties of the system. Finally, we show that knowledge of landmark locations allows for the efficient determination of their relative free energies via enhanced sampling techniques.
Torrent Burgues, J. (Departamento de Ingenieria Quimica, Universidad Politecnica de Cataluna, Tarrasa (Spain))
1994-01-01
A thermodynamic treatment has been used to obtain, with different degrees of approximation, the total change in the Gibbs energy for the crystallization of hydrated and non-hydrated solids. Different equations have been deduced and their degree of accuracy tested for several electrolytes. Calculations have been done to show the applicability of the change in the Gibbs energy for the simultaneous precipitation of electrolytes with different stoichiometry and a common ion. (Author) 17 refs.
Analyticity of the Free Energy of a Closed 3-Manifold
Stavros Garoufalidis
2008-11-01
Full Text Available The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant of a closed 3-manifold with gauge group U(N for arbitrary N. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus g part of the free energy is convergent in a neighborhood of zero, independent of the genus. Our results follow from an estimate of the LMO invariant, in a particular gauge, and from recent results of Bender-Gao-Richmond on the asymptotics of the number of rooted maps for arbitrary genus. We illustrate our results with an explicit formula for the free energy of a Lens space. In addition, using the Painlevé differential equation, we obtain an asymptotic expansion for the number of cubic graphs to all orders, stengthening the results of Bender-Gao-Richmond.
Exploiting Lipid Permutation Symmetry to Compute Membrane Remodeling Free Energies
Bubnis, Greg; Risselada, Herre Jelger; Grubmüller, Helmut
2016-10-01
A complete physical description of membrane remodeling processes, such as fusion or fission, requires knowledge of the underlying free energy landscapes, particularly in barrier regions involving collective shape changes, topological transitions, and high curvature, where Canham-Helfrich (CH) continuum descriptions may fail. To calculate these free energies using atomistic simulations, one must address not only the sampling problem due to high free energy barriers, but also an orthogonal sampling problem of combinatorial complexity stemming from the permutation symmetry of identical lipids. Here, we solve the combinatorial problem with a permutation reduction scheme to map a structural ensemble into a compact, nondegenerate subregion of configuration space, thereby permitting straightforward free energy calculations via umbrella sampling. We applied this approach, using a coarse-grained lipid model, to test the CH description of bending and found sharp increases in the bending modulus for curvature radii below 10 nm. These deviations suggest that an anharmonic bending term may be required for CH models to give quantitative energetics of highly curved states.
Supersymmetric Langevin equation to explore free-energy landscapes.
Mossa, Alessandro; Clementi, Cecilia
2007-04-01
The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.
Path finding on high-dimensional free energy landscapes
Díaz Leines, G.; Ensing, B.
2012-01-01
We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the
A NOTE ON THE PROJECTION OF GIBBS MEASURES
LORINCZI, J; VANDEVELDE, K
1994-01-01
We give an example of a projection which maps two Gibbs measures for the same interaction into Gibbs measures for different interactions. As a corollary we find a case where by decimation a non-Gibbsian measure is transformed into a Gibbs measure.
Looking for some free energy? Call JEFREE (…).
Zerbetto, Mirco; Piserchia, Andrea; Frezzato, Diego
2014-09-30
In this communication, we present the Jarzynski's Equality FREe Energy (JEFREE) library, an efficient and easy-to-use C++ library targeted to the calculation of the free energy profile along a selected generalized coordinate of a system, within the framework of the nonequilibrium steered transformations as introduced by Jarzynski [Phys. Rev. E, 1997, 56, 5018]. JEFREE can be readily integrated into any code, since both C and FORTRAN wrappers have been developed, and easily customizable by a user thanks to the object-oriented programming paradigm offered by the C++ language. Also, JEFREE implements the novel idea of making a total "morphing" of the system energy landscape before initiating the proper steering stage. This proves to be an efficient mean to overtake the problematic sampling of the initial equilibrium state when the number of degrees of freedom is high and the landscape owns many local minima separated by large energy barriers. The calculation of the free energy profile for the rotation along torsion angles in alkyl chains is presented as an example of application of our tool.
The free energy cost of accurate biochemical oscillations
Cao, Yuansheng; Ouyang, Qi; Tu, Yuhai
2015-01-01
Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study four different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. We find that the phase diffusion constant follows the same inverse dependence on the free energy dissipation per period for all systems studied. This relationship between the phase diffusion and energy dissipation is shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this un...
A new principle of synthetic cascade utilization of chemical energy and physical energy
JIN; Hongguang; HONG; Hui; WANG; Baoqun; HAN; Wei; LIN; Rum
2005-01-01
We propose a new principle of the cascade utilization of both chemical energy and physical energy in energy systems with the integration of chemical processes and thermal cycles. Particularly, a general equation of energy levels of substance, Gibbs free energy of chemical reaction and physical energy is explicitly founded. On the basis of this equation, a chemical-looping combustion and an indirect combustion are investigated. Furthermore, a mechanism of energy release, with the combination of decreasing the energy level of Gibbs free energy and upgrading the energy level of low or middle- temperature thermal energy, is clarified. The promising results obtained here establish a theoretical basis for the further investigation of multi-function systems in which energy and the environment are compatible, and create a new approach to improve the performance of traditional thermal cycles.
Escobedo, Fernando A
2014-03-07
In this work, a variant of the Gibbs-Duhem integration (GDI) method is proposed to trace phase coexistence lines that combines some of the advantages of the original GDI methods such as robustness in handling large system sizes, with the ability of histogram-based methods (but without using histograms) to estimate free-energies and hence avoid the need of on-the-fly corrector schemes. This is done by fitting to an appropriate polynomial function not the coexistence curve itself (as in GDI schemes) but the underlying free-energy function of each phase. The availability of a free-energy model allows the post-processing of the simulated data to obtain improved estimates of the coexistence line. The proposed method is used to elucidate the phase behavior for two non-trivial hard-core mixtures: a binary blend of spheres and cubes and a system of size-polydisperse cubes. The relative size of the spheres and cubes in the first mixture is chosen such that the resulting eutectic pressure-composition phase diagram is nearly symmetric in that the maximum solubility of cubes in the sphere-rich solid (∼20%) is comparable to the maximum solubility of spheres in the cube-rich solid. In the polydisperse cube system, the solid-liquid coexistence line is mapped out for an imposed Gaussian activity distribution, which produces near-Gaussian particle-size distributions in each phase. A terminal polydispersity of 11.3% is found, beyond which the cubic solid phase would not be stable, and near which significant size fractionation between the solid and isotropic phases is predicted.
无
2008-01-01
2008年7月10日，为工模具制造商和零部件制造商提供CAD／CAM完整解决方案的领导者Cimatron有限公司宣布，其子公司Microsystem Srl．公司将在意大利销售先进的加工软件解决方案GibbsCAM，并提供技术支持。GibbsCAM软件解决方案为加工、车、车铣复合、旋转铣削、墓石加工系统、线切割、多刀塔／多主轴机床等提供广泛的CNC编程功能。专门适用于制造业的建模功能性调谐，支持线框、曲面、实体等的创建和操作。GibbsCAM软件采用了直观用户界面，内置结合性与仿真功能，能使制造商提高生产力，提高对客户要求的反应速度。GibbsCAM软件支持先进的供应商的控制器和机床，包括GE Fanuc，Infimatic，西门子，Doosan Infracore，Haas，index，MAG Fadal，Matsuura，Mazak，三菱，Mori Seiki，Nakamura Tome和Tornos等。
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.
Energy and the Canada-US Free Trade Agreement
Carmichael, E.A.
1988-01-01
The Canada-USA Free Trade Agreement has raised concerns in both countries with respect to its provisions that may affect security of energy supplies, market access, and energy policy. This document summarizes what the Agreement actually says with regard to energy questions, and reviews Canadian and US energy policies in the postwar period. Three distinct stages of North American energy policy are identified, according to the oil price situation in each stage. From this review, a number of observations are made on the effects of various energy-related policies, and it is noted that past policies of trade restrictions, price controls, and discriminatory treatment of foreign supplies have proven to be wasteful. On the other hand, this is not taken to mean that Canada and the USA should not give up the ability to conduct independent, constructive energy policies, and the exact provisions of the Agreement's energy chapter are examined with that point in mind. The benefits of the Agreement for Canada are outlined, notably in the uranium, oil/gas, and electricity sectors. It is concluded that the Agreement does not reduce Canada's energy supply security, and that it should enhance the energy security of both Canada and the USA. 11 refs.
Photospheric Magnetic Free Energy Density of Solar Active Regions
Zhang, Hongqi
2016-12-01
We present the photospheric energy density of magnetic fields in two solar active regions (one of them recurrent) inferred from observational vector magnetograms, and compare it with other available differently defined energy parameters of magnetic fields in the photosphere. We analyze the magnetic fields in Active Regions NOAA 6580-6619-6659 and 11158. The quantity 1/4π{B}n\\cdot{B}p is an important energy parameter that reflects the contribution of magnetic shear to the difference between the potential (Bp) and the non-potential magnetic field (Bn), and also the contribution to the free magnetic energy near the magnetic neutral lines in the active regions. It is found that the photospheric mean magnetic energy density shows clear changes before the powerful solar flares in Active Region NOAA 11158, which is consistent with the change in magnetic fields in the flaring lower atmosphere.
A new energy transfer model for turbulent free shear flow
Liou, William W.-W.
1992-01-01
A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.
Photospheric Magnetic Free Energy Density of Solar Active Regions
Zhang, Hongqi
2016-01-01
We present the photospheric energy density of magnetic fields in two solar active regions inferred from observational vector magnetograms, and compare it with the possible different defined energy parameters of magnetic fields in the photosphere. We analyze the magnetic fields in active region NOAA 6580-6619-6659 and 11158. It is noticed that the quantity 1/4pi Bn.Bp is an important energy parameter that reflects the contribution of magnetic shear on the difference between the potential magnetic field (Bp) and non-potential one (Bn), and also the contribution to the free magnetic energy near the magnetic neutral lines in the active regions. It is found that the photospheric mean magnetic energy density changes obviously before the powerful solar flares in the active region NOAA 11158, it is consistent with the change of magnetic fields in the lower atmosphere with flares.
Liquid-drop formalism and free-energy surfaces in binary homogeneous nucleation theory
Laaksonen, A. [Department of Applied Physics, University of Kuopio, P.O. Box 1627, 70211 Kuopio (Finland)]|[Department of Physics, P.O. Box 9, 00014 University of Helsinki, Helsinki (Finland); McGraw, R. [Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States); Vehkamaeki, H. [Department of Physics, P.O. Box 9, 00014 University of Helsinki, Helsinki (Finland)]|[University College London, Department of Physics and Astronomy, Gower Street, London WC1E 6BT (United Kingdom)
1999-08-01
Three different derivations of the classical binary nucleation theory are considered in detail. It is shown that the derivation originally presented by Wilemski [J. Chem. Phys. {bold 80}, 1370 (1984)] is consistent with more extensive derivations [Oxtoby and Kashchiev, J. Chem. Phys. {bold 100}, 7665 (1994)]; Debenedetti, {ital Metastable Liquids: Concepts and Principles} (Princeton University Press, Princeton, 1996) if and only if the assumption is made that the surface of tension of the binary nucleus coincides with the dividing surface specified by the surface condition {summation}n{sub si}v{sub li}=0, where the n{sub si} denote surface excess numbers of molecules of species {ital i}, and the v{close_quote}s are partial molecular volumes. From this condition, it follows that (1) the surface tension is curvature independent and (2) that the nucleus volume is V={summation}n{sub li}v{sub li}={summation}g{sub i}v{sub li}, where the n{sub li} are the numbers of molecules in the uniform liquid phase of the droplet model encompassed by the surface of tension, and the g{sub i} are the total molecular occupation numbers contained by the nucleus. We show, furthermore, that the above surface condition leads to explicit formulas for the surface excess numbers n{sub si} in the nucleus. Computations for the ethanol{endash}water system show that the surface number for water molecules (n{sub s,H{sub 2}O}) causes the negative occupation numbers (g{sub H{sub 2}O}) obtained earlier using the classical nucleation theory. The unphysical behavior produced by the classical theory for surface active systems is thus a direct consequence of the assumption of curvature independence of surface tension. Based on the explicit formulas for n{sub si}, we calculate the full free-energy surfaces for binary nucleation in the revised classical theory and compare these with the free-energy surfaces in the Doyle (unrevised classical) theory. Significant differences in nucleus size and composition
Free energy option and its relevance to improve domestic energy demands in southern Nigeria
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.
Real single ion solvation free energies with quantum mechanical simulation
Duignan, Timothy TS; Baer, Marcel D.; Schenter, Gregory K.; Mundy, Christopher J.
2017-09-01
Single ion solvation free energies are one of the most important properties of electrolyte solution and yet there is ongoing debate about what these values are. Experimental methods can only determine the values for neutral ion pairs. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A new method to rigorously correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium’s solvation energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model. We would like to thank Thomas Beck, Shawn Kathmann and Sotiris Xantheas for helpful discussions. Computing resources were generously allocated by PNNLs Institutional Computing program. This research also used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. TTD, GKS and CJM were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. MDB was supported by MS3 (Materials Synthesis and Simulation Across Scales) Initiative, a Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated by Battelle for the U.S. Department of Energy.
Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship
Lin, Shu-Kun
2008-01-01
Information (I) is defined as the amount of the data after data compression. The first law of information theory: the total amount of data L (the sum of entropy S and information I) of an isolated system remains unchanged. The second law of information theory: Information I of an isolated system decreases to a minimum at equilibrium. The third law of information theory: For a solid structure of perfect symmetry (e.g., a perfect crystal), the information I is zero and the (information theory) entropy (called by me as static entropy for solid state) S is at the maximum. Gibbs Paradox has been resolved. Spontaneously mixed substances at gaseous state can be spontaneously separated at condensed phases (solid or liquid states), driving only by information loss or by the increase in (information theory) entropy. None of the typical pure mixing or separation processes are driving by free energy minimization and the free energy (or total amount of chemical potential) has no change during the processes of ideal mixtur...
Characterization of a free air ionization chamber for low energies
Silva, Natalia F.; Xavier, Marcos; Vivolo, Vitor; Caldas, Linda V.E., E-mail: nsilva@ipen.br, E-mail: mxavier@ipen.br, E-mail: vivolo@ipen.br, E-mail: lcaldas@ipen.br [Instituto de Pesquisas Energeticas e Nucleres (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2015-07-01
Free air ionization chambers are used by most primary metrology laboratories as primary standards of the quantities air kerma and exposure in X-ray beams. The free air ionization chamber for low energies of the Calibration Laboratory (LCI) of IPEN showed in a characterization test a problem in the set responsible for the variation of its sensitive volume. After a modification in the support of the micrometers used for the movement of the internal cylinder and the establishment of a new alignment system protocol, the tests were redone. The objective of this work was to present the results obtained in the new condition. (author)
Feasibility study of thermal energy harvesting using lead free pyroelectrics
Karim, Hasanul; Sarker, Md Rashedul H.; Shahriar, Shaimum; Arif Ishtiaque Shuvo, Mohammad; Delfin, Diego; Hodges, Deidra; (Bill Tseng, Tzu-Liang; Roberson, David; Love, Norman; Lin, Yirong
2016-05-01
Energy harvesting has significant potential for applications in energizing wireless sensors and charging energy storage devices. To date, one of the most widely investigated materials for mechanical and thermal energy harvesting is lead zirconate titanate (PZT). However, lead has detrimental effects on the environment and on health. Hence, alternative materials are required for this purpose. In this paper, a lead free material, lithium niobate (LNB) is investigated as a potential material for pyroelectric energy harvesting. Although its theoretical pyroelectric properties are lower compared to PZT, it has better properties than other lead free alternatives such as ZnO. In addition, LNB has a high Curie temperature of about 1142 °C, which makes it applicable for high temperature energy harvesting, where other pyroelectric ceramics are not suitable. Herein, an energy harvesting and storage system composed of a single crystal LNB and a porous carbon-based super-capacitor was investigated. It is found that with controlled heating and cooling, a single wafer of LNB (75 mm diameter and 0.5 mm thickness) could generate 437.72 nW cm-3 of power and it could be used to charge a super-capacitor with a charging rate of 2.63 mV (h cm3)-1.
Free-Free Transitions in the Presence of Laser Fields at Very Low Incident Electron Energy
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.
FreeSolv: a database of experimental and calculated hydration free energies, with input files.
Mobley, David L; Guthrie, J Peter
2014-07-01
This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .
Jia, Xiangyu; Wang, Meiting; Shao, Yihan; König, Gerhard; Brooks, Bernard R; Zhang, John Z H; Mei, Ye
2016-02-09
In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.
The leading term of the Yang-Mills free energy
Chatterjee, Sourav
2016-01-01
The construction of quantum Yang-Mills theories is a central open question in mathematical physics, famously posed as one of the millennium prize problems by the Clay Institute. Although huge strides were made in the Eighties, the problem has remained unsolved in dimensions three and four. This article makes a new contribution to this quest, by explicitly calculating the leading term of the free energy of three dimensional $U(N)$ lattice gauge theory for any $N$, as the lattice spacing tends to zero. This is a small step towards the complete solution of the above problem, since the main question can be rephrased as the problem of determining of the full asymptotics of the free energy, rather than only the leading term. The proof is based on a novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four dimensional theory, but only in the weak coupling limit.
Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors
Fosco, C D; Mazzitelli, F D
2016-01-01
We evaluate the difference between the Casimir free energies corresponding to either grounded or isolated perfect conductors, at high temperatures. We show that a general and simple expression for that difference can be given, in terms of the electrostatic capacitance matrix for the system of conductors. For the case of close conductors, we provide approximate expressions for that difference, by evaluating the capacitance matrix using the proximity force approximation. Since the high-temperature limit for the Casimir free energy for a medium described by a frequency-dependent conductivity diverging at zero frequency coincides with that of an isolated conductor, our results may shed light on the corrections to the Casimir force in the presence of real materials.
A Parallel-pulling Protocol for Free Energy Evaluation
Ngo, Van
2011-01-01
Jarzynski's equality (JE) allows us to compute free energy differences (FEDs) from distributions of work performed on a system. We show that it is possible to generate the work distributions in single step-wise pulling simulations in order to compute FEDs by JE without generating many trajectories using virtual optical traps. We suggest an alternative method for directly computing FEDs in both sequential- and parallel-pulling protocols based on measurements of averaged reaction coordinates along pathways. In comparison with the commonly used Potential of Mean Force method applied to stretching a Deca-Alanine molecule, we show that the parallel-pulling protocol is at least 20 times faster than slow sequential-pulling protocols for producing the same free energy barrier with the uncertainty less than 2.0 kcal/mol.
Free energy landscapes of ion coordination in aqueous solution.
Brancato, Giuseppe; Barone, Vincenzo
2011-11-10
We show how the fruitful concept of free energy landscape, as invoked in the description of complex biological systems, can be rather easily extended to build up a simple and accurate picture about solvent coordination around ions. This may represent a revealing key element for the qualitative and quantitative physical-chemical interpretation of a large number of phenomena occurring in solution, such as water exchange mechanisms, ion mobility, solvation dynamics, ion channel selectivity, and so on. In particular, using a computational approach rooted into molecular dynamics simulations and enhanced sampling techniques, we show how the free energy landscapes of ion coordination in solution can be very easily and accurately obtained in a number of illustrative examples.
Solid/liquid interfacial free energies in binary systems
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.
Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics
Christoph Dellago
2013-12-01
Full Text Available As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate, driving the system away from equilibrium. In this article, we first briefly review the Jarzynski identity and the Crooks fluctuation theorem and then survey various algorithms building on these relations. We pay particular attention to the statistical efficiency of these methods and discuss practical issues arising in their implementation and the analysis of the results.
Energy and the NAFTA [North American Free Trade Agreement
Plourde, A.
1993-05-01
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.
Harris, Robert C; Deng, Nanjie; Levy, Ronald M; Ishizuka, Ryosuke; Matubayasi, Nobuyuki
2016-12-23
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.
Characterizing structural transitions using localized free energy landscape analysis.
Nilesh K Banavali
Full Text Available BACKGROUND: 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. METHODOLOGY/PRINCIPAL FINDINGS: 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. CONCLUSIONS/SIGNIFICANCE: 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.
Surface Free Energy Determination of APEX Photosensitive Glass
William R. Gaillard; Emanuel Waddell; Williams, John D.
2016-01-01
Surface free energy (SFE) plays an important role in microfluidic device operation. Photosensitive glasses such as APEX offer numerous advantages over traditional glasses for microfluidics, yet the SFE for APEX has not been previously reported. We calculate SFE with the Owens/Wendt geometric method by using contact angles measured with the Sessile drop technique. While the total SFE for APEX is found to be similar to traditional microstructurable glasses, the polar component is lower, which i...
Methods for the calculation of surface free energy of solids
M. Żenkiewicz
2007-01-01
Purpose: The main purpose of this paper is the analysis of the most common methods for the calculation of the surface free energy (SFE) of solids, utilising the results of the contact angle measurements. The calculation deals also with the SFE at the interface, especially that at the surface of polymers and polymeric materials. The survey has been meant to ease the understanding of physical processes occurring at the solid-liquid interface and to help to find proper measuring methods with res...
Free energy topological expansion for the 2-matrix model
Chekhov, Leonid [Steklov Mathematical Institute, ITEP and Poncelet Laboratoire, Moscow (Russian Federation); Eynard, Bertrand [Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex (France); Orantin, Nicolas [Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex (France)
2006-12-15
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.
Surface free energy analysis of adsorbents used for radioiodine adsorption
González-García, C.M. [Departamento de Física Aplicada, Universidad de Extremadura, Avda. Elvas s/n, 06006 Badajoz (Spain); Román, S., E-mail: sroman@unex.es [Departamento de Física Aplicada, Universidad de Extremadura, Avda. Elvas s/n, 06006 Badajoz (Spain); González, J.F.; Sabio, E. [Departamento de Física Aplicada, Universidad de Extremadura, Avda. Elvas s/n, 06006 Badajoz (Spain); Ledesma, B. [Departamento de Ingeniería Mecánica, Energética y de los Materiales, Universidad de Extremadura, Avda. Elvas s/n, 06006 Badajoz (Spain)
2013-10-01
In this work, the surface free energy of biomass-based activated carbons, both fresh and impregnated with triethylenediamine, has been evaluated. The contribution of Lifshitz van der Waals components was determined by the model proposed by van Oss et al. The results obtained allowed predicting the most probable configurations of the impregnant onto the carbon surface and its influence on the subsequent adsorption of radioactive methyl iodide.
Calculating Free Energies Using Scaled-Force Molecular Dynamics Algorithm
Darve, Eric; Wilson, Micahel A.; Pohorille, Andrew
2000-01-01
One common objective of molecular simulations in chemistry and biology is to calculate the free energy difference between different states of the system of interest. Examples of problems that have such an objective are calculations of receptor-ligand or protein-drug interactions, associations of molecules in response to hydrophobic, and electrostatic interactions or partition of molecules between immiscible liquids. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), 'native' state. Perhaps the best example of such a problem is folding of proteins or short RNA molecules. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to 'quasi non-ergodicity', whereby a part of phase space is inaccessible on timescales of the simulation. A host of strategies has been developed to improve efficiency of sampling the phase space. For example, some Monte Carlo techniques involve large steps which move the system between low-energy regions in phase space without the need for sampling the configurations corresponding to energy barriers (J-walking). Most strategies, however, rely on modifying probabilities of sampling low and high-energy regions in phase space such that transitions between states of interest are encouraged. Perhaps the simplest implementation of this strategy is to increase the temperature of the system. This approach was successfully used to identify denaturation pathways in several proteins, but it is clearly not applicable to protein folding. It is also not a successful method for determining free energy differences. Finally, the approach is likely to fail for systems with co-existing phases, such as water-membrane systems, because it may lead to spontaneous
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
Rudolf A. Treumann
2014-08-01
Full Text Available We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative $T$ claim.
Emotional valence and the free-energy principle.
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.
Emotional valence and the free-energy principle.
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.
Surface free energy of a solid from contact angle hysteresis.
Chibowski, Emil
2003-04-25
Nature of contact angle hysteresis is discussed basing on the literature data (Colloids Surf. A 189 (2001) 265) of dynamic advancing and receding contact angles of n-alkanes and n-alcohols on a very smooth surface of 1,1,2,-trichloro-1,2,2,-trifluoroethane (FC-732) film deposited on a silicon plate. The authors considered the liquid absorption and/or retention (swelling) processes responsible for the observed hysteresis. In this paper hysteresis is considered to be due to the liquid film left behind the drop during retreating of its contact line. Using the contact angle hysteresis an approach is suggested for evaluation of the solid surface free energy. Molecular spacing and the film structure are discussed to explain the difference in n-alkanes and n-alcohols behaviour as well as to explain the difference between dispersion free energy gamma(s)(d) and total surface free energy gamma(s)(tot) of FC-732, as determined from the advancing contact angles and the hysteresis, respectively.
Calculating free energies of organic molecules on insulating substrates.
Gaberle, Julian; Gao, David Z; Shluger, Alexander L
2017-01-01
The challenges and limitations in calculating free energies and entropies of adsorption and interaction of organic molecules on an insulating substrate are discussed. The adhesion of 1,3,5-tri(4'-cyano-[1,1'-biphenyl]-4-yl)benzene (TCB) and 1,4-bis(4-cyanophenyl)-2,5-bis(decyloxy)benzene (CDB) molecules to step edges on the KCl(001) surface and the formation of molecular dimers were studied using classical molecular dynamics. Both molecules contain the same anchoring groups and benzene ring structures, yet differ in their flexibility. Therefore, the entropic contributions to their free energy differ, which affects surface processes. Using potential of mean force and thermodynamic integration techniques, free energy profiles and entropy changes were calculated for step adhesion and dimer formation of these molecules. However, converging these calculations is nontrivial and comes at large computational cost. We illustrate the difficulties as well as the possibilities of applying these methods towards understanding dynamic processes of organic molecules on insulating substrates.
Free-Energy Bounds for Hierarchical Spin Models
Castellana, Michele; Barra, Adriano; Guerra, Francesco
2014-04-01
In this paper we study two non-mean-field (NMF) spin models built on a hierarchical lattice: the hierarchical Edward-Anderson model (HEA) of a spin glass, and Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence of the thermodynamic limit of the free energy and the replica-symmetry-breaking (RSB) free-energy bounds previously derived for the Sherrington-Kirkpatrick model of a spin glass. These RSB mean-field bounds are exact only if the order-parameter fluctuations (OPF) vanish: given that such fluctuations are not negligible in NMF models, we develop a novel strategy to tackle part of OPF in hierarchical models. The method is based on absorbing part of OPF of a block of spins into an effective Hamiltonian of the underlying spin blocks. We illustrate this method for DHM and show that, compared to the mean-field bound for the free energy, it provides a tighter NMF bound, with a critical temperature closer to the exact one. To extend this method to the HEA model, a suitable generalization of Griffith's correlation inequalities for Ising ferromagnets is needed: since correlation inequalities for spin glasses are still an open topic, we leave the extension of this method to hierarchical spin glasses as a future perspective.
Free Energy Landscape of GAGA and UUCG RNA Tetraloops
Bottaro, Sandro; Sponer, Jiri; Bussi, Giovanni
2016-01-01
We report the folding thermodynamics of ccUUCGgg and ccGAGAgg RNA tetraloops using atomistic molecular dynamics simulations. We obtain a previously unreported estimation of the folding free energy using parallel tempering in combination with well-tempered metadynamics. A key ingredient is the use of a recently developed metric distance, eRMSD, as a biased collective variable. We find that the native fold of both tetraloops is not the global free energy minimum using the Amber\\c{hi}OL3 force field. The estimated folding free energies are 30.2kJ/mol for UUCG and 7.5 kJ/mol for GAGA, in striking disagreement with experimental data. We evaluate the viability of all possible one-dimensional backbone force field corrections. We find that disfavoring the gauche+ region of {\\alpha} and {\\zeta} angles consistently improves the existing force field. The level of accuracy achieved with these corrections, however, cannot be considered sufficient by judging on the basis of available thermodynamic data and solution experim...
Deconstructing Free Energies in the Law of Matching Water Affinities.
Shi, Yu; Beck, Thomas
2017-03-09
The law of matching water affinities (LMWA) is explored in classical molecular dynamics simulations of several alkali halide ion pairs, spanning the size range from small kosmotropes to large chaotropes. The ion-ion potentials of mean force (PMFs) are computed using three methods: the local molecular field theory (LMFT), the weighted histogram analysis method (WHAM), and integration of the average force. All three methods produce the same total PMF for a given ion pair. In addition, LMFT-based partitioning into van der Waals and local and far-field electrostatic free energies and assessment of the enthalpic, entropic, and ion-water components yield insights into the origins of the observed free energy profiles in water. The results highlight the importance of local electrostatic interactions in determining the shape of the PMFs, while longer-ranged interactions enhance the overall ion-ion attraction, as expected in a dielectric continuum model. The association equilibrium constants are estimated from the smooth WHAM curves and compared to available experimental conductance data. By examining the variations in the average hydration numbers of ions with ion-ion distance, a correlation of the water structure in the hydration shells with the free energy features is found.
Jiang, Wei; Roux, Benoît
2010-07-01
Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of free energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" can improve the statistical convergence in calculations of absolute binding free energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor lambda in the extended ensemble is further coupled with a set of replicas evolving on a biased energy surface with boosting potentials used to accelerate the inter-conversion among different rotameric states of the side chains in the neighborhood of the binding site. Exchanges are allowed to occur alternatively along the axes corresponding to the thermodynamic coupling parameter lambda and the boosting potential, in an extended dual array of coupled lambda- and H-REMD simulations. The method is implemented on the basis of new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. As an illustrative example, the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme was calculated. The tests demonstrate that the dual lambda-REMD and H-REMD simulation scheme greatly accelerates the configurational sampling of the rotameric states of the side chains around the binding pocket, thereby improving the convergence of the FEP computations.
Emmerik, van P.T.; Smolders, C.A.
1973-01-01
The free enthalpy correction parameter g in the Flory-Huggins equation for the Gibbs free enthalpy of mixing in polymer solutions is considered generally as a concentration- and temperature-independent parameter. It has been extended here with linear concentration- and temperature-dependent terms. W
The Virasoro Gibbs state and BTZ black holes
Garbarz, Alan
2016-01-01
We show that the Virasoro Gibbs state accurately describes the thermodynamics of BTZ black holes at large temperatures and in the strong-coupling regime $c<1$. We first give a simple heuristic argument by showing that at high temperatures and arbitrary $c$, the energies are much larger than Planck mass. Then we give a detailed analysis of the quantum fluctuations of the Gibbs state on unitary irreducible representations of Virasoro group and explicitly show that they go to zero in the high-temperature limit by means of representation theory results. This implies the state has a sensible thermodynamic limit which actually holds for any $c$. Finally, the matching with BTZ thermodynamics for $c<1$ is obtained by using the known asymptotic behaviour of the characters of the Virasoro discrete series. This result supports the idea that minimal models could describe quantum gravity at strong coupling. We make no use of the Euclidean path integral nor assume modular invariance of the partition functions, althou...
Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling
无
2007-01-01
The free energy at low temperature in ID sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose Geld method.
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)...
Hayata, Tomoya; Hongo, Masaru; Noumi, Toshifumi
2015-01-01
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time-evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without choice of frame such as the Landau-Lifshitz or Eckart frame.
Dodsworth, Jeremy A; McDonald, Austin I; Hedlund, Brian P
2012-08-01
To inform hypotheses regarding the relative importance of chemolithotrophic metabolisms in geothermal environments, we calculated free energy yields of 26 chemical reactions potentially supporting chemolithotrophy in two US Great Basin hot springs, taking into account the effects of changing reactant and product activities on the Gibbs free energy as each reaction progressed. Results ranged from 1.2 × 10(-5) to 3.6 J kg(-1) spring water, or 3.7 × 10(-5) to 11.5 J s(-1) based on measured flow rates, with aerobic oxidation of CH(4) or NH4 + giving the highest average yields. Energy yields calculated without constraining pH were similar to those at constant pH except for reactions where H(+) was consumed, which often had significantly lower yields when pH was unconstrained. In contrast to the commonly used normalization of reaction chemical affinities per mole of electrons transferred, reaction energy yields for a given oxidant varied by several orders of magnitude and were more sensitive to differences in the activities of products and reactants. The high energy yield of aerobic ammonia oxidation is consistent with previous observations of significant ammonia oxidation rates and abundant ammonia-oxidizing archaea in sediments of these springs. This approach offers an additional lens through which to view the thermodynamic landscape of geothermal springs.
Temperature extrapolation of multicomponent grand canonical free energy landscapes
Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.
2017-08-01
We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.
Sellers, Michael S; Lísal, Martin; Brennan, John K
2016-03-21
We present an extension of various free-energy methodologies to determine the chemical potential of the solid and liquid phases of a fully-flexible molecule using classical simulation. The methods are applied to the Smith-Bharadwaj atomistic potential representation of cyclotrimethylene trinitramine (RDX), a well-studied energetic material, to accurately determine the solid and liquid phase Gibbs free energies, and the melting point (Tm). We outline an efficient technique to find the absolute chemical potential and melting point of a fully-flexible molecule using one set of simulations to compute the solid absolute chemical potential and one set of simulations to compute the solid-liquid free energy difference. With this combination, only a handful of simulations are needed, whereby the absolute quantities of the chemical potentials are obtained, for use in other property calculations, such as the characterization of crystal polymorphs or the determination of the entropy. Using the LAMMPS molecular simulator, the Frenkel and Ladd and pseudo-supercritical path techniques are adapted to generate 3rd order fits of the solid and liquid chemical potentials. Results yield the thermodynamic melting point Tm = 488.75 K at 1.0 atm. We also validate these calculations and compare this melting point to one obtained from a typical superheated simulation technique.
Wahle, Chris W; Ross, David S; Thurston, George M
2012-07-21
minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures.
Heterogeneous nucleation in solutions: generalized Gibbs' approach.
Abyzov, Alexander S; Schmelzer, Jürn W P
2014-06-28
Heterogeneous nucleation in solutions on planar solid surfaces is modeled taking into account changes of the state parameters of the critical clusters in dependence on supersaturation. The account of the variation of the state parameters of the cluster phase on nucleation is performed in the framework of the generalized Gibbs' approach. A regular solution is chosen as a model for the analysis of the basic qualitative characteristics of the process. It is shown that, employing the generalized Gibbs approach, contact angle and catalytic activity factor for heterogeneous nucleation become dependent on the degree of metastability (supersaturation) of the solution. For the case of formation of a cluster in supersaturated solutions on a surface of low wettability (the macroscopic equilibrium contact angles being larger than 90°), the solid surface has only a minor influence on nucleation. In the alternative case of high wettability (for macroscopic equilibrium contact angles being less than 90°), nucleation is significantly enhanced by the solid surface. Effectively, the existence of the solid surface results in a significant shift of the spinodal to lower supersaturations as compared with homogeneous nucleation. Qualitatively, the same behavior is observed now near the new (solid surface induced) limits of instability of the solution as compared with the behavior near to the spinodal curve in the case of homogeneous nucleation.
Generalized Gibbs' approach in heterogeneous nucleation.
Abyzov, Alexander S; Schmelzer, Jürn W P
2013-04-28
Heterogeneous nucleation (condensation and boiling) on planar solid surfaces is described taking into account changes of the state parameters of the critical clusters in dependence on supersaturation. The account of the variation of the state parameters of the cluster phase on nucleation is performed in the framework of the generalized Gibbs' approach. One-component van der Waals fluids are chosen as a model for the analysis of the basic qualitative characteristics of the process. The analysis is performed for both hydrophobic and hydrophilic surfaces and similarities and differences between condensation and boiling processes are discussed for the two different cases. It is shown that, in the generalized Gibbs' approach, contact angle and catalytic factor for heterogeneous nucleation become dependent on the degree of metastability (undercooling or superheating) of the fluid. For the case of formation of a droplet in supersaturated vapor on a hydrophobic surface and bubble formation in a liquid on a hydrophilic surface the solid surface has only a minor influence on nucleation. In the alternative cases of condensation of a droplet on a hydrophilic surface and of bubble formation in a liquid on a hydrophobic surface, nucleation is significantly enhanced by the solid. Effectively, the existence of the solid surface results in a significant shift of the spinodal to lower supersaturations as compared with homogeneous nucleation. Qualitatively the same behavior is observed now near the new (solid surface induced) limits of instability of the fluid as compared with the behavior near to the spinodal curve in the case of homogeneous nucleation.
Approximate scaling properties of RNA free energy landscapes
Baskaran, S.; Stadler, P. F.; Schuster, P.
1996-01-01
RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.
Reflections on Gibbs: From Statistical Physics to the Amistad
Kadanoff, Leo P
2014-01-01
This note is based upon a talk given at a celebration in Austin Texas of the achievements of J. Willard Gibbs. J. Willard Gibbs, the younger, was the first American physical sciences theorist. He was one of the inventors of statistical physics. He introduced and developed the concepts of phase space, phase transitions, and thermodynamic surfaces in a remarkably correct and elegant manner. These three concepts form the basis of different areas of physics. The connection among these areas has been a subject of deep reflection from Gibbs' time to our own. This talk therefore tries to celebrate Gibbs by talking about modern ideas about how different parts of physics fit together. At the end of the talk, I shall get to a more personal note. Our own J. Willard Gibbs had all his achievements concentrated in science. His father, also J. Willard Gibbs, also a Professor at Yale, had one great achievement that remains unmatched in our day. I shall describe it.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-14
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations
Lee, Tai-Sung; Radak, Brian K.; Pabis, Anna; York, Darrin M.
2013-01-01
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem. PMID:23457427
A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations.
Lee, Tai-Sung; Radak, Brian K; Pabis, Anna; York, Darrin M
2013-01-08
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.
Minimal Self-Models and the Free Energy Principle
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.
Investigation of Multipole Electrostatics in Hydration Free Energy Calculations
Shi, Yue; Wu, Chuanjie; Ponder, Jay W.; Ren, Pengyu
2010-01-01
Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio (BAR) method. We have compared two approaches to derive the atomic multipoles from quantum mechanical (QM) calculations: one directly from the new distributed multipole analysis (DMA) and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-ccpVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12Å, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the hydration free energy calculation. PMID:20925089
Energy : Free trade and the price we paid
Pratt, L.; Finn, E. (ed.)
2001-02-01
This paper presented a critique of the North American Free Trade Agreement (NAFTA) claiming it has eliminated and superseded Canadian energy policy and sovereignty. Seven years after the completion of NAFTA, Canadians have had their eyes opened by the recent crisis in high energy prices. It was argued that because of NAFTA, the government of Canada lacks the power to intervene to protect Canadian consumers from rising energy prices. During the winter of 2000-2001 gasoline prices rose even while crude oil was in surplus. Also, natural gas heating charges skyrocketed in Canada mostly due to California's shortage of electricity and natural gas. This report ties the crisis in gas and oil prices to NAFTA. There is no shortage of oil or gas in Canada that can justify these price hikes. The so called shortage has been merely imported through trade agreements. NAFTA has removed the power of the Canadian government to intervene in the energy sector, deregulated exports, and freed Canadian producers to meet the energy demands of an insatiable U.S. market. In addition, NAFTA ties the hands of Canadians who want to cut back exports and conserve our precious non-renewable resources. This report also showed that gas deregulation in North America has caused instability and left many gas users vulnerable to market power and monopoly. The author argued that natural gas, like electric power, needs state regulation because of natural monopoly and to protect consumers. refs., figs.
Free electron lasers for transmission of energy in space
Segall, S. B.; Hiddleston, H. R.; Catella, G. C.
1981-01-01
A one-dimensional resonant-particle model of a free electron laser (FEL) is used to calculate laser gain and conversion efficiency of electron energy to photon energy. The optical beam profile for a resonant optical cavity is included in the model as an axial variation of laser intensity. The electron beam profile is matched to the optical beam profile and modeled as an axial variation of current density. Effective energy spread due to beam emittance is included. Accelerators appropriate for a space-based FEL oscillator are reviewed. Constraints on the concentric optical resonator and on systems required for space operation are described. An example is given of a space-based FEL that would produce 1.7 MW of average output power at 0.5 micrometer wavelength with over 50% conversion efficiency of electrical energy to laser energy. It would utilize a 10 m-long amplifier centered in a 200 m-long optical cavity. A 3-amp, 65 meV electrostatic accelerator would provide the electron beam and recover the beam after it passes through the amplifier. Three to five shuttle flights would be needed to place the laser in orbit.
Kinetic reconstruction of the free-energy landscape.
Wedekind, Jan; Reguera, David
2008-09-04
We present a new general method to trace back a lot of valuable information from direct simulations and experiments of activated processes. In particular, it allows the reconstruction of the free-energy landscape for an arbitrary reaction coordinate directly from the out-of-equilibrium dynamics of the process. We demonstrate the power of this concept by its application to a molecular dynamics simulation of nucleation of a Lennard-Jones vapor. The same method can be also applied to Brownian dynamics and stochastic simulations.
Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
Derrida, B.; Lebowitz, J. L.; Speer, E. R.
2001-10-01
We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size N, the probability of any macroscopic density profile ρ(x) is exp[-NF(\\{ρ\\})] F thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for F is a nonlocal functional of ρ, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.
Electrostatic free energy landscapes for nucleic acid helix assembly
Tan, Zhi-Jie; Chen, Shi-Jie
2006-01-01
Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na + and Mg2+ play distinctive roles in helix–helix assembly. High [Na+] (>0.3 M) causes a reduced helix–helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix–helix attraction and results i...
On Large N Expansion of the Sphere Free Energy
Tarnopolsky, Grigory
2016-01-01
We propose formulas for the $1/N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small $\\epsilon$ near various integer dimensions we find a perfect agreement with results obtained using $\\epsilon$-expansion technique. In $d=3$, the large $N$ results with the $1/N$ correction included are in good agreement with the Pade resummed $\\epsilon$-expansion.
On exact superpotentials, free energies and matrix models
Hailu, Girma; Georgi, Howard [Jefferson Laboratory of Physics, Harvard University, Cambridge, MA (United States)]. E-mail addresses: hailu@feynman.harvard.edu; georgi@physics.harvard.edu
2004-02-01
We discuss exact results for the full nonperturbative effective superpotentials of four dimensional N=1 supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large-N limit. (author)
Tension-dependent Free Energies of Nucleosome Unwrapping
Lequieu, Joshua; Schwartz, David C; de Pablo, Juan J
2016-01-01
Nucleosomes form the basic unit of compaction within eukaryotic genomes and their locations represent an important, yet poorly understood, mechanism of genetic regulation. Quantifying the strength of interactions within the nucleosome is a central problem in biophysics and is critical to understanding how nucleosome positions influence gene expression. By comparing to single-molecule experiments, we demonstrate that a coarse-grained molecular model of the nucleosome can reproduce key aspects of nucleosome unwrapping. Using detailed simulations of DNA and histone proteins, we calculate the tension-dependent free energy surface corresponding to the unwrapping process. The model reproduces quantitatively the forces required to unwrap the nucleosome, and reveals the role played by electrostatic interactions during this process. We then demonstrate that histone modifications and DNA sequence can have significant effects on the energies of nucleosome formation. Most notably, we show that histone tails are crucial f...
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins
A. May; R. Pool; E. van Dijk; J. Bijlard; S. Abeln; J. Heringa; K.A. Feenstra
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 at
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins
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
Long-Wavelength, Free-Free Spectral Energy Distributions from Porous Stellar Winds
Ignace, Richard
2016-01-01
The influence of macroclumps for free-free spectral energy distributions (SEDs) of ionized winds is considered. The goal is to emphasize distinctions between microclumping and macroclumping effects. Microclumping can alter SED slopes and flux levels if the volume filling factor of the clumps varies with radius; however, the modifications are independent of the clump geometry. To what extent does macroclumping alter SED slopes and flux levels? In addressing the question, two specific types of macroclump geometries are explored: shell fragments ("pancake"-shaped) and spherical clumps. Analytic and semi-analytic results are derived in the limiting case that clumps never obscure one another. Numerical calculations based on a porosity formalism is used when clumps do overlap. Under the assumptions of a constant expansion, isothermal, and fixed ionization wind, the fragment model leads to results that are essentially identical to the microclumping result. Mass-loss rate determinations are not affected by porosity e...
The Canada-U. S. Free Trade Agreement and energy
Tomic, S.
1988-04-01
One of the most controversial sections of the Canada-U.S. Free Trade Agreement (FTA) pertains to the energy sector. Opponents to the FTA say it will lead to a massive sellout of Canada's national resources and is a threat to national security. Allies say the FTA will improve Canadian access to U.S. markets; enhance investor confidence in Canada; improve economies of scale; and lead to increased revenue and capital spending. These issues were addressed at the January meeting of the Canadian chapter of International Association of Energy Economists (IAEE). Canada and the U.S. are partners, exchanging goods and services each year worth roughly $140 billion. Energy trade amounts to about $10 billion a year with Canada exporting mainly oil, gas and natural gas liquids, and coal. Both Canada and the U.S. have recognized they have a common interest in ensuring access to each other's market and enhancing their mutual security of supply. Under the FTA, both countries would refrain from new quantitative restrictions on energy exports, taxes, and minimum price requirements subject to limited exceptions. Canadian government is not obliged to deliver any particular quantity but only to refrain from imposing restrictions that would reduce exports below the proportion of Canadian supply which U.S. buyers had purchased during the previous 36 months. The U.S. will also eliminate the restriction on enrichment of Canadian uranium and will allow exports of Alaskan oil to Canada. This article discusses specific elements involving uranium, electrical power, oil and natural gas. The Canada-US Free Trade Agreement, signed by Prime Minister Mulroney and President Reagan on Jan. 2, 1988 has become the focus of vigorous debate not only regarding the rules which will cover trade between the two countries, but also regarding different visions of Canada's future.
Work and entropy production in generalised Gibbs ensembles
Perarnau-Llobet, Martí; Riera, Arnau; Gallego, Rodrigo; Wilming, Henrik; Eisert, Jens
2016-12-01
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.
Tomar, Dheeraj S; Asthagiri, D; Weber, Valéry
2013-09-17
The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.
Iterative free-energy optimization for recurrent neural networks (INFERNO).
Pitti, Alexandre; Gaussier, Philippe; Quoy, Mathias
2017-01-01
The intra-parietal lobe coupled with the Basal Ganglia forms a working memory that demonstrates strong planning capabilities for generating robust yet flexible neuronal sequences. Neurocomputational models however, often fails to control long range neural synchrony in recurrent spiking networks due to spontaneous activity. As a novel framework based on the free-energy principle, we propose to see the problem of spikes' synchrony as an optimization problem of the neurons sub-threshold activity for the generation of long neuronal chains. Using a stochastic gradient descent, a reinforcement signal (presumably dopaminergic) evaluates the quality of one input vector to move the recurrent neural network to a desired activity; depending on the error made, this input vector is strengthened to hill-climb the gradient or elicited to search for another solution. This vector can be learned then by one associative memory as a model of the basal-ganglia to control the recurrent neural network. Experiments on habit learning and on sequence retrieving demonstrate the capabilities of the dual system to generate very long and precise spatio-temporal sequences, above two hundred iterations. Its features are applied then to the sequential planning of arm movements. In line with neurobiological theories, we discuss its relevance for modeling the cortico-basal working memory to initiate flexible goal-directed neuronal chains of causation and its relation to novel architectures such as Deep Networks, Neural Turing Machines and the Free-Energy Principle.
Flavour Fields in Steady State: Stress Tensor and Free Energy
Banerjee, Avik; Kundu, Sandipan
2015-01-01
The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane ...
Effective string theory description of the interface free energy
Billo, M; Ferro, L; Hasenbusch, M; Panero, M
2007-01-01
We compare the predictions of the Nambu-Goto effective string model with a set of high precision Monte Carlo results for interfaces with periodic boundary conditions in the 3D Ising model. We compute the free energy in the covariant gauge exactly, up to the inclusion of the Liouville mode. The perturbative expansion of this result agrees both with the result evaluated several years ago by Dietz and Filk in the physical gauge and with a recent calculation with the Polchinski-Strominger action. We also derive the effective string spectrum which, because of the different boundary conditions, is very different from the well known one of Arvis. Taking into proper account the effective string corrections and exploiting some technical improvements in the simulations we obtain precise estimate of the amplitude ratios T_c/\\sqrt{sigma}, m_{0++}/\\sqrt{\\sigma} and sigma xi_{2nd}^2. We also discuss the behaviour of the effective string free energy in the dimensional reduction limit (i.e., near the deconfinement transition...
Free-energy calculation methods for collective phenomena in membranes
Smirnova, Yuliya G.; Fuhrmans, Marc; Barragan Vidal, Israel A.; Müller, Marcus
2015-09-01
Collective phenomena in membranes are those which involve the co-operative reorganization of many molecules. Examples of these are membrane fusion, pore formation, bending, adhesion or fission. The time and length scales, on which these processes occur, pose a challenge for atomistic simulations. Therefore, in order to solve the length scale problem it is popular to introduce a coarse-grained representation. To facilitate sampling of the relevant states additional computational techniques, which encourage the system to explore the free-energy landscape far from equilibrium and visit transition states, are needed. These computational techniques provide insights about the free-energy changes involved in collective transformations of membranes, yielding information about the rate limiting states, the transformation mechanism and the influence of architectural, compositional and interaction parameters. A common approach is to identify an order parameter (or reaction coordinate), which characterizes the pathway of membrane reorganization. However, no general strategy exists to define such an order parameter that can properly describe cooperative reorganizations in membranes. Recently developed methods can overcome this problem of the order-parameter choice and allow us to study collective phenomena in membranes. We will discuss such methods as thermodynamic integration, umbrella sampling, and the string method and results provided by their applications to particle-based simulations, particularly focusing on membrane fusion and pore formation.
Iterative free-energy optimization for recurrent neural networks (INFERNO)
2017-01-01
The intra-parietal lobe coupled with the Basal Ganglia forms a working memory that demonstrates strong planning capabilities for generating robust yet flexible neuronal sequences. Neurocomputational models however, often fails to control long range neural synchrony in recurrent spiking networks due to spontaneous activity. As a novel framework based on the free-energy principle, we propose to see the problem of spikes’ synchrony as an optimization problem of the neurons sub-threshold activity for the generation of long neuronal chains. Using a stochastic gradient descent, a reinforcement signal (presumably dopaminergic) evaluates the quality of one input vector to move the recurrent neural network to a desired activity; depending on the error made, this input vector is strengthened to hill-climb the gradient or elicited to search for another solution. This vector can be learned then by one associative memory as a model of the basal-ganglia to control the recurrent neural network. Experiments on habit learning and on sequence retrieving demonstrate the capabilities of the dual system to generate very long and precise spatio-temporal sequences, above two hundred iterations. Its features are applied then to the sequential planning of arm movements. In line with neurobiological theories, we discuss its relevance for modeling the cortico-basal working memory to initiate flexible goal-directed neuronal chains of causation and its relation to novel architectures such as Deep Networks, Neural Turing Machines and the Free-Energy Principle. PMID:28282439
Non-Equilibrium Properties from Equilibrium Free Energy Calculations
Pohorille, Andrew; Wilson, Michael A.
2012-01-01
Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.
ANISOTROPY OF (1× 1)-SURFACE FREE ENERGIES OF CRYSTALS
Z.M.Yu; A. Flodstrom
2001-01-01
The surface free energy (SFE) of (1× 1)-surfaces of crystals, without reconstructionand adsorption, is calculated using a bond-broken mode. In the mode, the potentialenergy of the crystals is treated as a sum of the energies of the bonds connectingpair-wise atoms (u-bonds). The SFE is calculated based on the bond energy and thearea density of dangling bonds which depends on the structure of the surface. Theresults provide a general expression for the SFE in terms of the bond energy (E)and the bond length (do) of the crystal and Miller indices hkl. The anisotropy ofthe SFE is therefore completely determined with the expression. As the examples,considering the nearest-neighboring bonding, the SFEs of sc, fcc, bcc and cth (cubictetrahedral) crystals are discussed, respectively. Wulff plots of bcc and fcc crystalsare then obtained. The equilibrium forms (EFs) of these crystals ave consequentlygot from their Wulff plots, respectively. It is found that the EFs of bcc and fcc arerespectively the rhombic dodecahedron and the truncated-octahedron that are their firstBrillouin zones, respectively.
A Gibbs Sampler for Multivariate Linear Regression
Mantz, Adam B
2015-01-01
Kelly (2007, hereafter K07) described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where these measurements may be correlated (for the same data point), where the response variable is affected by intrinsic scatter in addition to measurement error, and where the prior distribution of covariates is modeled by a flexible mixture of Gaussians rather than assumed to be uniform. Here I extend the K07 algorithm in two ways. First, the procedure is generalized to the case of multiple response variables. Second, I describe how to model the prior distribution of covariates using a Dirichlet process, which can be thought of as a Gaussian mixture where the number of mixture components is learned from the data. I present an example of multivariate regression using the extended algorithm, namely fitting scaling relations of the gas mass, temperature, and luminosity of dynamica...
New active asteroid 313P/Gibbs
Jewitt, David; Hui, Man-To; Li, Jing [Department of Earth, Planetary and Space Sciences, UCLA, 595 Charles Young Drive East, Los Angeles, CA 90095-1567 (United States); Agarwal, Jessica [Max Planck Institute for Solar System Research, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany); Peixinho, Nuno [Unidad de Astronomía, Fac. de Ciencias Básicas, Universidad de Antofagasta, Avda. U. de Antofagasta 02800, Antofagasta (Chile); Weaver, Harold [The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, Maryland, MD 20723 (United States); Mutchler, Max [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Larson, Stephen, E-mail: jewitt@ucla.edu [Lunar and Planetary Laboratory, University of Arizona, 1629 E. University Blvd. Tucson AZ 85721-0092 (United States)
2015-02-01
We present initial observations of the newly discovered active asteroid 313P/Gibbs (formerly P/2014 S4), taken to characterize its nucleus and comet-like activity. The central object has a radius ∼0.5 km (geometric albedo 0.05 assumed). We find no evidence for secondary nuclei and set (with qualifications) an upper limit to the radii of such objects near 20 m, assuming the same albedo. Both aperture photometry and a morphological analysis of the ejected dust show that mass-loss is continuous at rates ∼0.2–0.4 kg s{sup −1}, inconsistent with an impact origin. Large dust particles, with radii ∼50–100 μm, dominate the optical appearance. At 2.4 AU from the Sun, the surface equilibrium temperatures are too low for thermal or desiccation stresses to be responsible for the ejection of dust. No gas is spectroscopically detected (limiting the gas mass-loss rate to <1.8 kg s{sup −1}). However, the protracted emission of dust seen in our data and the detection of another episode of dust release near perihelion, in archival observations from 2003, are highly suggestive of an origin by the sublimation of ice. Coincidentally, the orbit of 313P/Gibbs is similar to those of several active asteroids independently suspected to be ice sublimators, including P/2012 T1, 238P/Read, and 133P/Elst–Pizarro, suggesting that ice is abundant in the outer asteroid belt.
Study of energy delivery and mean free path of low energy electrons in EUV resists
Bhattarai, Suchit; Neureuther, Andrew R.; Naulleau, Patrick P.
2016-03-01
The relative importance of secondary electrons in delivering energy in photoresist films was assessed by performing large area exposures and by quantifying the inelastic mean free path of electrons in a leading chemically amplified positive tone EUV resist. A low energy electron microscope was used to directly pattern large (~15μm x 20μm) features with 15-80 eV electrons followed by analyzing the resulting dissolution rate contrast curve data. In the 40 to 80 eV regime the energy delivery was found to scale roughly proportionally with electron energy. In 15 to 30 eV regime however, this energy scaling did not explain the resist thickness loss data. The dose required to lower the resist thickness down to 20 nm was found to be 2-5X larger for 15 eV electrons than for 20, 25 and 30 eV electrons. Using scattering models from the literature including phonon scattering and optical data deduced electron energy loss spectroscopy and optical reflectometry, the inelastic mean free path values at energies between 10 eV and 92 eV range between about 2.8 and 0.6 nm respectively.
A brief critique of the Adam-Gibbs entropy model
Dyre, J. C.; Hecksher, Tina; Niss, Kristine
2009-01-01
This paper critically discusses the entropy model proposed by Adam and Gibbs in 1965 for the dramatic temperature dependence of glass-forming liquids' average relaxation time, which is one of the most influential models during the last four decades. We discuss the Adam-Gibbs model's theoretical...
Free energy methods for efficient exploration of mixture posterior densities
Chopin, Nicolas; Stoltz, Gabriel
2010-01-01
Because of their multimodality, mixture posterior densities are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure which originates from computational statistical physics. The principle is first to choose a "reaction coordinate", that is, a direction in which the target density is multimodal. In a second step, the marginal log-density of the reaction coordinate is estimated; this quantity is called "free energy" in the computational statistical physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their invariant distribution on the fly, in order to overcome sampling barriers along the chosen reaction coordinate. Finally, we perform an importance sampling step in order to remove the bias and recover the true posterior. A crucial point is the choice of the reaction coordinate. We show that a convenient and efficient reaction coordinate is the hyper-para...
Surface Free Energy Determination of APEX Photosensitive Glass
William R. Gaillard
2016-02-01
Full Text Available Surface free energy (SFE plays an important role in microfluidic device operation. Photosensitive glasses such as APEX offer numerous advantages over traditional glasses for microfluidics, yet the SFE for APEX has not been previously reported. We calculate SFE with the Owens/Wendt geometric method by using contact angles measured with the Sessile drop technique. While the total SFE for APEX is found to be similar to traditional microstructurable glasses, the polar component is lower, which is likely attributable to composition. The SFE was modified at each stage of device fabrication, but the SFE of the stock and fully processed glass was found to be approximately the same at a value of 51 mJ·m−2. APEX exhibited inconsistent wetting behavior attributable to an inhomogeneous surface chemical composition. Means to produce more consistent wetting of photosensitive glass for microfluidic applications are discussed.
Identification of HIV inhibitors guided by free energy perturbation calculations.
Acevedo, Orlando; Ambrose, Zandrea; Flaherty, Patrick T; Aamer, Hadega; Jain, Prashi; Sambasivarao, Somisetti V
2012-01-01
Free energy perturbation (FEP) theory coupled to molecular dynamics (MD) or Monte Carlo (MC) statistical mechanics offers a theoretically precise method for determining the free energy differences of related biological inhibitors. Traditionally requiring extensive computational resources and expertise, it is only recently that its impact is being felt in drug discovery. A review of computer-aided anti-HIV efforts employing FEP calculations is provided here that describes early and recent successes in the design of human immunodeficiency virus type 1 (HIV-1) protease and non-nucleoside reverse transcriptase inhibitors. In addition, our ongoing work developing and optimizing leads for small molecule inhibitors of cyclophilin A (CypA) is highlighted as an update on the current capabilities of the field. CypA has been shown to aid HIV-1 replication by catalyzing the cis/trans isomerization of a conserved Gly-Pro motif in the Nterminal domain of HIV-1 capsid (CA) protein. In the absence of a functional CypA, e.g., by the addition of an inhibitor such as cyclosporine A (CsA), HIV-1 has reduced infectivity. Our simulations of acylurea-based and 1-indanylketone-based CypA inhibitors have determined that their nanomolar and micromolar binding affinities, respectively, are tied to their ability to stabilize Arg55 and Asn102. A structurally novel 1-(2,6-dichlorobenzamido) indole core was proposed to maximize these interactions. FEP-guided optimization, experimental synthesis, and biological testing of lead compounds for toxicity and inhibition of wild-type HIV-1 and CA mutants have demonstrated a dose-dependent inhibition of HIV-1 infection in two cell lines. While the inhibition is modest compared to CsA, the results are encouraging.
The ground state energy of the mean field spin glass model
Koukiou, Flora
2008-01-01
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\\epsilon_0$ \\[\\epsilon_0\\geq -0.7833...,\\] close to the replica symmetry breaking and numerical simulations values.
A MultiScale Gibbs-Helmholtz Constrained Cubic Equation of State
Angelo Lucia
2010-01-01
Full Text Available This paper presents a radically new approach to cubic equations of state (EOS in which the Gibbs-Helmholtz equation is used to constrain the attraction or energy parameter, a. The resulting expressions for (, for pure components and (,, for mixtures contain internal energy departure functions and completely avoid the need to use empirical expressions like the Soave alpha function. Our approach also provides a novel and thermodynamically rigorous mixing rule for (,,. When the internal energy departure function is computed using Monte Carlo or molecular dynamics simulations as a function of current bulk phase conditions, the resulting EOS is a multiscale equation of state. The proposed new Gibbs-Helmholtz constrained (GHC cubic equation of state is used to predict liquid densities at high pressure and validated using experimental data from literature. Numerical results clearly show that the GHC EOS provides fast and accurate computation of liquid densities at high pressure, which are needed in the determination of gas hydrate equilibria.
Calculation of the free energy and cooperativity of protein folding.
Alex Kentsis
Full Text Available Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.
Enzymatic minimum free energy path calculations using swarms of trajectories.
Sanchez-Martinez, Melchor; Field, Martin; Crehuet, Ramon
2015-01-22
The development of approaches for simulating rare events in complex molecular systems is a central concern in chemical physics. In recent work, Roux and co-workers proposed a novel, swarms of trajectories (SoT) method for determining the transition paths of such events. It consists of the dynamical refinement on the system's free energy surface of a putative transition path that is parametrized in terms of a set of collective variables (CVs) that are identified as being important for the transition. In this work, we have implemented the SoT method and used it to investigate the catalytic mechanisms of two enzymatic reactions using hybrid QM/MM potentials. Our aim has been to test the performance of SoT for enzyme systems and to devise robust simulation protocols that can be employed in future studies of this type. We identify the conditions under which converged results can be obtained using inertial and Brownian dynamical evolutions of the CVs, show that the inclusion of several CVs can give significant additional insight into the mechanisms of the reactions, and show that the use of minimum energy paths as starting guesses can greatly accelerate path refinement.
McCarty, J.; Clark, A. J.; Copperman, J.; Guenza, M. G.
2014-05-01
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.
Long-wavelength, free-free spectral energy distributions from porous stellar winds
Ignace, R.
2016-04-01
The influence of macroclumps for free-free spectral energy distributions (SEDs) of ionized winds is considered. The goal is to emphasize distinctions between microclumping and macroclumping effects. Microclumping can alter SED slopes and flux levels if the volume filling factor of the clumps varies with radius; however, the modifications are independent of the clump geometry. To what extent does macroclumping alter SED slopes and flux levels? In addressing the question, two specific types of macroclump geometries are explored: shell fragments (pancake-shaped) and spherical clumps. Analytic and semi-analytic results are derived in the limiting case that clumps never obscure one another. Numerical calculations based on a porosity formalism is used when clumps do overlap. Under the assumptions of a constant expansion, isothermal, and fixed ionization wind, the fragment model leads to results that are essentially identical to the microclumping result. Mass-loss rate determinations are not affected by porosity effects for shell fragments. By contrast, spherical clumps can lead to a reduction in long-wavelength fluxes, but the reductions are only significant for extreme volume filling factors.
Free trade and energy. Le libre-echange et l'energie
1988-01-01
This booklet was prepared and issued by the federal Department of Energy Mines and Resources to explain some of the energy implications of the Canada-U.S. Free Trade Agreement. The booklet covers economic opportunities, including secure and expanded market access for petroleum, natural gas, electricity, uranium, and petrochemicals, and access to increased amounts of capital to develop those megaprojects projected to play an increasing role in domestic energy production. Another important aspect is that of energy security, best achieved through the effective functioning of markets and their openness to international influences. The final question dealt with is that of sovereignty. The booklet points out that Canada retains its existing right to create energy policies and programs, ownership of resources remains with the provinces, and the Government of Canada retains regulation of foreign ownership in the oil and gas industry. The conclusion places the Canada-U.S. Free Trade Agreement on the spectrum of similar moves to remove trade barriers and increase international trade opportunities.
Finite-size corrections to the free energies of crystalline solids
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 ene
Finite-size corrections to the free energies of crystalline solids
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
A Gibbs Sampler for Learning DAGs
Goudie, Robert J. B.; Mukherjee, Sach
2017-01-01
We propose a Gibbs sampler for structure learning in directed acyclic graph (DAG) models. The standard Markov chain Monte Carlo algorithms used for learning DAGs are random-walk Metropolis-Hastings samplers. These samplers are guaranteed to converge asymptotically but often mix slowly when exploring the large graph spaces that arise in structure learning. In each step, the sampler we propose draws entire sets of parents for multiple nodes from the appropriate conditional distribution. This provides an efficient way to make large moves in graph space, permitting faster mixing whilst retaining asymptotic guarantees of convergence. The conditional distribution is related to variable selection with candidate parents playing the role of covariates or inputs. We empirically examine the performance of the sampler using several simulated and real data examples. The proposed method gives robust results in diverse settings, outperforming several existing Bayesian and frequentist methods. In addition, our empirical results shed some light on the relative merits of Bayesian and constraint-based methods for structure learning.
New Active Asteroid 313P/Gibbs
Jewitt, David; Peixinho, Nuno; Weaver, Harold; Mutchler, Max; Hui, Man-To; Li, Jing; Larson, Stephen
2014-01-01
We present initial observations of the newly-discovered active asteroid 313P/Gibbs (formerly P/2014 S4), taken to characterize its nucleus and comet-like activity. The central object has a radius $\\sim$0.5 km (geometric albedo 0.05 assumed). We find no evidence for secondary nuclei and set (with qualifications) an upper limit to the radii of such objects near 25 m, assuming the same albedo. Both aperture photometry and a morphological analysis of the ejected dust show that mass-loss is continuous at rates $\\sim$0.2 to 0.4 kg s$^{-1}$, inconsistent with an impact origin. Large dust particles, with radii $\\sim$50 to 100 $\\mu$m, dominate the optical appearance. At 2.4 AU from the Sun, the surface equilibrium temperatures are too low for thermal or desiccation stresses to be responsible for the ejection of dust. No gas is spectroscopically detected (limiting the gas mass loss rate to $<$1.8 kg s$^{-1}$). However, the protracted emission of dust seen in our data and the detection of another episode of dust rele...
Psychoanalytic Interpretation of Blueberries by Susan Gibb
Maya Zalbidea Paniagua
2014-06-01
Full Text Available Blueberries (2009 by Susan Gibb, published in the ELO (Electronic Literature Organization, invites the reader to travel inside the protagonist’s mind to discover real and imaginary experiences examining notions of gender, sex, body and identity of a traumatised woman. This article explores the verbal and visual modes in this digital short fiction following semiotic patterns as well as interpreting the psychological states that are expressed through poetical and technological components. A comparative study of the consequences of trauma in the protagonist will be developed including psychoanalytic theories by Sigmund Freud, Jacques Lacan and the feminist psychoanalysts: Melanie Klein and Bracha Ettinger. The reactions of the protagonist will be studied: loss of reality, hallucinations and Electra Complex, as well as the rise of defence mechanisms and her use of the artistic creativity as a healing therapy. The interactivity of the hypermedia, multiple paths and endings will be analyzed as a literary strategy that increases the reader’s capacity of empathizing with the speaker.
Sign preference in ion-induced nucleation: contributions to the free energy barrier.
Keasler, Samuel J; Kim, Hyunmi; Chen, Bin
2012-11-07
We have performed a series of computer simulations using the AVUS-HR approach to better understand the origin of the sign preference in ion-induced nucleation. In particular, we emphasize the importance of distinguishing between the total formation free energy of a cluster, and the nucleation free energy, which involves only those steps contributing to the free energy barrier. We have separately considered how the ion-water potential energy, the water-water potential energy, and the entropy contribute to both the cluster formation free energy, and the nucleation free energy. These simulations have shown that while the ion-water potential energies make the largest contribution to the formation free energy difference between positive and negative ions, the entropy is the contribution leading to lower nucleation free energy barriers for negative ions. The primary reason for this is the larger stable (but precritical) clusters formed around negative ions. We have further shown that the distinction between formation and nucleation free energies is of particular importance when comparing small cations with larger anions where the formation free energies can be much lower for the cationic clusters, even though the nucleation barriers are lower for the anionic clusters.
Relative Binding Free Energy Calculations Applied to Protein Homology Models.
Cappel, Daniel; Hall, Michelle Lynn; Lenselink, Eelke B; Beuming, Thijs; Qi, Jun; Bradner, James; Sherman, Woody
2016-12-27
A significant challenge and potential high-value application of computer-aided drug design is the accurate prediction of protein-ligand binding affinities. Free energy perturbation (FEP) using molecular dynamics (MD) sampling is among the most suitable approaches to achieve accurate binding free energy predictions, due to the rigorous statistical framework of the methodology, correct representation of the energetics, and thorough treatment of the important degrees of freedom in the system (including explicit waters). Recent advances in sampling methods and force fields coupled with vast increases in computational resources have made FEP a viable technology to drive hit-to-lead and lead optimization, allowing for more efficient cycles of medicinal chemistry and the possibility to explore much larger chemical spaces. However, previous FEP applications have focused on systems with high-resolution crystal structures of the target as starting points-something that is not always available in drug discovery projects. As such, the ability to apply FEP on homology models would greatly expand the domain of applicability of FEP in drug discovery. In this work we apply a particular implementation of FEP, called FEP+, on congeneric ligand series binding to four diverse targets: a kinase (Tyk2), an epigenetic bromodomain (BRD4), a transmembrane GPCR (A2A), and a protein-protein interaction interface (BCL-2 family protein MCL-1). We apply FEP+ using both crystal structures and homology models as starting points and find that the performance using homology models is generally on a par with the results when using crystal structures. The robustness of the calculations to structural variations in the input models can likely be attributed to the conformational sampling in the molecular dynamics simulations, which allows the modeled receptor to adapt to the "real" conformation for each ligand in the series. This work exemplifies the advantages of using all-atom simulation methods with
Correlation between surface free energy and anchoring energy of 6CHBT on polyimide surface
Borycki, Jerzy; Okulska-Bozek, Malgorzata; Kedzierski, Jerzy; Kojdecki, Marek A.
2002-06-01
Polyimides were prepared in the classical two-step method via poly(amic acids). Poly(amic acids) were obtained from 3,3',4,4'-biphenyltetracarboxylic dianhydride (BPDA), 4,4'- (hexafluoroisopropylidene)diphthalic anhydride (6FDA), pyromellitic dianhydride (PMDA), 3,3',4,4'- diphenylsulfonetetracarboxylic dianhydride (DSDA), 4,4'- oxydiphthalic anhydride (ODPA) and amines 4,4'-oxydianiline (ODA), 1,3-phenylenediamine (MPD), 1,4-phenylenediamine (PPD), 4,4'-diaminodiphenylmethane (MDA), 4,4'- ethylenedianiline (DAB), 2,4,6-trimethyl-1,3- phenylenediamine (TMPD), 4-methyl-1,3-phenylenediamine (MMPD) and 2,3,5,6-tetramethyl-1,4-phenylenediamine (DAD) in dimethylformamide. The indium tin oxide (ITO)-glass plates were spin-coated with the poly(amic acids) solutions and dried. A thermal imidization process was then carried out at 250 degree(s)C for 4 h. In this study the anchoring energies of 6CHBT molecules were evaluated on rubbing aligning layers of PI films. The polar anchoring energy coefficient was determined by wedge cell method. The surface free energy and its components of polyimide layers were determined by measuring the contact angles of water, ethylene glycol, formamide and diiodomethane drops on the rubbing polymer surfaces. The Lifshitz-van der Waals and acidic-basic components of surface free energies were found from van Oss equation.
Schmid, L. A.
1977-01-01
The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.
Stephenson, Brian C; Stafford, Kate A; Beers, Kenneth J; Blankschtein, Daniel
2008-02-14
The widespread use of surfactant mixtures and surfactant/solubilizate mixtures in practical applications motivates the development of predictive theoretical approaches to improve fundamental understanding of the behavior of these complex self-assembling systems and to facilitate the design and optimization of new surfactant and surfactant/solubilizate mixtures. This paper is the first of two articles introducing a new computer simulation-free-energy/molecular thermodynamic (CS-FE/MT) model. The two articles explore the application of computer simulation free-energy methods to quantify the thermodynamics associated with mixed surfactant/cosurfactant and surfactant/solubilizate micelle formation in aqueous solution. In this paper (article 1 of the series), a theoretical approach is introduced to use computer simulation free-energy methods to compute the free-energy change associated with changing micelle composition (referred to as DeltaDeltaGi). In this approach, experimental critical micelle concentration (CMC) data, or a molecular thermodynamic model of micelle formation, is first used to evaluate the free energy associated with single (pure) surfactant micelle formation, g(form,single), in which the single surfactant micelle contains only surfactant A molecules. An iterative approach is proposed to combine the estimated value of gform,single with free-energy estimates of DeltaDeltaGi based on computer simulation to determine the optimal free energy of mixed micelle formation, the optimal micelle aggregation number and composition, and the optimal bulk solution composition. After introducing the CS-FE/MT modeling framework, a variety of free-energy methods are briefly reviewed, and the selection of the thermodynamic integration free-energy method is justified and selected to implement the CS-FE/MT model. An alchemical free-energy pathway is proposed to allow evaluation of the free-energy change associated with exchanging a surfactant A molecule with a surfactant
Crystalline free energies of micelles of diblock copolymer solutions
D'Adamo, Giuseppe; 10.1063/1.3509391
2012-01-01
We report a characterization of the relative stability and structural behavior of various micellar crystals of an athermal model of AB-diblock copolymers in solution. We adopt a previously devel- oped coarse-graining representation of the chains which maps each copolymer on a soft dumbbell. Thanks to this strong reduction of degrees of freedom, we are able to investigate large aggregated systems, and for a specific length ratio of the blocks f = MA/(MA + MB) = 0.6, to locate the order-disorder transition of the system of micelles. Above the transition, mechanical and thermal properties are found to depend on the number of particles per lattice site in the simulation box, and the application of a recent methodology for multiple occupancy crystals (B.M. Mladek et al., Phys. Rev. Lett. 99, 235702 (2007)) is necessary to correctly define the equilibrium state. Within this scheme we have performed free energy calculations at two reduced density {\\rho}/{\\rho}\\ast = 4,5 and for several cubic structures as FCC,BCC,A1...
From quantum chemical formation free energies to evaporation rates
I. K. Ortega
2012-01-01
Full Text Available Atmospheric new particle formation is an important source of atmospheric aerosols. Large efforts have been made during the past few years to identify which molecules are behind this phenomenon, but the actual birth mechanism of the particles is not yet well known. Quantum chemical calculations have proven to be a powerful tool to gain new insights into the very first steps of particle formation. In the present study we use formation free energies calculated by quantum chemical methods to estimate the evaporation rates of species from sulfuric acid clusters containing ammonia or dimethylamine. We have found that dimethylamine forms much more stable clusters with sulphuric acid than ammonia does. On the other hand, the existence of a very deep local minimum for clusters with two sulfuric acid molecules and two dimethylamine molecules hinders their growth to larger clusters. These results indicate that other compounds may be needed to make clusters grow to larger sizes (containing more than three sulfuric acid molecules.
Protein Transfer Free Energy Obeys Entropy-Enthalpy Compensation.
Mills, Eric A; Plotkin, Steven S
2015-11-05
We have found significant entropy-enthalpy compensation for the transfer of a diverse set of two-state folding proteins from water into water containing a diverse set of cosolutes, including osmolytes, denaturants, and crowders. In extracting thermodynamic parameters from experimental data, we show the potential importance of accounting for the cosolute concentration-dependence of the heat capacity change upon unfolding, as well as the potential importance of the temperature-dependence of the heat capacity change upon unfolding. We introduce a new Monte Carlo method to estimate the experimental uncertainty in the thermodynamic data and use this to show by bootstrapping methods that entropy-enthalpy compensation is statistically significant, in spite of large, correlated scatter in the data. We show that plotting the data at the transition midpoint provides the most accurate experimental values by avoiding extrapolation errors due to uncertainty in the heat capacity, and that this representation exhibits the strongest evidence of compensation. Entropy-enthalpy compensation is still significant at lab temperature however. We also find that compensation is still significant when considering variations due to heat capacity models, as well as typical measurement discrepancies lab-to-lab when such data is available. Extracting transfer entropy and enthalpy along with their uncertainties can provide a valuable consistency check between experimental data and simulation models, which may involve tests of simulated unfolded ensembles and/or models of the transfer free energy; we include specific applications to cold shock protein and protein L.
Exploring the free energy surface using ab initio molecular dynamics
Samanta, Amit; Morales, Miguel A.; Schwegler, Eric
2016-04-01
Efficient exploration of configuration space and identification of metastable structures in condensed phase systems are challenging from both computational and algorithmic perspectives. In this regard, schemes that utilize a set of pre-defined order parameters to sample the relevant parts of the configuration space [L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006); J. B. Abrams and M. E. Tuckerman, J. Phys. Chem. B 112, 15742 (2008)] have proved useful. Here, we demonstrate how these order-parameter aided temperature accelerated sampling schemes can be used within the Born-Oppenheimer and the Car-Parrinello frameworks of ab initio molecular dynamics to efficiently and systematically explore free energy surfaces, and search for metastable states and reaction pathways. We have used these methods to identify the metastable structures and reaction pathways in SiO2 and Ti. In addition, we have used the string method [W. E, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002); L. Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] within the density functional theory to study the melting pathways in the high pressure cotunnite phase of SiO2 and the hexagonal closed packed to face centered cubic phase transition in Ti.
Free-energy Minimization and The Dark Room Problem
Karl eFriston
2012-05-01
Full Text Available Recent years have seen the emergence of an important new fundamental theory of brain function. This theory brings information-theoretic, Bayesian, neuroscientific, and machine learning approaches into a single framework whose overarching principle is the minimization of surprise (or, equivalently, the maximization of expectation. The most comprehensive such treatment is the ‘free energy minimization’ formulation due to Karl Friston (see e.g. Friston and Stephan (2007, Friston (2010 – see also Thornton (2010, Fiorillo (2010 A recurrent puzzle raised by critics of these models is that biological systems do not seem to avoid surprises. We do not simply seek a dark, unchanging chamber and stay there. This is the ‘Dark Room Problem’. Here, we describe the problem and further unpack the issues to which it speaks. Using the same format as the prologue of Eddington’s Space, Time and Gravitation (Eddington 1920 we present our discussion as a conversation between:An Information THEORIST (ThorntonA PHYSICIST (Friston A PHILOSOPHER (Clark
How the diffusivity profile reduces the arbitrariness of protein folding free energies
Hinczewski, Michael; Dzubiella, Joachim; Netz, Roland R
2010-01-01
The concept of a protein diffusing in its free energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free energy profiles for different RCs exhibit significant variation, some having an activation barrier, others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free energy and diffusivity effects into a single function, the rescaled free energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately d...
NAIDOO Kevin J.
2012-01-01
The development and implementation of a computational method able to produce free energies in multiple dimensions,descriptively named the free energies from adaptive reaction coordinate forces (FEARCF) method is described in this paper.While the method can be used to calculate free energies of association,conformation and reactivity here it is shown in the context of chemical reaction landscapes.A reaction free energy surface for the Claisen rearrangement of chorismate to prephenate is used as an illustration of the method's efficient convergence.FEARCF simulations are shown to achieve fiat histograms for complex multidimensional free energy volumes.The sampling efficiency by which it produces multidimensional free energies is demonstrated on the complex puckering of a pyranose ring,that is described by a three dimensional W(θ1,θ2,θ3) potential of mean force.
An ab initio approach to free-energy reconstruction using logarithmic mean force dynamics.
Nakamura, Makoto; Obata, Masao; Morishita, Tetsuya; Oda, Tatsuki
2014-05-14
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.
Reconstructing multiple free energy pathways of DNA stretching from single molecule experiments.
Frey, Eric W; Li, Jingqiang; Wijeratne, Sithara S; Kiang, Ching-Hwa
2015-04-23
Free energy landscapes provide information on the dynamics of proteins and nucleic acid folding. It has been demonstrated that such landscapes can be reconstructed from single molecule force measurement data using Jarzynski's equality, which requires only stretching data. However, when the process is reversible, the Crooks fluctuation theorem combines both stretch and relaxation force data for the analysis and can offer more rapid convergence of free energy estimates of different states. Here we demonstrate that, similar to Jarzynski's equality, the Crooks fluctuation theorem can be used to reconstruct the full free energy landscapes. In addition, when the free energy landscapes exhibit multiple folding pathways, one can use Jarzynski's equality to reconstruct individual free energy pathways if the experimental data show distinct work distributions. We applied the method to reconstruct the overstretching transition of poly(dA) to demonstrate that the nonequilibrium work theorem combined with single molecule force measurements provides a clear picture of the free energy landscapes.
Front instability and energy of the free surface
Beltrame, Philippe
2014-05-01
In recent years, there has been a proliferation of research devoted to the formation of preferential flow paths occurring without macroscopic heterogeneity of the porous media. DiCarlo (2013) points out the connection between "overshoot" and the front instability. Extension of the standard Richards equation is required to capture this phenomenon. In most of the improvements, interfacial phenomena as the triple line at the front are considered. For instance, velocity dependent contact angle (Wang et al., 2013) or contact angle hysteresis (Rätz and Schweizer, 2012) allow to simulate successfully the instability. Another approach proposed by Cueto-Felgueroso and Juanes (2009) introduces a macroscopic surface tension related to the existence of the water/air interface. As previously, the simulation of an advancing front displays physical looking fingering displacements. The goal of this contribution is to better understand the role of the different surface energies in the emergence of the front instability. We propose a model involving both the macroscopic surface tension and the soil wettability. This latter allows to define a contact angle and possibly hysteresis using heterogeneous wettability (Beltrame et al., 2011). Therefore, we employ the phase field approach developed by Felgueroso and Juanes, 2009 to which we add a free energy term corresponding to the wettability: a disjoining or conjoining pressure resulting from effective molecular interactions between the substrate and the free surface (DeGennes, 1985). The difference with the classical suction pressure is the hydrophobic behavior for ultra-thin film (small water saturation). Such a water repellency was recently estimated in the soil (Diamantopoulos et al. 2013). Stability analysis of an advancing front in an uniform porous media shows that macroscopic surface tension and wettability may independently produce the instability growth. In contrast, for a front stopping when reaching the layers interface of
Sampling Free Energy Surfaces as Slices by Combining Umbrella Sampling and Metadynamics
Awasthi, Shalini; Kapil, Venkat; Nair, Nisanth N.
2015-01-01
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...
Ionization By Impact Electrons in Solids: Electron Mean Free Path Fitted Over A Wide Energy Range
Ziaja, B; London, R A; Hajdu, J
2005-06-09
We propose a simple formula for fitting the electron mean free paths in solids both at high and at low electron energies. The free-electron-gas approximation used for predicting electron mean free paths is no longer valid at low energies (E < 50 eV), as the band structure effects become significant at those energies. Therefore we include the results of the band structure calculations in our fit. Finally, we apply the fit to 9 elements and 2 compounds.
Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation
Dai, Shibin; Li, Bo; Lu, Jianfeng
2017-08-01
We study a phase-field variational model for the solvation of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals-Cahn-Hilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the Poisson-Boltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics—its potential, free energy, and dielectric boundary force—with respect to the perturbation of the dielectric boundary. We also prove the {Γ} -convergence of the phase-field free-energy functionals to their sharp-interface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals-Cahn-Hilliard functionals with minimal assumptions.
Gibbs-Butzer differential operators on locally compact Vilenkin groups
苏维宜
1996-01-01
The concept of para-differential operators over locally compact Vilenkin groups is given and their properties are studied. By means of para-linearization theorem, efforts are made to establish the basic theory of Gibbs-Butzer differential operators.
Craddock, David
2008-01-01
Studies have shown that the average North American family will spend more than a quarter of a million dollars on energy in a lifetime. What many other countries, including Germany, Spain, France, Denmark, China, Brazil, and even Iceland, have realized is that there is a better way to power our homes, businesses, and cars by using renewable energy sources. Recently, the United States has begun to understand the importance of reducing its reliance on coal, natural gas, nuclear power, and hydropower plants, which comprise the majority of the nation's electricity, due to increasing oil prices.
Gibbs measures and phase transitions in one-dimensional models
Mallak, Saed
2000-01-01
Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2000. Thesis (Ph.D.) -- Bilkent University, 2000. Includes bibliographical references leaves 63-64 In this thesis we study the problem of limit Gibbs measures in one-dimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for one-dimensional models. VVe construct a one-dimensional model disproving a uniqueness conjecture formulated before for...
Scaling laws of free magnetic energy stored in a solar emerging flux region
Magara, Tetsuya
2014-01-01
This Letter reports scaling laws of free magnetic energy stored in a solar emerging flux region which is a key to understanding the energetics of solar active phenomena such as solar flares and coronal mass ejections. By performing 3-dimensional magnetohydrodynamic simulations that reproduce several emerging flux regions of different magnetic configurations, we derive power law relationships among emerged magnetic flux, free magnetic energy and relative magnetic helicity in these emerging flux regions. Since magnetic flux is an observable quantity, the scaling law between magnetic flux and free magnetic energy may give a way to estimate invisible free magnetic energy responsible for solar active phenomena.
Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining
Desgranges, Caroline; Delhommelle, Jerome
2017-02-01
Using molecular simulation, we determine Ginzburg-Landau free energy functions for molecular fluids. To this aim, we extend the Expanded Wang-Landau method to calculate the partition functions, number distributions and Landau free energies for Ar,CO2 and H2O . We then parametrize a coarse-grained free energy function of the density order parameter and assess the performance of this free energy function on its ability to model the onset of criticality in these systems. The resulting parameters can be readily used in hybrid atomistic/continuum simulations that connect the microscopic and mesoscopic length scales.
Calculation of free energy of Al-Cu-Li alloy under electric field
ZHANG Jian-jun; WANG Yong-xin; CHEN Zheng; LIU Bing
2007-01-01
Based on Thomas-Fermi model, the interior potential boundary condition with the effect of electric field was defined, the calculation method of free energy for atom cluster under electric field was established. The change of free energy of Al-Cu-Li alloy under the effect of electric field was calculated quantitatively. It is shown that: near the zero electric field and the side of positive electric field, the free energy of Cu4LiAl7 compound at aging temperature 460 K is higher than that of free energy at solid solution temperature 725 K, but once the negative electric field increases to certain degree there will be opposite result. Under the effect of electric field, at 725 K the free energy of Cu4LiAl7 is higher than that of Al-1.0%Li-4.0%Cu, and at 460 K the free energy of compound is lower than that of solid solution. When the copper content in the Al-Li-Cu solid solution is below 5%, under the effect of electric field the free energy of solid solution increases gradually with the increasing of copper content, but the increasing amplitude reduces with the increasing of copper content. The free energy of binary solid solution increases with the addition of lithium, and with the increasing of electric field intensity the free energy margin of two kinds of solid solution becomes bigger.
The global mean energy balance under cloud-free conditions
Wild, Martin; Hakuba, Maria; Folini, Dois; Ott, Patricia; Long, Charles
2017-04-01
A long standing problem of climate models is their overestimation of surface solar radiation not only under all-sky, but also under clear-sky conditions (Wild et al. 1995, Wild et al. 2006). This overestimation reduced over time in consecutive model generations due to the simulation of stronger atmospheric absorption. Here we analyze the clear sky fluxes of the latest climate model generation from the Coupled Model Intercomparison Project Phase 5 (CMIP5) against an expanded and updated set of direct observations from the Baseline Surface Radiation Network (BSRN). Clear sky climatologies from these sites have been composed based on the Long and Ackermann (2000) clear sky detection algorithm (Hakuba et al. 2017), and sampling issues when comparing with model simulated clear sky fluxes have been analyzed in Ott (2017). Overall, the overestimation of clear sky insolation in the CMIP5 models is now merely 1-2 Wm-2 in the multimodel mean, compared to 4 Wm-2 in CMIP3 and 6 Wm-2 in AMIPII (Wild et al. 2006). Still a considerable spread in the individual model biases is apparent, ranging from -2 Wm-2 to 10 Wm-2 when averaged over 53 globally distributed BSRN sites. This bias structure is used to infer best estimates for present day global mean clear sky insolation, following an approach developped in Wild et al. (2013, 2015, Clim. Dyn.) for all sky fluxes. Thereby the flux biases in the various models are linearly related to their respective global means. A best estimate can then be inferred from the linear regression at the intersect where the bias against the surface observations becomes zero. This way we obtain a best estimate of 247 Wm-2 for the global mean insolation at the Earth surface under cloud free conditions, and a global mean absorbed solar radiation of 214 Wm-2 in the cloud-free atmosphere, assuming a global mean surface albedo of 13.5%. Combined with a best estimate for the net influx of solar radiation at the Top of Atmosphere under cloud free conditions
Rock climbing: A local-global algorithm to compute minimum energy and minimum free energy pathways
Templeton, Clark; Chen, Szu-Hua; Fathizadeh, Arman; Elber, Ron
2017-10-01
The calculation of minimum energy or minimum free energy paths is an important step in the quantitative and qualitative studies of chemical and physical processes. The computations of these coordinates present a significant challenge and have attracted considerable theoretical and computational interest. Here we present a new local-global approach to study reaction coordinates, based on a gradual optimization of an action. Like other global algorithms, it provides a path between known reactants and products, but it uses a local algorithm to extend the current path in small steps. The local-global approach does not require an initial guess to the path, a major challenge for global pathway finders. Finally, it provides an exact answer (the steepest descent path) at the end of the calculations. Numerical examples are provided for the Mueller potential and for a conformational transition in a solvated ring system.
A Gibbs Formulation for Reactive Materials with Phase Change
Stewart, D. Scott
2015-11-01
A large class of applications have pure, condensed phase constituents that come into contact, chemically react and simultaneously undergo phase change. Phase change in a given molecular material has often been considered to be separate from chemical reaction. Continuum modelers of phase change often use a phase field model whereby an indicator function is allowed to change from one value to another in regions of phase change, governed by evolutionary (Ginzburg-Landau) equations, whereas classic chemical kinetics literally count species concentrations and derive kinetics evolution equations based on species mass transport. We argue the latter is fundamental and is the same as the former, if all species, phase or chemical are treated as distinct chemical species. We pose a self-consistent continuum, thermo-mechanical model to account for significant energetic quantities with correct molecular and continuum limits in the mixture. A single stress tensor, and a single temperature is assumed for the mixture with specified Gibbs potentials for all relevant species, and interaction energies. We discuss recent examples of complex reactive material modeling, drawn from thermitic and propellant combustion that use this new model. DSS supported by DTRA, ONR and AFOSR.
Ulstrup, Jens; Jortner, Joshua
1975-01-01
-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum...... and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of ''activationless'' regions. Isotope effects are discussed as also are the oscillatory free energy...
Heavy quark free energies for three quark systems at finite temperature
Hübner, K; Kaczmarek, O; Vogt, O
2007-01-01
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.
Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.
Boulougouris, Georgios C
2014-05-15
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be
Beam characteristics of energy-matched flattening filter free beams
Paynter, D.; Weston, S. J.; Cosgrove, V. P. [St James Institute of Oncology The Leeds Teaching Hospitals NHS Trust, Medical Physics, Leeds LS9 7TF (United Kingdom); Evans, J. A. [LIGHT Institute University of Leeds Leeds LS2 9JT, Division of Medical Physics, Leeds (United Kingdom); Thwaites, D. I. [LIGHT Institute University of Leeds Leeds LS2 9JT, Division of Medical Physics, Leeds, United Kingdom and Institute of Medical Physics, School of Physics, University of Sydney (Australia)
2014-05-15
Purpose: Flattening filter free (FFF) linear accelerators can increase treatment efficiency and plan quality. There are multiple methods of defining a FFF beam. The Elekta control system supports tuning of the delivered FFF beam energy to enable matching of the percentage depth-dose (PDD) of the flattened beam at 10 cm depth. This is compared to FFF beams where the linac control parameters are identical to those for the flattened beam. All beams were delivered on an Elekta Synergy accelerator with an Agility multi-leaf collimator installed and compared to the standard, flattened beam. The aim of this study is to compare “matched” FFF beams to both “unmatched” FFF beams and flattened beams to determine the benefits of matching beams. Methods: For the three modes of operation 6 MV flattened, 6 MV matched FFF, 6 MV unmatched FFF, 10 MV flattened, 10 MV matched FFF, and 10 MV unmatched FFF beam profiles were obtained using a plotting tank and were measured in steps of 0.1 mm in the penumbral region. Beam penumbra was defined as the distance between the 80% and 20% of the normalized dose when the inflection points of the unflattened and flattened profiles were normalized with the central axis dose of the flattened field set as 100%. PDD data was obtained at field sizes ranging from 3 cm × 3 cm to 40 cm × 40 cm. Radiation protection measurements were additionally performed to determine the head leakage and environmental monitoring through the maze and primary barriers. Results: No significant change is made to the beam penumbra for FFF beams with and without PDD matching, the maximum change in penumbra for a 10 cm × 10 cm field was within the experimental error of the study. The changes in the profile shape with increasing field size are most significant for the matched FFF beam, and both FFF beams showed less profile shape variation with increasing depth when compared to flattened beams, due to consistency in beam energy spectra across the radiation field
Energy transfer and energy level decay processes of Er3+ in water-free tellurite glass
Gomes, Laercio; Rhonehouse, Daniel; Nguyen, Dan T.; Zong, Jie; Chavez-Pirson, Arturo; Jackson, Stuart D.
2015-12-01
This report details the fundamental spectroscopic properties of a new class of water-free tellurite glasses studied for future applications in mid-infrared light generation. The fundamental excited state decay processes relating to the 4I11/2 → 4I13/2 transition in singly Er3+-doped Tellurium Zinc Lanthanum glass have been investigated using time-resolved fluorescence spectroscopy. The excited state dynamics was analyzed for Er2O3 concentrations between 0.5 mol% and 4 mol%. Selective laser excitation of the 4I11/2 energy level at 972 nm and selective laser excitation of the 4I13/2 energy level at 1485 nm has established that in a similar way to other Er3+-doped glasses, a strong energy-transfer upconversion by way of a dipole-dipole interaction between two excited erbium ions in the 4I13/2 level populates the 4I11/2 upper laser level of the 3 μm transition. The 4I13/2 and 4I11/2 energy levels emitted luminescence with peaks located at 1532 nm and 2734 nm respectively with luminescence efficiencies of 100% and 8% for the higher (4 mol.%) concentration sample. Results from numerical simulations showed that a population inversion is reached at a threshold pumping intensity of ∼57 kW cm-2 for a CW laser pump at 976 nm for [Er2O3] = 2 mol.%.
Towards a Continental Energy Market: From the Energy Crisis to the Free Trade Agreement, 1970-88.
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)
Meng, Yilin; Dashti, Danial Sabri; Roitberg, Adrian E
2011-09-13
Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.
Solid–liquid interfacial free energy of small colloidal hard-sphere crystals
Cacciuto, A.; Auer, S.; Frenkel, D.
2003-01-01
Using free-energy calculations on small crystalline clusters, we estimate the free-energy density γSL for the solid–liquid equimolar interface of a system of hard-sphere colloids. By studying the behavior of a crystallite at coexistence, we determine the dependence of γSL on the radius of curvature
Sørensen, Jesper; Hamelberg, Donald; McCammon, J. Andrew
experimental results have helped to explain this aberrant behavior of TTR, however, structural insights of the amyloidgenic process are still lacking. Therefore, we have used all-atom molecular dynamics simulation and free energy calculations to study the initial phase of this process. We have calculated...... the free energy changes of the initial tetramer dissociation under different conditions and in the presence of thyroxine....
Sørensen, Jesper; Hamelberg, Donald; McCammon, J. Andrew
experimental results have helped to explain this aberrant behavior of TTR, however, structural insights of the amyloidgenic process are still lacking. Therefore, we have used all-atom molecular dynamics simulation and free energy calculations to study the initial phase of this process. We have calculated...... the free energy changes of the initial tetramer dissociation under different conditions and in the presence of thyroxine....
CAN THE STABILITY OF PROTEIN MUTANTS BE PREDICTED BY FREE-ENERGY CALCULATIONS
YUNYU, S; MARK, AE; WANG, CX; HUANG, FH; BERENDSEN, HJC; VANGUNSTEREN, WF
1993-01-01
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 comp
Free energy change of off-eutectic binary alloys on solidification
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.
CAN THE STABILITY OF PROTEIN MUTANTS BE PREDICTED BY FREE-ENERGY CALCULATIONS
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
Incorporating the effect of ionic strength in free energy calculations using explicit ions
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
On the Surface Free Energy of PVC/EVA Polymer Blends: Comparison of Different Calculation Methods.
Michalski; Hardy; Saramago
1998-12-01
The surface free energy of polymeric films of polyvinylchloride (PVC) + poly(ethylene-co-vinylacetate) (EVA) blends was calculated using the van Oss treatment (Lifshitz and electron donor-electron acceptor components of surface free energy) and the Owens-Wendt treatment (dispersive and nondispersive components of surface free energy). Surface free energy results were found to be greatly dependent on the calculation method and on the number of standard liquids used for contact angle measurements. The nondispersive/donor-acceptor surface free energy component and the total surface free energy of polymeric films were always higher when the van Oss treatment was used compared to the Owens-Wendt treatment. Conversely, both methods led to similar apolar/Lifshitz components. All the calculation methods were in good agreement for the surface free energy of PVC; however, a discrepancy between the methods arose as EVA content in the blends increased. It seems that there is not yet a definite solution for the calculation of solid surface free energy. Further developments of existing models are needed in order to gain consistency when calculating this important physicochemical quantity. Copyright 1998 Academic Press.
Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics.
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
Tian, Pu
2015-01-01
Free energy is arguably the most important thermodynamic property for physical systems. Despite the fact that free energy is a state function, presently available rigorous methodologies, such as those based on thermodynamic integration (TI) or non-equilibrium work (NEW) analysis, involve energetic calculations on path(s) connecting the starting and the end macrostates. Meanwhile, presently widely utilized approximate end-point free energy methods lack rigorous treatment of conformational variation within end macrostates, and are consequently not sufficiently reliable. Here we present an alternative and rigorous end point free energy calculation formulation based on microscopic configurational space coarse graining, where the configurational space of a high dimensional system is divided into a large number of sufficiently fine and uniform elements, which were termed conformers. It was found that change of free energy is essentially decided by change of the number of conformers, with an error term that accounts...
Free energy simulations with the AMOEBA polarizable force field and metadynamics on GPU platform.
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.
Graph's Topology and Free Energy of a Spin Model on the Graph
Choi, Jeong-Mo; Gilson, Amy I.; Shakhnovich, Eugene I.
2017-02-01
In this Letter we investigate a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and energetic contributions to the free energy, and find that considering the topology is sufficient to qualitatively compare the free energies of different graph systems at high temperature, even when the energetics are not fully known. This method was applied to the metal lattice system with defects, and we found that it partially explains why point defects are more stable than high-dimensional defects. Given the energetics, we can even quantitatively compare free energies of different graph structures via a closed form of linear graph contributions. The closed form is applied to predict the sequence-space free energy of lattice proteins, which is a key factor determining the designability of a protein structure.
A Prediction Method of Binding Free Energy of Protein and Ligand
Yang, Kun; Wang, Xicheng
2010-05-01
Predicting the binding free energy is an important problem in bimolecular simulation. Such prediction would be great benefit in understanding protein functions, and may be useful for computational prediction of ligand binding strengths, e.g., in discovering pharmaceutical drugs. Free energy perturbation (FEP)/thermodynamics integration (TI) is a classical method to explicitly predict free energy. However, this method need plenty of time to collect datum, and that attempts to deal with some simple systems and small changes of molecular structures. Another one for estimating ligand binding affinities is linear interaction energy (LIE) method. This method employs averages of interaction potential energy terms from molecular dynamics simulations or other thermal conformational sampling techniques. Incorporation of systematic deviations from electrostatic linear response, derived from free energy perturbation studies, into the absolute binding free energy expression significantly enhances the accuracy of the approach. However, it also is time-consuming work. In this paper, a new prediction method based on steered molecular dynamics (SMD) with direction optimization is developed to compute binding free energy. Jarzynski's equality is used to derive the PMF or free-energy. The results for two numerical examples are presented, showing that the method has good accuracy and efficiency. The novel method can also simulate whole binding proceeding and give some important structural information about development of new drugs.
Smart Energy Choices Free Up Dollars for Capital Improvements.
Ritchey, David
2003-01-01
Describes several ways to design or renovate school building to save thousand of dollars of energy costs. Considers site design, energy-efficient building envelope, renewable energy systems, lighting and electrical systems, mechanical and ventilation systems, water conservation, and transportation. Describes how to obtain information about the…
Wirth, Erin A.; Long, Maureen D.; Moriarty, John C.
2017-01-01
Teleseismic receiver functions contain information regarding Earth structure beneath a seismic station. P-to-SV converted phases are often used to characterize crustal and upper-mantle discontinuities and isotropic velocity structures. More recently, P-to-SH converted energy has been used to interrogate the orientation of anisotropy at depth, as well as the geometry of dipping interfaces. Many studies use a trial-and-error forward modeling approach for the interpretation of receiver functions, generating synthetic receiver functions from a user-defined input model of Earth structure and amending this model until it matches major features in the actual data. While often successful, such an approach makes it impossible to explore model space in a systematic and robust manner, which is especially important given that solutions are likely non-unique. Here, we present a Markov chain Monte Carlo algorithm with Gibbs sampling for the interpretation of anisotropic receiver functions. Synthetic examples are used to test the viability of the algorithm, suggesting that it works well for models with a reasonable number of free parameters (<˜20). Additionally, the synthetic tests illustrate that certain parameters are well constrained by receiver function data, while others are subject to severe trade-offs-an important implication for studies that attempt to interpret Earth structure based on receiver function data. Finally, we apply our algorithm to receiver function data from station WCI in the central United States. We find evidence for a change in anisotropic structure at mid-lithospheric depths, consistent with previous work that used a grid search approach to model receiver function data at this station. Forward modeling of receiver functions using model space search algorithms, such as the one presented here, provide a meaningful framework for interrogating Earth structure from receiver function data.
Havenaar, D.
2009-01-15
Servers in data centres produce a large amount of heat, which has to be removed by ventilation and air conditioning systems. These systems have a vast energy consumption. Increasing energy costs and limited resources of available electricity are forcing the data centre industry to the use of energy efficient technical equipment. Dynamic Free Cooling is a contrN concept for data centre's air conditioning systems combining Hybrid Indirect Free Cooling Precision Air Conditiening Units, Fan Speed Controlled Dry Coolers and Speed Controlled Central Pumps to highly efficient precision cooling system. All system components are centrally controlled to minimize overall energy consumption depending on the Ambient Temperature and the Room Load Status. [Dutch] Servers in datacenters produceren een grote hoeveelheid warmte die moet worden afgevoerd door middel van ventilatie- en airconditioningsystemen. Deze systemen gebruiken een forse hoeveelheid elektrische energie. Toenemende energiekosten en de beperkte beschikbaarheid van elektriciteit zorgen ervoor dat datacenters steeds meer overgaan op het installeren van energie-efficiente systemen. Dynamic Free Cooling is een regelconcept voor airconditioningsystemen in combinatie met hybride indirecte vrije koeling in precisie-airconditioningunits, ventilatorgeregetde droge koelers en toerengeregetde centrale pompsystemen. AI deze systeemcomponenten worden centraal geregeld om het totale energiegebruik, afhankelijk van de omgevingstemperatuur en de koellast te minimaliseren.
Discovering free energy basins for macromolecular systems via guided multiscale simulation.
Sereda, Yuriy V; Singharoy, Abhishek B; Jarrold, Martin F; Ortoleva, Peter J
2012-07-26
An approach for the automated discovery of low free energy states of macromolecular systems is presented. The method does not involve delineating the entire free energy landscape but proceeds in a sequential free energy minimizing state discovery; i.e., it first discovers one low free energy state and then automatically seeks a distinct neighboring one. These states and the associated ensembles of atomistic configurations are characterized by coarse-grained variables capturing the large-scale structure of the system. A key facet of our approach is the identification of such coarse-grained variables. Evolution of these variables is governed by Langevin dynamics driven by thermal-average forces and mediated by diffusivities, both of which are constructed by an ensemble of short molecular dynamics runs. In the present approach, the thermal-average forces are modified to account for the entropy changes following from our knowledge of the free energy basins already discovered. Such forces guide the system away from the known free energy minima, over free energy barriers, and to a new one. The theory is demonstrated for lactoferrin, known to have multiple energy-minimizing structures. The approach is validated using experimental structures and traditional molecular dynamics. The method can be generalized to enable the interpretation of nanocharacterization data (e.g., ion mobility-mass spectrometry, atomic force microscopy, chemical labeling, and nanopore measurements).
Zimmer, Hans-Josef [EnBW Energie Baden-Wuerttemberg AG, Karlsruhe (Germany)
2008-07-01
The worldwide energy demand will increase over the coming years. This is also causing a rise in demand for new fossil power plant capacities and at the same time we also need to achieve reductions in CO{sub 2} emissions in order to protect the climate. Ultimately, the only CO{sub 2}-free energy conversion methods that are open to us are renewables and nuclear energy. We need an open dialogue about our future energy mix. (orig.)
Communication: system-size scaling of Boltzmann and alternate Gibbs entropies.
Vilar, Jose M G; Rubi, J Miguel
2014-05-28
It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.
Minezawa, Noriyuki
2014-10-28
Examining photochemical processes in solution requires understanding the solvent effects on the potential energy profiles near conical intersections (CIs). For that purpose, the CI point in solution is determined as the crossing between nonequilibrium free energy surfaces. In this work, the nonequilibrium free energy is described using the combined method of linear-response free energy and collinear spin-flip time-dependent density functional theory. The proposed approach reveals the solvent effects on the CI geometries of stilbene in an acetonitrile solution and those of thymine in water. Polar acetonitrile decreases the energy difference between the twisted minimum and twisted-pyramidalized CI of stilbene. For thymine in water, the hydrogen bond formation stabilizes significantly the CI puckered at the carbonyl carbon atom. The result is consistent with the recent simulation showing that the reaction path via this geometry is open in water. Therefore, the present method is a promising way of identifying the free-energy crossing points that play an essential role in photochemistry of solvated molecules.
Bhatia, Anand
2012-01-01
We study the free-free transition in electron-helium ion in the ground state and embedded in a Debye potential in the presence of an external laser field at very low incident electron energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen as monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing Volkov wave function for it. The scattering wave function for the incident electron on the target embedded in a Debye potential is solved numerically by taking into account the effect of electron exchange. We calculate the laser-assisted differential and total cross sections for free-free transition for absorption/emission of a single photon or no photon exchange. The results will be presented at the conference.
Bhatia, Anand
2013-05-01
We study the free-free transition in e-He+ system in the ground state and embedded in a Debye potential in the presence of an external laser field which is monochromatic, linearly polarized and homogeneous, at very low incident electron energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing Volkov wave function. The scattering function for the incident electron on the target is solved numerically by taking into account the effect of electron exchange. We calculate the laser-assisted differential and total cross sections for free-free transitions for absorption/emission of a single photon or no photon exchange. The cross sections for e-He+ system are much larger than e-H system. The results will be presented at the conference.
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
König, Gerhard; Hudson, Phillip S; Boresch, Stefan; Woodcock, H Lee
2014-04-08
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
无
2007-01-01
Gibbs free binding energy and adsorption energy between cations and charged soil particles were used to evaluate the interactions between ions and soil particles. The distribution of Gibbs free adsorption energies could not be determined experimentally before the development of Wien effect measurements in dilute soil suspensions. In the current study, energy relationships between heavy metal ions and particles of Hapli-Udic Argosol (Alfisol) and Ferri-Udic Argosol were inferred from Wien effect measurements in dilute suspensions of homoionic soil particles (＜ 2 μm) of the two soils, which were saturated with ions of five heavy metals, in deionized water. The mean Gibbs free binding energies of the heavy metal ions with Hapli-Udic Argosol and Ferri-Udic Argosol particles diminished in the order of Pb2+＞Cd2+＞Cu2+＞ Zn2+ ＞Cr3+, where the range of binding energies for Hapli-Udic Argosol (7.25-9.32 kJ mol-1) was similar to that for Ferri-Udic Argosol (7.43-9.35 kJ mol-1). The electrical field-dependent mean Gibbs free adsorption energies of these heavy metal ions for Hapli-Udic Argosol and for Ferri-Udic Argosol descended in the order: Cu2+≥ Cd2+≥ Pb2+ ＞ Zn2+＞Cr3+,and Cd2+ ＞Cu2+＞Pb2+＞Zn2+＞Cr3+, respectively. The mean Gibbs free adsorption energies of Cu2+, Zn2+, Cd2+,Pb2+, and Cr3+ at a field strength of 200 kV cm-1, for example, were in the range of 0.8-3.2 kJ mol-1 for the two soils.
Free-energy analysis of spin models on hyperbolic lattice geometries
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.
Lesage, Adrien; Lelièvre, Tony; Stoltz, Gabriel; Hénin, Jérôme
2016-12-27
We report a theoretical description and numerical tests of the extended-system adaptive biasing force method (eABF), together with an unbiased estimator of the free energy surface from eABF dynamics. Whereas the original ABF approach uses its running estimate of the free energy gradient as the adaptive biasing force, eABF is built on the idea that the exact free energy gradient is not necessary for efficient exploration, and that it is still possible to recover the exact free energy separately with an appropriate estimator. eABF does not directly bias the collective coordinates of interest, but rather fictitious variables that are harmonically coupled to them; therefore is does not require second derivative estimates, making it easily applicable to a wider range of problems than ABF. Furthermore, the extended variables present a smoother, coarse-grain-like sampling problem on a mollified free energy surface, leading to faster exploration and convergence. We also introduce CZAR, a simple, unbiased free energy estimator from eABF trajectories. eABF/CZAR converges to the physical free energy surface faster than standard ABF for a wide range of parameters.
Free-energy analysis of spin models on hyperbolic lattice geometries.
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.
Computational Approach to Explore the B/A Junction Free Energy in DNA.
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.
The elastic free energy of a tandem modular protein under force.
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.
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.
Glycoside hydrolase processivity is directly related to oligosaccharide binding free energy.
Payne, Christina M; Jiang, Wei; Shirts, Michael R; Himmel, Michael E; Crowley, Michael F; Beckham, Gregg T
2013-12-18
Many glycoside hydrolase (GH) enzymes act via a processive mechanism whereby an individual carbohydrate polymer chain is decrystallized and hydrolyzed along the chain without substrate dissociation. Despite considerable structural and biochemical studies, a molecular-level theory of processivity that relates directly to structural features of GH enzymes does not exist. Here, we hypothesize that the degree of processivity is directly linked to the ability of an enzyme to decrystallize a polymer chain from a crystal, quantified by the binding free energy of the enzyme to the cello-oligosaccharide. We develop a simple mathematical relationship formalizing this hypothesis to quantitatively relate the binding free energy to experimentally measurable kinetic parameters. We then calculate the absolute ligand binding free energy of cellulose chains to the biologically and industrially important GH Family 7 processive cellulases with free energy perturbation/replica-exchange molecular dynamics. Taken with previous observations, our results suggest that degree of processivity is directly correlated to the binding free energy of cello-oligosaccharide ligands to GH7s. The observed binding free energies also suggest candidate polymer morphologies susceptible to enzyme action when compared to the work required to decrystallize cellulose chains. We posit that the ligand binding free energy is a key parameter in comparing the activity and function of GHs and may offer a molecular-level basis toward a general theory of carbohydrate processivity in GHs and other enzymes able to process linear carbohydrate polymers, such as cellulose and chitin synthases.
Binding effects in multivalent Gibbs-Donnan equilibrium
Castelnovo, M; Castelnovo, Martin; Evilevitch, Alex
2005-01-01
The classical Gibbs-Donnan equilibrium describes excess osmotic pressure associated with confined colloidal charges embedded in an electrolyte solution. In this work, we extend this approach to describe the influence of multivalent ion binding on the equilibrium force acting on a charged rod translocating between two compartments, thereby mimicking ionic effects on force balance during in vitro DNA ejection from bacteriophage. The subtle interplay between Gibbs-Donnan equilibrium and adsorption equilibrium leads to a non-monotonic variation of the ejection force as multivalent salt concentration is increased, in qualitative agreement with experimental observations.
Non-Equilibrium Gibbs' Criterion for Completely Wetting Volatile Liquids
Tsoumpas, Yannis; Galvagno, Mariano; Rednikov, Alexey; Ottevaere, Heidi; Thiele, Uwe; Colinet, Pierre
2014-01-01
During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that for completely wetting volatile liquids there also exists a dynamically-produced critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning, that accounts for the non-equilibrium effect of evaporation.
A computational thermodynamics approach to the Gibbs-Thomson effect
Shahandeh, Sina [Department of Material Science and Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)]. E-mail: sinashahandeh@yahoo.com; Nategh, Said [Department of Material Science and Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2007-01-15
In two-phase system, curvature of interface leads to increase of solute concentration in matrix. This effect plays a significant role in solidification, precipitation, nucleation and growth and coarsening. There are number of models and formulas for Gibbs-Thomson effect in binary alloys. In this paper with the help of CALPHAD calculations, new approach for describing this effect in binary and multicomponent systems is proposed. In this generalized method no traditional simplifying assumption are considered and this yield to more accurate result for Gibbs-Thomson phenomenon. This model is compared with previous formulas in some case alloying systems.
Magnetic energy dissipation in force-free jets
Choudhuri, Arnab Rai; Konigl, Arieh
1986-01-01
It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.
Canada's new free trade agreement. Energy. Notre nouvelle accord de libre-echange
1989-01-01
This pamphlet presents a brief overview of the economic impact of the energy industry in 1985, the future interaction between Canada and the United States under the Free Trade Agreement, and the methods used to deal with shortages, if they develop. It also addresses energy sovereignty, and the regional and national advantages of the agreement to the energy industry.
ENERGY BUDGETS IN FREE-LIVING GREEN IGUANAS IN A SEASONAL ENVIRONMENT
LICHTENBELT, WDV; WESSELINGH, RA; VOGEL, JT; ALBERS, KBM
1993-01-01
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 O
Minh, David D L
2012-09-14
A rigorous formalism for estimating noncovalent binding free energies and thermodynamic expectations from calculations in which receptor configurations are sampled independently from the ligand is derived. Due to this separation, receptor configurations only need to be sampled once, facilitating the use of binding free energy calculations in virtual screening. Demonstrative calculations on a host-guest system yield good agreement with previous free energy calculations and isothermal titration calorimetry measurements. Implicit ligand theory provides guidance on how to improve existing molecular docking algorithms and insight into the concepts of induced fit and conformational selection in noncovalent macromolecular recognition.
Cyclic Heating-Annealing and Boltzmann Distribution of Free Energies in a Spin-Glass System
ZHOU Hai-Jun
2007-01-01
Ergodicity of a spin-glass is broken at low temperatures; the system is trapped in one of many ergodic configurational domains. Transitions between different ergodic domains are achievable through a heating-annealing procedure. If this experiment is repeated infinite times, all ergodic configurational domains will be visited with frequences that decreasing exponentially with their free energies. The mean free energy density of a spin-glass system on a random graph is calculated based on this free energy Boltzmann distribution in the present work, by means of the cavity approach.
Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation
Watanabe, Yusuke
2010-01-01
We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.
Liu, Hailiang; Wang, Zhongming
2017-01-01
We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.
Sampling errors in free energy simulations of small molecules in lipid bilayers.
Neale, Chris; Pomès, Régis
2016-10-01
Free energy simulations are a powerful tool for evaluating the interactions of molecular solutes with lipid bilayers as mimetics of cellular membranes. However, these simulations are frequently hindered by systematic sampling errors. This review highlights recent progress in computing free energy profiles for inserting molecular solutes into lipid bilayers. Particular emphasis is placed on a systematic analysis of the free energy profiles, identifying the sources of sampling errors that reduce computational efficiency, and highlighting methodological advances that may alleviate sampling deficiencies. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
A Simple Free Energy for the Isotropic-Nematic Phase Transition of Rods
Remco Tuinier
2016-01-01
Full Text Available 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 deviation of the predicted binodals. The new free energy proposed here is based upon a rationalized correction to the orientational and packing entropies when using the Gaussian ODF. In combination with Parsons-Lee theory or scaled particle theory, it enables describing the isotropic-nematic phase coexistence concentrations of rods accurately using the simple Gaussian ODF for a wide range of aspect ratios.
Nuclear energy in a nuclear weapon free world
Pilat, Joseph [Los Alamos National Laboratory
2009-01-01
The prospect of a nuclear renaissance has revived a decades old debate over the proliferation and terrorism risks of the use of nuclear power. This debate in the last few years has taken on an added dimension with renewed attention to disarmament. Increasingly, concerns that proliferation risks may reduce the prospects for realizing the vision of a nuclear-weapon-free world are being voiced.
Shkel, Irina A; Record, M Thomas
2012-08-23
We investigate how the coulombic Gibbs free energy and salt ion association per phosphate charge of DNA oligomers vary with oligomer size (i.e. number of charged residues ∣ZD∣) at 0.15 M univalent salt by non-linear Poisson Boltzmann (NLPB) analysis of all-atom DNA models. Calculations of these quantities ([Formula: see text], [Formula: see text]) are performed for short and long double-stranded (ds) and single-stranded (ss) DNA oligomers, ranging from 4 to 118 phosphates (ds) and from 2 to 59 phosphates (ss). Behaviors of [Formula: see text] and [Formula: see text] as functions of ∣ZD∣ provide a measure of the range of the coulombic end effect and determine the size of an oligomer at which an interior region with the properties (per charge) of the infinite-length polyelectrolyte first appears. This size (10-11 phosphates at each end for ds DNA and 6-9 for ss DNA at 0.15 M salt) is in close agreement with values obtained previously by Monte Carlo and NLPB calculations for cylindrical models of polyions, and by analysis of binding of oligocations to DNA oligomers. Differences in [Formula: see text] and in [Formula: see text] between ss and ds DNA are used to predict effects of oligomeric size and salt concentration on duplex stability in the vicinity of 0.15 M salt. Results of all-atom calculations are compared with results of less structurally detailed models and with experimental data.
Study of Surface Cell Madelung Constant and Surface Free Energy of Nanosized Crystal Grain
ZHANG Wei-Jia; WANG Tian-Min; CUI Min
2005-01-01
Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new ap- proximative expression of surface energy and relevant thermodynamic data was used in this cal- culation. A new formula and computing method for calculating the Madelung constant α of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nano- sized crystal grains as well as Madelung constant of some complex crystals are theoretically cal- culated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface elec- trostatic energy(absolute value) of nanosized crystal grain α-Al2O3 are found to be the biggest among other crystal grains.
Study of surface cell Madelung constant and surface free energy of nanosized crystal grain
Zhang Wei-Jia; Wang Tian-Min; Rong Ai-Lun; Cui Min
2006-01-01
Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains,which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth.A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation.New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed,and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper.The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy (absolute value) of nanosized-crystal-grain α-A12O3 are found to be the biggest among all the crystal grains including those of other species.
CHARMM-GUI Ligand Binder for absolute binding free energy calculations and its application.
Jo, Sunhwan; Jiang, Wei; Lee, Hui Sun; Roux, Benoît; Im, Wonpil
2013-01-28
Advanced free energy perturbation molecular dynamics (FEP/MD) simulation methods are available to accurately calculate absolute binding free energies of protein-ligand complexes. However, these methods rely on several sophisticated command scripts implementing various biasing energy restraints to enhance the convergence of the FEP/MD calculations, which must all be handled properly to yield correct results. Here, we present a user-friendly Web interface, CHARMM-GUI Ligand Binder ( http://www.charmm-gui.org/input/gbinding ), to provide standardized CHARMM input files for calculations of absolute binding free energies using the FEP/MD simulations. A number of features are implemented to conveniently set up the FEP/MD simulations in highly customizable manners, thereby permitting an accelerated throughput of this important class of computations while decreasing the possibility of human errors. The interface and a series of input files generated by the interface are tested with illustrative calculations of absolute binding free energies of three nonpolar aromatic ligands to the L99A mutant of T4 lysozyme and three FK506-related ligands to FKBP12. Statistical errors within individual calculations are found to be small (~1 kcal/mol), and the calculated binding free energies generally agree well with the experimental measurements and the previous computational studies (within ~2 kcal/mol). Therefore, CHARMM-GUI Ligand Binder provides a convenient and reliable way to set up the ligand binding free energy calculations and can be applicable to pharmaceutically important protein-ligand systems.
Relationship between quark-antiquark potential and quark-antiquark free energy in hadronic matter
SHEN Zhen-Yu; XU Xiao-Ming
2015-01-01
In high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision,the quark-antiquark potential depends on the temperature.The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations.This requires one to study the relationship between the quark-antiquark potential and the quark-antiquark free energy.When the system's temperature is above the critical temperature,the potential of a heavy quark and a heavy antiquark almost equals the free energy,but the potential of a light quark and a light antiquark,of a heavy quark and a light antiquark and of a light quark and a heavy antiquark is substantially larger than the free energy.When the system's temperature is below the critical temperature,the quark-antiquark free energy can be taken as the quark-antiquark potential.This allows one to apply the quark-antiquark free energy to study hadron properties and hadron-hadron reactions in hadronic matter.
Outer Membrane Protein Folding and Topology from a Computational Transfer Free Energy Scale.
Lin, Meishan; Gessmann, Dennis; Naveed, Hammad; Liang, Jie
2016-03-02
Knowledge of the transfer free energy of amino acids from aqueous solution to a lipid bilayer is essential for understanding membrane protein folding and for predicting membrane protein structure. Here we report a computational approach that can calculate the folding free energy of the transmembrane region of outer membrane β-barrel proteins (OMPs) by combining an empirical energy function with a reduced discrete state space model. We quantitatively analyzed the transfer free energies of 20 amino acid residues at the center of the lipid bilayer of OmpLA. Our results are in excellent agreement with the experimentally derived hydrophobicity scales. We further exhaustively calculated the transfer free energies of 20 amino acids at all positions in the TM region of OmpLA. We found that the asymmetry of the Gram-negative bacterial outer membrane as well as the TM residues of an OMP determine its functional fold in vivo. Our results suggest that the folding process of an OMP is driven by the lipid-facing residues in its hydrophobic core, and its NC-IN topology is determined by the differential stabilities of OMPs in the asymmetrical outer membrane. The folding free energy is further reduced by lipid A and assisted by general depth-dependent cooperativities that exist between polar and ionizable residues. Moreover, context-dependency of transfer free energies at specific positions in OmpLA predict regions important for protein function as well as structural anomalies. Our computational approach is fast, efficient and applicable to any OMP.
The free energies of partially open coronal magnetic fields
Low, B. C.; Smith, D. F.
1993-01-01
A simple model of the low corona is examined in terms of a static polytropic atmosphere in equilibrium with a global magnetic field. The question posed is whether magnetostatic states with partially open magnetic fields may contain magnetic energies in excess of those in fully open magnetic fields. Based on the analysis presented here, it is concluded that the cross-field electric currents in the pre-eruption corona are a viable source of the bulk of the energies in a mass ejection and its associated flare.
A logistic regression estimating function for spatial Gibbs point processes
Baddeley, Adrian; Coeurjolly, Jean-François; Rubak, Ege
We propose a computationally efficient logistic regression estimating function for spatial Gibbs point processes. The sample points for the logistic regression consist of the observed point pattern together with a random pattern of dummy points. The estimating function is closely related...
Calculation of the chemical potential in the Gibbs ensemble
Smit, B.; Frenkel, D.
1989-01-01
An expression for the chemical potential in the Gibbs ensemble is derived. For finite system sizes this expression for the chemical potential differs system-atically from Widom's test particle insertion method for the N, V, T ensemble. In order to compare these two methods for calculating the chemic
Multifractal Analysis of Local Entropies for Gibbs Measures
Takens, Floris; Verbitski, Evgeni
1998-01-01
Recently a complete multifractal analysis of local dimensions, entropies and Lyapunov exponents of conformal expanding maps and surface Axion A diffeomorphisms for Gibbs measures was performed. The main goal of this was primarily the analysis of the local (pointwise) dimensions. This is an extremely
Bayesian Estimation of the DINA Model with Gibbs Sampling
Culpepper, Steven Andrew
2015-01-01
A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
Bobrov, V. B., E-mail: vic5907@mail.ru, E-mail: satron@mail.ru [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13, Bd. 2, Moscow 125412 (Russian Federation); National Research University “MPEI,” Krasnokazarmennaya str. 14, Moscow 111250 (Russian Federation); Trigger, S. A., E-mail: vic5907@mail.ru, E-mail: satron@mail.ru [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13, Bd. 2, Moscow 125412 (Russian Federation); Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, Berlin D-12489 (Germany)
2014-10-15
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.
Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Ghosh, Jonaki B.
2011-01-01
This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…
Kjærgaard, Christian Hauge; Rossmeisl, Jan; Nørskov, Jens Kehlet
2010-01-01
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......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...
A temperature-dependent surface free energy model for solid single crystals
Cheng, Tianbao; Fang, Daining; Yang, Yazheng
2017-01-01
A temperature-dependent theoretical model for the surface free energy of the solid single crystals is established. This model relates the surface free energy at the elevated temperatures to that at the reference temperature, the temperature-dependent specific heat at constant pressure and coefficient of the linear thermal expansion, the heat of phase transition, the melting heat, and the vapor heat. As examples, the surface free energies of Fe, Cu, Al, Ni, and Pb from 0 K to melting points are calculated and are in reasonable agreement with these from Tyson's theories and the experimental results. This model has obvious advantages compared to Tyson's semi-empirical equations from the aspect of physical meaning, applicable condition, and accuracy. The study shows that the surface free energy of the solid single crystals firstly remains approximately constant and then decreases linearly as temperature increases from 0 K to melting point.
The free energy cost of reducing noise while maintaining a high sensitivity
Sartori, Pablo; Tu, Yuhai
2016-01-01
Living systems need to be highly responsive, and also to keep fluctuations low. These goals are incompatible in equilibrium systems due to the Fluctuation Dissipation Theorem (FDT). Here, we show that biological sensory systems, driven far from equilibrium by free energy consumption, can reduce their intrinsic fluctuations while maintaining high responsiveness. By developing a continuum theory of the E. coli chemotaxis pathway, we demonstrate that adaptation can be understood as a non-equilibrium phase transition controlled by free energy dissipation, and it is characterized by a breaking of the FDT. We show that the maximum response at short time is enhanced by free energy dissipation. At the same time, the low frequency fluctuations and the adaptation error decrease with the free energy dissipation algebraically and exponentially, respectively. PMID:26406857
The free energy cost of reducing noise while maintaining a high sensitivity
Sartori, Pablo
2015-01-01
Living systems need to be highly responsive, and also to keep fluctuations low. These goals are incompatible in equilibrium systems due to the Fluctuation Dissipation Theorem (FDT). Here, we show that biological sensory systems, driven far from equilibrium by free energy consumption, can reduce their intrinsic fluctuations while maintaining high responsiveness. By developing a continuum theory of the E. coli chemotaxis pathway, we demonstrate that adaptation can be understood as a non-equilibrium phase transition controlled by free energy dissipation, and it is characterized by a breaking of the FDT. We show that the maximum response at short time is enhanced by free energy dissipation. At the same time, the low frequency fluctuations and the adaptation error decrease with the free energy dissipation algebraically and exponentially, respectively.
Hummer, G; Hummer, Gerhard; Kevrekidis, Ioannis G.
2002-01-01
We present a ``coarse molecular dynamics'' approach and apply it to studying the kinetics and thermodynamics of a peptide fragment dissolved in water. Short bursts of appropriately initialized simulations are used to infer the deterministic and stochastic components of the peptide motion parametrized by an appropriate set of coarse variables. Techniques from traditional numerical analysis (Newton-Raphson, coarse projective integration) are thus enabled; these techniques help analyze important features of the free-energy landscape (coarse transition states, eigenvalues and eigenvectors, transition rates, etc.). Reverse integration of (irreversible) expected coarse variables backward in time can assist escape from free energy minima and trace low-dimensional free energy surfaces. To illustrate the ``coarse molecular dynamics'' approach, we combine multiple short (0.5-ps) replica simulations to map the free energy surface of the ``alanine dipeptide'' in water, and to determine the ~ 1/(1000 ps) rate of interconv...
Experimental free energy measurements of kinetic molecular states using fluctuation theorems
Alemany, Anna; Junier, Ivan; Ritort, Felix; 10.1038/nphys2375
2013-01-01
Recent advances in non-equilibrium statistical mechanics and single molecule technologies make it possible to extract free energy differences from irreversible work measurements in pulling experiments. To date, free energy recovery has been focused on native or equilibrium molecular states, whereas free energy measurements of kinetic states (i.e. finite lifetime states that are generated dynamically and are metastable) have remained unexplored. Kinetic states can play an important role in various domains of physics, such as nanotechnology or condensed matter physics. In biophysics, there are many examples where they determine the fate of molecular reactions: protein and peptide-nucleic acid binding, specific cation binding, antigen-antibody interactions, transient states in enzymatic reactions or the formation of transient intermediates and non-native structures in molecular folders. Here we demonstrate that it is possible to obtain free energies of kinetic states by applying extended fluctuation relations. T...
Free Energy and the Generalized Optimality Equations for Sequential Decision Making
Ortega, Pedro A
2012-01-01
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments. We derive generalized sequential optimality equations that not only include the Bellman optimality equations as a limit case, but also lead to well-known decision-rules such as Expectimax, Minimax and Expectiminimax. We show how these decision-rules can be derived from a single free energy principle that assigns a resource parameter to each node in the decision tree. These resource parameters express a concrete computational cost that can be measured as the amount of samples that are needed from the distribution that belongs to each node. The free energy principle therefore provides the normative basis for generalized optimality equations t...
Conjugate Acid-Base Pairs, Free Energy, and the Equilibrium Constant
Beach, Darrell H.
1969-01-01
Describes a method of calculating the equilibrium constant from free energy data. Values of the equilibrium constants of six Bronsted-Lowry reactions calculated by the author's method and by a conventional textbook method are compared. (LC)
Study on the Surface Free Energy of Ground CaO by IGC
无
2002-01-01
CaO formed by decomposing CaCO3 at 1450℃ was ground in a vibrational mill,then the long-time ground sample was reheated at different temperatures.Inverse Gas Chromatography (IGC) was used to measure the variation of the sample′s surface free energy under grinding and reheating.It is concluded that the total surface free energy and the London dispersive component of the surface free energy increases with grinding,while the polar component first increases with grinding,and then decreases,and finally disappears.When the long-time ground sample was reheated,its total surface free energy decreases,among which the London component decreases,but the polar component appears again.
Wai, C. M.; Hutchinson, S. G.
1989-01-01
Discusses the calculation of free energy in reactions between silicon dioxide and carbon. Describes several computer programs for calculating the free energy minimization and their uses in chemistry classrooms. Lists 16 references. (YP)
The Pillars of Power. How the free trade agenda promotes dirty energy
Martinez, N. [Sustainable Energy and Economy Network, Institute for Policy Studies, Washington, DC (United States)
2003-01-01
This report demonstrates how the Bush/Cheney administration, international financial institutions like the World Bank and the Inter-American Development Bank, and multilateral free trade agreements like the Free Trade Area of the Americas (FTAA) and the General Agreement on Trade in Services (GATS), together promote a corporate driven, anti-environment energy agenda in Latin America and elsewhere.
Kuehn, T. J.; Nawrocki, P. M.
1978-01-01
It is suggested that federal programs for hastening the adoption of alternative energy sources must operate within the free market structure. Five phases of the free market commercialization process are described. Federal role possibilities include information dissemination and funding to stimulate private sector activities within these five phases, and federally sponsored procedures for accelerating commercialization of solar thermal small power systems are considered.
A Low-Energy-Spread Rf Accelerator for a Far-Infrared Free-Electron Laser
van der Geer, C. A. J.; Bakker, R. J.; van der Meer, A. F. G.; van Amersfoort, P. W.; Gillespie, W. A.; Saxon, G.; Poole, M. W.
1993-01-01
A high electron current and a small energy spread are essential for the operation of a free electron laser (FEL). In this paper we discuss the design and performance of the accelerator for FELIX, the free electron laser for infrared experiments. The system consists of a thermionic gun, a prebuncher,
High energy pulsewidth tunable CPA free picosecond source
Pouysegur, Julien; Guichard, Florent; Zaouter, Yoann; Hanna, Marc; Druon, Frédéric; Hönninger, Clemens; Mottay, Eric; Georges, Patrick
2016-03-01
A hybrid ytterbium-doped fiber - bulk laser source generating up to 116MW peak power for 3ps pulse duration at 50kHz repetition rate and 1030nm wavelength is presented. Tunability of the pulse duration is made by spectral compression occurring into the seeder. Divided Pulse Amplification scheme is investigated to study energy capabilities of the setup.
SAAMBE: Webserver to Predict the Charge of Binding Free Energy Caused by Amino Acids Mutations.
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/.
Prediction about precipitation sequence in 18Cr-8Ni steel by system free energy method
Toda, Y.; Abe, F. [National Institute for Materials Science (NIMS), Tsukuba (Japan)
2008-07-01
The applicability of theoretical energy analysis to the evolution of microstructures in heat-resistant steels was explored by using the system free energy method to predict the precipitation of M{sub 23}C{sub 6} (where M means metallic alloying element) carbide and {sigma} phase within grains in 18Cr-8Ni austenitic steels. The chemical free energy of Fe-CCr- Ni quaternary steel and the interfacial and elastic strain energies between austenitic ({gamma}) matrix and the M{sub 23}C{sub 6} and o phase were estimated for the system free energy of microstructures wherein coherent or incoherent M{sub 23}C{sub 6} and the incoherent {sigma} phase were precipitated within {gamma} grains. By identifying the minimum-energy path through a determination of system free energy hierarchies, the precipitation initiation curves of precipitates in Fe-0.07C-18.95Cr-9.57Ni steel for temperatures between 823-973 K were theoretically predicted. The calculated curves agreed well with experimental results for Type 304H austenitic steels; this suggests that the system free energy method is suitable for predicting the evolution of microstructures in heatresistant steels. (orig.)
Adhesion Evaluation of Asphalt-Aggregate Interface Using Surface Free Energy Method
Jie Ji; Hui Yao; Luhou Liu; Zhi Suo; Peng Zhai; Xu Yang; Zhanping You
2017-01-01
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 establis...
Perturbation theory of solid-liquid interfacial free energies of bcc metals.
Warshavsky, Vadim B; Song, Xueyu
2012-09-01
A perturbation theory is used to calculate bcc solid-liquid interfacial free energies of metallic systems with embedded-atom model potentials. As a reference system for bcc crystals we used a single-occupancy cell, hard-sphere bcc system. Good agreements between the perturbation theory results and the corresponding results from simulations are found. The strategy to extract hard-sphere bcc solid-liquid interfacial free energies may have broader applications for other crystal lattices.
A Python tool to set up relative free energy calculations in GROMACS.
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.
An Expansion of the Free Energy of Anharmonic Oscillator Based on the Variational Result
Lu, W F; Bak, J; Kim, C K; Nahm, K; Lu, Wen-Fa; You, Sang Koo; Bak, Jino; Kim, Chul Koo; Nahm, Kyun
2002-01-01
Based on the variational result, we performed a Taylor series expansion of the free energy of an anharmonic oscillator within the functional integral formalism. The variationally extremized condition makes Cactus Feynman diagrams disappear from any higher-order diagrams, and accordingly Feynman diagrams are simplified. We obtained the analytical expression of the free energy up to the fourth order, and compared our results with exact, accurate and variational results.
Metadyn View: Fast web-based viewer of free energy surfaces calculated by metadynamics
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.
Free energy and hidden barriers of the β-sheet structure of prion protein.
Paz, S Alexis; Abrams, Cameron F
2015-10-13
On-the-fly free-energy parametrization is a new collective variable biasing approach akin to metadynamics with one important distinction: rather than acquiring an accelerated distribution via a history-dependent bias potential, sampling on this distribution is achieved from the beginning of the simulation using temperature-accelerated molecular dynamics. In the present work, we compare the performance of both approaches to compute the free-energy profile along a scalar collective variable measuring the H-bond registry of the β-sheet structure of the mouse Prion protein. Both methods agree on the location of the free-energy minimum, but free-energy profiles from well-tempered metadynamics are subject to a much higher degree of statistical noise due to hidden barriers. The sensitivity of metadynamics to hidden barriers is shown to be a consequence of the history dependence of the bias potential, and we detail the nature of these barriers for the prion β-sheet. In contrast, on-the-fly parametrization is much less sensitive to these barriers and thus displays improved convergence behavior relative to that of metadynamics. While hidden barriers are a frequent and central issue in free-energy methods, on-the-fly free-energy parametrization appears to be a robust and preferable method to confront this issue.
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.
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.
Modeling of the magnetic free energy of self-diffusion in bcc Fe
Sandberg, N.; Chang, Z.; Messina, L.; Olsson, P.; Korzhavyi, P.
2015-11-01
A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.
YANGGuo-Hong; WANGYu-Sheng; DUANYi-Shi
2004-01-01
In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange's method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.
YANG Guo-Hong; WANG Yu-Sheng; DUAN Yi-Shi
2004-01-01
In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange's method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.
Sakuraba, Shun; Matubayasi, Nobuyuki
2014-08-05
ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed-phase systems of the solution of interest and the reference solvent with test-particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free-energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano-inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod.
Free Energy-Based Conformational Search Algorithm Using the Movable Type Sampling Method.
Pan, Li-Li; Zheng, Zheng; Wang, Ting; Merz, Kenneth M
2015-12-08
In this article, we extend the movable type (MT) sampling method to molecular conformational searches (MT-CS) on the free energy surface of the molecule in question. Differing from traditional systematic and stochastic searching algorithms, this method uses Boltzmann energy information to facilitate the selection of the best conformations. The generated ensembles provided good coverage of the available conformational space including available crystal structures. Furthermore, our approach directly provides the solvation free energies and the relative gas and aqueous phase free energies for all generated conformers. The method is validated by a thorough analysis of thrombin ligands as well as against structures extracted from both the Protein Data Bank (PDB) and the Cambridge Structural Database (CSD). An in-depth comparison between OMEGA and MT-CS is presented to illustrate the differences between the two conformational searching strategies, i.e., energy-based versus free energy-based searching. These studies demonstrate that our MT-based ligand conformational search algorithm is a powerful approach to delineate the conformational ensembles of molecular species on free energy surfaces.
A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies.
Cave-Ayland, Christopher; Skylaris, Chris-Kriton; Essex, Jonathan W
2017-02-14
Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are postprocessed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation, however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semiempirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.
USA-Canada free trade agreement and energy problem
Ogushi, Nobuyuki
1988-11-01
The USA and Canada occupying approx. 70 and 20%, respectively, of the export/import amount of the opponent country, the free trade agreement is regarded as a matter of course, also judging from the geographical condition between both countries. Energywise to analyze the influence of that agreement, if concluded, as for oil, Canada is exporting 30% of produced oil to the USA, which will not be influential in the short term. However in the long term, it will be problematic as the oil reserve is being exhausted in Canada. As for natural gas, Canadian supply of natural gas to the USA being in excess at present, the agreement, if concluded, would be influential on the present disturbance to be solved. Canada exports 9% of produced electric power to the USA, where there domestically exist pros and cons of the liberalization of power importation. By the agreement if concluded, the USA will be assured of the stable supply of uranium and exempt from the required uranium manufacture. But the conclusion of agreement, depending upon the political situation in Canada, is not easily predictable. 8 tables.
Free Energy Relationships in the Electrical Double Layer over Single-Layer Graphene
Achtyl, Jennifer L. [Northwestern University, Evanston; Vlassiouk, Ivan V [ORNL; Fulvio, Pasquale F [ORNL; Mahurin, Shannon Mark [ORNL; Dai, Sheng [ORNL; Geiger, Franz M. [Northwestern University, Evanston
2013-01-01
Fluid/solid interfaces containing singlelayer graphene are important in the areas of chemistry, physics, biology, and materials science, yet this environment is difficult to access with experimental methods, especially under flow conditions and in a label-free manner. Herein, we demonstrate the use of second harmonic generation to quantify the interfacial free energy at the fused silica/single-layer graphene/water interface at pH 7 and under conditions of flowing aqueous electrolyte solutions ranging in NaCl concentrations from 10 4 to 10 1 M. Our analysis reveals that single-layer graphene reduces the interfacial free energy density of the fused silica/water interface by a factor of up to 7, which is substantial given that many interfacial processes, including those that are electrochemical in nature, are exponentially sensitive to interfacial free energy density.
QM/MM Minimum Free Energy Path: Methodology and Application to Triosephosphate Isomerase.
Hu, Hao; Lu, Zhenyu; Yang, Weitao
2007-03-01
Structural and energetic changes are two important characteristic properties of a chemical reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost associated with the quantum mechanical calculations and phase space sampling. Although the combined quantum mechanics/molecular mechanics (QM/MM) approach significantly reduces the amount of the quantum mechanical calculations and facilitates the simulation of solution phase and enzyme catalyzed reactions, the required quantum mechanical calculations remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mechanical methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the minimum energy path. Such ab initio QM/MM calculations have previously been performed with the QM/MM-Free Energy (QM/MM-FE) method of Zhang et al.1 to generate the free energy profile along the reaction coordinate using free energy perturbation calculations at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the determination of the minimum energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties associated with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to determine the QM/MM minimum free energy path (QM/MM-MFEP) for chemical reaction processes in solution and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodynamics of the system. The free energy difference between two QM conformations is evaluated by the QM
A magnetic-free high-resolution parabolic mirror time-of-flight electron energy spectrometer
张戈; 沈鸿元; 曾瑞荣; 黄呈辉; 林文雄; 黄见洪
2001-01-01
The principle and structure of a magnetic-free high-resolution high-efficiency parabolic mirror time-offligght electron energy spectrometer are presented. The electron energy spectrum of Nz in a flight tube is measured using a 105 fs Ti:sappbire laser under different gas pressures.
Kaliakin, Danil S.; Zaari, Ryan R.; Varganov, Sergey A.
2015-01-01
Teaching fundamental physical chemistry concepts such as the potential energy surface, transition state, and reaction path is a challenging task. The traditionally used oversimplified 2D representation of potential and free energy surfaces makes this task even more difficult and often confuses students. We show how this 2D representation can be…
Free energy and structure of dislocation cores in two-dimensional crystals
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
Characteristic properties of the Casimir free energy for metal films deposited on metallic plates
Klimchitskaya, G. L.; Mostepanenko, V. M.
2016-04-01
The Casimir free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into account by using the complete optical data of film and plate metals. It is shown that for films of several tens of nanometers thickness the Casimir free energy and pressure calculated using these approaches differ by hundreds and thousands percent and can be easily discriminated experimentally. According to our results, the free energy of a metal film does not vanish in the limiting case of ideal metal if the Drude model approach is used in contradiction with the fact that the fluctuating field cannot penetrate in its interior. Numerical computations of the Casimir free energy and pressure of Ag and Au films deposited on Cu and Al plates have been performed using both theoretical approaches. It is shown that the free energy of a film can be both negative and positive depending on the metals used. For a Au film on a Ag plate and vice versa the Casimir energy of a film changes its sign with increasing film thickness. Applications of the obtained results for resolving the Casimir puzzle and the problem of stability of thin films are discussed.
Analytic second derivatives of the energy in the fragment molecular orbital method.
Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro
2013-04-28
We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm(-1) in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.
Roadmaps through free energy landscapes calculated using the multi-dimensional vFEP approach.
Lee, Tai-Sung; Radak, Brian K; Huang, Ming; Wong, Kin-Yiu; York, Darrin M
2014-01-14
The variational free energy profile (vFEP) method is extended to two dimensions and tested with molecular simulation applications. The proposed 2D-vFEP approach effectively addresses the two major obstacles to constructing free energy profiles from simulation data using traditional methods: the need for overlap in the re-weighting procedure and the problem of data representation. This is especially evident as these problems are shown to be more severe in two dimensions. The vFEP method is demonstrated to be highly robust and able to provide stable, analytic free energy profiles with only a paucity of sampled data. The analytic profiles can be analyzed with conventional search methods to easily identify stationary points (e.g. minima and first-order saddle points) as well as the pathways that connect these points. These "roadmaps" through the free energy surface are useful not only as a post-processing tool to characterize mechanisms, but can also serve as a basis from which to direct more focused "on-the-fly" sampling or adaptive force biasing. Test cases demonstrate that 2D-vFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct stable, converged analytic free energy profiles. In a classic test case, the two dimensional free energy profile of the backbone torsion angles of alanine dipeptide, 2D-vFEP needs less than 1% of the original data set to reach a sampling accuracy of 0.5 kcal/mol in free energy shifts between windows. A new software tool for performing one and two dimensional vFEP calculations is herein described and made publicly available.
Computational scheme for pH-dependent binding free energy calculation with explicit solvent.
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.
Wahle, Chris W; Ross, David S; Thurston, George M
2013-09-28
We extend methods of solution of a light scattering partial differential equation for the free energy of mixing to apply to connected, isotropic ternary liquid composition domains that do not touch all three binary axes. To do so we mathematically analyze the problem of inferring needed Dirichlet boundary data, and solving for the free energy, with use of hypothetical static light scattering measurements that correspond to dielectric composition gradient vectors that have distinct directions. The physical idea behind the technique is that contrasting absorption properties of mixture components can result in such distinctly directed dielectric composition gradient vectors, due to their differing wavelength dependences of dielectric response. At suitably chosen wavelengths, contrasting light scattering efficiency patterns in the ternary composition triangle can then correspond to the same underlying free energy, and enlarge the scope of available information about the free energy, as shown here. We show how to use distinctly directed dielectric gradients to measure the free energy on both straight lines and curves within the ternary composition triangle, so as to provide needed Dirichlet conditions for light scattering partial differential equation solution. With use of Monte Carlo simulations of noisy light scattering data, we provide estimates of the overall system measurement time and sample spacing needed to determine the free energy to a desired degree of accuracy, for various angles between the assumed dielectric gradient vectors, and indicate how the measurement time depends on instrumental throughput parameters. The present analysis methods provide a way to use static light scattering to measure, directly, mixing free energies of many systems that contain such restricted liquid domains, including aqueous solutions of biological macromolecules, micellar mixtures and microemulsions, and many small molecule systems that are important in separation technology.
Thermodynamic Free Energy Methods to Investigate Shape Transitions In Bilayer Membranes
Ramakrishnan, N; Radhakrishnan, Ravi
2015-01-01
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 a...
Detailed balance condition and effective free energy in the primitive chain network model
Uneyama, Takashi; Masubuchi, Yuichi
2011-11-01
We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.
Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach.
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.
The growth of maize seedlings as function of free energy and redox potential
Dragičević Vesna D.
2010-01-01
Full Text Available The difference in the growth of maize seedlings originating from seeds injured by accelerated ageing, as well as those altered by restoring with low 2,4-D (2,4-dichlorophenoxyacetic acid concentrations was examined, from the point of view of free energy and redox potential. The ageing decreased germination ability, the seedling growth and free energy, with no remarkable influence on the redox capacity. Meanwhile, the 2,4-D treatment increased the germination percentage and the seedling growth, by better energy utilisation, with shifting of the redox balance to a reducing environment. From this point of view, the free energy and the redox potential are useful tools for the determination of biological vitality.
Jumper, John M; Sosnick, Tobin R
2016-01-01
To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we propose a new methodology that computes a self-consistent approximation of the side chain free energy at every integration step. In analogy with the adiabatic Born-Oppenheimer approximation in which the nuclear dynamics are governed by the energy of the instantaneously-equilibrated electronic degrees of freedom, the protein backbone dynamics are simulated as preceding according to the dictates of the free energy of an instantaneously-equilibrated side chain potential. The side chain free energy is computed on the fly; hence, the protein backbone dynamics traverse a greatly smoothed energetic landscape, resulting in extremely rapid equilibration and sampling of the Boltzmann distribution. Because our method employs a reduced model involving single-bead side chains, we also provide a novel, maximum-likelihood type method to parameterize the side chain model using...
Detailed balance condition and effective free energy in the primitive chain network model.
Uneyama, Takashi; Masubuchi, Yuichi
2011-11-14
We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.
Accuracy of Parameter Estimation in Gibbs Sampling under the Two-Parameter Logistic Model.
Kim, Seock-Ho; Cohen, Allan S.
The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal…
Mi, Bin-Zhou; Zhai, Liang-Jun; Hua, Ling-Ling
2016-01-01
The effect of magnetic spin correlation on the thermodynamic properties of Heisenberg ferromagnetic single-walled nanotubes are comprehensively investigated by use of the double-time Green's function method. The influence of temperature, spin quantum number, diameter of the tube, anisotropy strength and external magnetic field to internal energy, free energy, and magnon specific heat are carefully calculated. Compared to the mean field approximation, the consideration of the magnetic correlation effect significantly improves the internal energy values at finite temperature, while it does not so near zero temperature, and this effect is related to the diameter of the tube, anisotropy strength, and spin quantum number. The magnetic correlation effect lowers the internal energy at finite temperature. As a natural consequence of the reduction of the internal energy, the specific heat is reduced, and the free energy is elevated.
Yang, Changwon; Kim, Eunae; Pak, Youngshang
2015-09-18
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.
Circular dichroism in free-free transitions of high energy electron-atom scattering
Cionga, Aurelia; Zloh, Gabriela; 10.1103/PhysRevA.62.063406
2013-01-01
We consider high energy electron scattering by hydrogen atoms in the presence of a laser field of moderate power and higher frequencies. If the field is a superposition of a linearly and a circularly polarized laser beam in a particular configuration, then we can show that circular dichroism in two photon transitions can be observed not only for the differential but also for the integrated cross sections, provided the laser-dressing of the atomic target is treated in second order perturbation theory and the coupling between hydrogenic bound and continuum states is involved.
Gibbs artifact reduction for POCS super-resolution image reconstruction
Chuangbai XIAO; Jing YU; Kaina SU
2008-01-01
The topic of super-resolution image reconstruc-tion has recently received considerable attention among the research community. Super-resolution image reconstruc-tion methods attempt to create a single high-resolution image from a number of low-resolution images (or a video sequence). The method of projections onto convex sets (POCS) for super-resolution image reconstruction attracts many researchers' attention. In this paper, we propose an improvement to reduce the amount of Gibbs artifacts pre-senting on the edges of the high-resolution image recon-structed by the POCS method. The proposed method weights the blur PSF centered at an edge pixel with an exponential function, and consequently decreases the coef-ficients of the PSF in the direction orthogonal to the edge. Experiment results show that the modification reduces effectively the visibility of Gibbs artifacts on edges and improves obviously the quality of the reconstructed high-resolution image.
Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis
Andrzejewski, D M
2011-09-12
The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.
Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
Horowitz, Jordan M.; Esposito, Massimiliano
2016-08-01
We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is, environments described by the generalized or Gibbs canonical ensemble. We demonstrate that small systems weakly coupled to such reservoirs exchange both heat and work by verifying a local detailed balance relation for the induced stochastic dynamics. Based on this analysis, we help to rationalize the observation that nonthermal reservoirs can increase the efficiency of thermodynamic heat engines.
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.
Echeverria, Ignacia; Amzel, L Mario
2012-09-13
Equilibrium free-energy differences can be computed from nonequilibrium molecular dynamics (MD) simulations using Jarzynski's equality (Jarzynski, C. Phys. Rev. Lett.1997, 78, 2690) by combining a large set of independent trajectories (path ensemble). Here we present the multistep trajectory combination (MSTC) method to compute free-energy differences, which by combining trajectories significantly reduces the number of trajectories necessary to generate a representative path ensemble. This method generates well-sampled work distributions, even for large systems, by combining parts of a relatively small number of trajectories carried out in steps. To assess the efficiency of the MSTC method, we derived analytical expressions and used them to compute the bias and the variance of the free-energy estimates along with numerically calculated values. We show that the MSTC method significantly reduces both the bias and variance of the free-energy estimates compared to the estimates obtained using single-step trajectories. In addition, because in the MSTC method the process is divided into steps, it is feasible to compute the reverse transition. By combining the forward and reverse processes, the free-energy difference can be computed using the Crooks' fluctuation theorem (Crooks, G. E. J. Stat. Phys.1998, 90, 1481 and Crooks, G. E. Phys. Rev. E 2000, 61, 2361) or Bennett's acceptance ratio (Bennett, C. H. J. Comput. Phys. 1976, 22, 245), which further reduces the bias and variance of the estimates.
Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics.
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.
Prior Flaring as a Complement to Free Magnetic Energy for Forecasting Solar Eruptions
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.
Surface Free Energy and Dynamic Wettability of Differently Machined Poplar Woods
Zhiyong Qin
2014-04-01
Full Text Available The surface free energy and dynamic wettability of wood are important to the performance of its adhesive bonding strength. In this work, the surface free energy of poplar wood samples machined with different processes were calculated by the OWRK (geometric mean and vOCG (acid-base methods, and the dynamic wettability of adhesives on wood samples was studied using the S-D wetting model. The results indicate that the contact angles of reference liquids on rotary wood samples were greater than those on planed or sawn wood, and the rotary wood samples were more hydrophobic. The effect of surface roughness on contact angle was insignificant compared with surface structure morphology. The total surface free energy was almost the same for the planed and sawn wood, as calculated by the OWRK and vOCG methods, and the surface free energy of rotary wood samples was lower than that of planed or sawn wood samples. The initial and equilibrium contact angle increased as the viscosity of adhesive increased for all the wood samples, and the contact angles of rotary wood samples were greater than those of planed or sawn wood; however, the K-value was lower. The wettability of the loose side was higher than that of the tight side. Contact angles decreased when surface free energy increased, while the K-value increased.
Nonlinear reconstruction of single-molecule free-energy surfaces from univariate time series.
Wang, Jiang; Ferguson, Andrew L
2016-03-01
The stable conformations and dynamical fluctuations of polymers and macromolecules are governed by the underlying single-molecule free energy surface. By integrating ideas from dynamical systems theory with nonlinear manifold learning, we have recovered single-molecule free energy surfaces from univariate time series in a single coarse-grained system observable. Using Takens' Delay Embedding Theorem, we expand the univariate time series into a high dimensional space in which the dynamics are equivalent to those of the molecular motions in real space. We then apply the diffusion map nonlinear manifold learning algorithm to extract a low-dimensional representation of the free energy surface that is diffeomorphic to that computed from a complete knowledge of all system degrees of freedom. We validate our approach in molecular dynamics simulations of a C(24)H(50) n-alkane chain to demonstrate that the two-dimensional free energy surface extracted from the atomistic simulation trajectory is - subject to spatial and temporal symmetries - geometrically and topologically equivalent to that recovered from a knowledge of only the head-to-tail distance of the chain. Our approach lays the foundations to extract empirical single-molecule free energy surfaces directly from experimental measurements.
Linking Neuromodulated Spike-Timing Dependent Plasticity with the Free-Energy Principle.
Isomura, Takuya; Sakai, Koji; Kotani, Kiyoshi; Jimbo, Yasuhiko
2016-09-01
The free-energy principle is a candidate unified theory for learning and memory in the brain that predicts that neurons, synapses, and neuromodulators work in a manner that minimizes free energy. However, electrophysiological data elucidating the neural and synaptic bases for this theory are lacking. Here, we propose a novel theory bridging the information-theoretical principle with the biological phenomenon of spike-timing dependent plasticity (STDP) regulated by neuromodulators, which we term mSTDP. We propose that by integrating an mSTDP equation, we can obtain a form of Friston's free energy (an information-theoretical function). Then we analytically and numerically show that dopamine (DA) and noradrenaline (NA) influence the accuracy of a principal component analysis (PCA) performed using the mSTDP algorithm. From the perspective of free-energy minimization, these neuromodulatory changes alter the relative weighting or precision of accuracy and prior terms, which induces a switch from pattern completion to separation. These results are consistent with electrophysiological findings and validate the free-energy principle and mSTDP. Moreover, our scheme can potentially be applied in computational psychiatry to build models of the faulty neural networks that underlie the positive symptoms of schizophrenia, which involve abnormal DA levels, as well as models of the NA contribution to memory triage and posttraumatic stress disorder.
Molecular mechanism of polyacrylate helix sense switching across its free energy landscape.
Pietropaolo, Adriana; Nakano, Tamaki
2013-04-17
Helical polymers with switchable screw sense are versatile frameworks for chiral functional materials. In this work, we reconstructed the free energy landscape of helical poly(2,7-bis(4-tert-butylphenyl)fluoren-9-yl acrylate) [poly(BBPFA)], as its racemization is selectively driven by light without any rearrangement of chemical bonds. The chirality inversion was enforced by atomistic free energy simulations using chirality indices as reaction coordinates. The free energy landscape reproduced the experimental electronic circular dichroism spectra. We propose that the chirality inversion of poly(BBPFA) proceeds from a left-handed 31 helix via multistate free energy pathways to reach the right-handed 31 helix. The inversion is triggered by the rotation of biphenyl units with an activation barrier of 38 kcal/mol. To the best of our knowledge, this is the first report on the chiral inversion mechanism of a helical polymer determined in a quantitative way in the framework of atomistic free energy simulations.
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.
Temperature of critical clusters in nucleation theory: generalized Gibbs' approach.
Schmelzer, Jürn W P; Boltachev, Grey Sh; Abyzov, Alexander S
2013-07-21
According to the classical Gibbs' approach to the description of thermodynamically heterogeneous systems, the temperature of the critical clusters in nucleation is the same as the temperature of the ambient phase, i.e., with respect to temperature the conventional macroscopic equilibrium conditions are assumed to be fulfilled. In contrast, the generalized Gibbs' approach [J. W. P. Schmelzer, G. Sh. Boltachev, and V. G. Baidakov, J. Chem. Phys. 119, 6166 (2003); and ibid. 124, 194503 (2006)] predicts that critical clusters (having commonly spatial dimensions in the nanometer range) have, as a rule, a different temperature as compared with the ambient phase. The existence of a curved interface may lead, consequently, to an equilibrium coexistence of different phases with different temperatures similar to differences in pressure as expressed by the well-known Laplace equation. Employing the generalized Gibbs' approach, it is demonstrated that, for the case of formation of droplets in a one-component vapor, the temperature of the critical droplets can be shown to be higher as compared to the vapor. In this way, temperature differences between critically sized droplets and ambient vapor phase, observed in recent molecular dynamics simulations of argon condensation by Wedekind et al. [J. Chem. Phys. 127, 064501 (2007)], can be given a straightforward theoretical interpretation. It is shown as well that - employing the same model assumptions concerning bulk and interfacial properties of the system under consideration - the temperature of critical bubbles in boiling is lower as compared to the bulk liquid.
Mandal, Gautam
2013-01-01
Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unita...
How to reconcile Information theory and Gibbs-Herz entropy for inverted populated systems
Gagliardi, Alessio
2015-01-01
In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and restate the validity of information theory applied to equilibrium statistical mechanics. We show that under these assumptions, entropy is always a monotone function of energy, irrespective to the shape of the density of states, leading always to positive temperatures even in the case of inverted population systems. In the second part we assume the validity of the Shannon entropy and thermodynamic temperature, T=dE/dS, extended to systems under non-equilibrium steady state. Contrary to equilibrium, we discuss the possibility and meaning of a negative temperature in this case. Finally we discuss on Carnot cycles operating with a non-equilibrium bath possessing a negative temperature and leading to apparent efficiencies larger than one, due to a wrong accounting af all the energy...
Rosen, G.
1973-01-01
A survey is presented of free radicals and electronically excited metastable species as high energy propellants for rocket engines. Nascent or atomic forms of diatomic gases are considered free radicals as well as the highly reactive diatomic triatomic molecules that posess unpaired electrons. Manufacturing and storage problems are described, and a review of current experimental work related to the manufacture of atomic hydrogen propellants is presented.
Gibbs Ensemble Monte-Carlo方法及其应用%GIBBS ENSEMBLE MONTE-CARLO SIMULATION AND ITS APPLICATION
无
2000-01-01
It introduces a Gibbs Ensemble Monte-Carlo method,which was recently invented.This method has been applied for studying the phase diagrams of Lennard-Jones mixtures,and Methane and Tetrafluoromethane.The obtained results of simulations are in good agreement with experimental and previous results.%介绍一种新的且非常实用的Gibbs Ensemble Monte-Carlo模拟技术。并给出模拟甲烷和氟甲烷混合物的液体-液体相图以及Lennard-Jones混合物相图。将模拟的相图与实验得出的相图进行了对比。
Nonequilibrium study of the intrinsic free-energy profile across a liquid-vapour interface
Braga, Carlos, E-mail: ccorreia@imperial.ac.uk; Muscatello, Jordan, E-mail: jordan.muscatello@imperial.ac.uk; Lau, Gabriel, E-mail: gabriel.lau07@imperial.ac.uk; Müller, Erich A., E-mail: e.muller@imperial.ac.uk; Jackson, George, E-mail: g.jackson@imperial.ac.uk [Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW72AZ (United Kingdom)
2016-01-28
We calculate an atomistically detailed free-energy profile across a heterogeneous system using a nonequilibrium approach. The path-integral formulation of Crooks fluctuation theorem is used in conjunction with the intrinsic sampling method to calculate the free-energy profile for the liquid-vapour interface of the Lennard-Jones fluid. Free-energy barriers are found corresponding to the atomic layering in the liquid phase as well as a barrier associated with the presence of an adsorbed layer as revealed by the intrinsic density profile. Our findings are in agreement with profiles calculated using Widom’s potential distribution theorem applied to both the average and the intrinsic profiles as well as the literature values for the excess chemical potential.
Using nonlocal electrostatics for solvation free energy computations ions and small molecules
Hildebrandt, A; Blossey, R; Lenhof, H P
2002-01-01
Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii in a consistent way. We test our approach on simple ions and small molecules for which both experimental results and other theoretical descriptions are available for quantitative comparison. We conclude that our approach is both physically transparent and quantitatively reliable.
Sampling Free Energy Surfaces as Slices by Combining Umbrella Sampling and Metadynamics
Kapil, Venkat; Nair, Nisanth N
2015-01-01
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 propose a scheme, named Well--Sliced MTD (WS--MTD), where 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 metadynamics reweighting within the Weighted Histogram Analysis Method (WHAM). WS--MTD will be an ideal strategy f...
Procacci, Piero
2016-01-01
In this contribution I critically revise the alchemical reversible approach in the context of the statistical mechanics theory of non covalent bonding in drug receptor systems. I show that most of the pitfalls and entanglements for the binding free energies evaluation in computer simulations are rooted in the equilibrium assumption that is implicit in the reversible method. These critical issues can be resolved by using a non-equilibrium variant of the alchemical method in molecular dynamics simulations, relying on the production of many independent trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, completing the decoupling of the ligand in a matter of few tens of picoseconds rather than nanoseconds. The absolute binding free energy can be recovered from the annihilation work distributions by applying an unbiased unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of normal distributions, whose compone...
Free energy barrier for dissociation of the guanosine monophosphate anion in water
Cornetta, Lucas M.; Coutinho, Kaline; Canuto, Sylvio; Varella, Márcio T. do N.
2016-08-01
We report free energy barriers for the ground-state dissociation of the guanosine nucleotide anion in solution, employing implicit and explicit solvation models. The latter was based on the Free Energy Perturbation technique and Monte Carlo simulations. For the lowest-energy structure, both solvation models indicate a solvent-induced transition from a dipole-bound state in the gas phase to a π∗ valence state in solution. The free barrier estimates obtained from explicit and implicit solvation are in fair agreement with each other, although significantly overestimated in comparison to a previously reported explicit solvation model based on ab initio molecular dynamics simulations. Accounting for corrections related to the different DFT functionals used in the present and previous studies significantly improves the agreement. Contribution to the Topical Issue "Advances in Positron and Electron Scattering", edited by Paulo Limao-Vieira, Gustavo Garcia, E. Krishnakumar, James Sullivan, Hajime Tanuma and Zoran Petrovic.
Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
Assel, Benjamin; Yamazaki, Masahito
2012-01-01
We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works (arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for 3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the type IIB action on the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We also extend our results to richer theories and argue that 1/2 N^2 ln N is the maximal free energy at large N in this class of gauge theories.
Exploring the free energy gain of phase separation via Markov state modeling
Biedermann, Myra; Heuer, Andreas
2017-07-01
The gain of free energy upon unmixing is determined via application of Markov state modeling (MSM), using an Ising model with a fixed number of up- and down-spins. MSM yields reasonable estimates of the free energies. However, a closer look reveals significant differences that point to residual non-Markovian effects. These non-Markovian effects are rather unexpected since the typical criteria to study the quality of Markovianity indicate complete Markovian behavior. We identify the sparse connectivity between different Markov states as a likely reason for the observed bias. By studying a simple five state model system, we can analytically elucidate different sources of the bias and thus explain the different deviations that were observed for the Ising model. Based on this insight, we can modify the determination of the count matrix in the MSM approach. In this way, the estimation of the free energy is significantly improved.
Quenched Point-to-Point Free Energy for Random Walks in Random Potentials
Rassoul-Agha, Firas
2012-01-01
We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and some steps of the walk. The potential can be unbounded, but it is subject to a moment assumption whose strictness is tied to the mixing of the environment, the best case being the i.i.d. environment. We prove that the infinite volume quenched point-to-point free energy exists and has a variational formula in terms of an entropy. We establish regularity properties of the point-to-point free energy, as a function of the potential and as a function on the convex hull of the admissible steps of the walk, and link it to the infinite volume free energy and quenched large deviations of the endpoint of the walk. One corollary is a quenched large deviation principle for random walk in an ergodic random environment, with a continuous rate function.