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Y A Omarbakiyeva - One of the best experts on this subject based on the ideXlab platform.
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cluster Virial Expansion of the equation of state for hydrogen plasma with e h 2 contributions
Physical Review E, 2015Co-Authors: Y A Omarbakiyeva, H Reinholz, G RopkeAbstract:The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ interaction. Traditional semiempirical concepts such as the excluded volume are improved using microscopic approaches to treat the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ problem. Within a cluster Virial Expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature-dependent second Virial coefficient. The scattering states are calculated using the phase Expansion method for the polarization interaction that incorporates experimental data for the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, and the second Virial coefficient due to the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the ${\mathrm{H}}_{2}$ and the free-electron components are abundant.
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cluster Virial Expansion for the equation of state of partially ionized hydrogen plasma
Physical Review E, 2010Co-Authors: Y A Omarbakiyeva, C Fortmann, T S Ramazanov, G RopkeAbstract:We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-Virial Expansion. We use the Beth-Uhlenbeck approach to calculate the second Virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-Virial Expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the Virial Expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second Virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.
Joaquin E Drut - One of the best experts on this subject based on the ideXlab platform.
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finite temperature equation of state of polarized fermions at unitarity
Physical Review Letters, 2018Co-Authors: Lukas Rammelmuller, Joaquin E Drut, Andrew C Loheac, Jens BraunAbstract:We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order Virial Expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization.
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pressure compressibility and contact of the two dimensional attractive fermi gas
Physical Review Letters, 2015Co-Authors: E R Anderson, Joaquin E DrutAbstract:Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e., Tan's contact) for a wide range of temperatures (mostly above the superfluid phase, including the pseudogap regime) and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order Virial Expansion, with which they are in excellent agreement in the low-fugacity regime.
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thermal equation of state of polarized fermions in one dimension via complex chemical potentials
Physical Review A, 2015Co-Authors: Andrew C Loheac, Jens Braun, Joaquin E Drut, Dietrich RoscherAbstract:We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order Virial Expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.
Brian B Laird - One of the best experts on this subject based on the ideXlab platform.
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Erratum: "Surface free energy of a hard-sphere fluid at curved walls: Deviations from morphometric thermodynamics" [J. Chem. Phys. 149, 174706 (2018)].
2019Co-Authors: Ruslan L Davidchack, Brian B LairdAbstract:Original article: The Journal of Chemical Physics 149 (17), 174706 (2018) In the original published article,1 there is an error in Fig. 7. That is, the solid blue line showing the third Virial coefficient for the surface free energy of a hard-sphere fluid at a spherical wall is too large by a factor of π. The corrected figure is shown below. figure FIG. 7. The cubic curvature coefficient, γsph3, for the hard-sphere fluid at a spherical wall as a function of packing fraction η. The solid circles represent the results for the current simulations. The blue line shows the exact Virial Expansion up to third order in η [Eq. (23)]. The inset shows the same data at low packing fraction. PPT|High-resolution The corrected figure does not change the discussion or conclusions significantly. The only change is that the penultimate sentence of paragraph 7 of Sec. IV should read “As can be seen in Fig. 7, the simulation data are consistent with the Virial Expansion results, except for the region between η ≈ 0.08 and 0.1, where small deviations outside the statistical error bars appear.
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surface free energy of a hard sphere fluid at curved walls deviations from morphometric thermodynamics
Journal of Chemical Physics, 2018Co-Authors: Ruslan L Davidchack, Brian B LairdAbstract:We report molecular-dynamics (MD) simulation results for the surface free energy of a hard-sphere fluid at cylindrical and spherical hard walls of different radii. The precision of the results is much higher than that in our previous study [B. B. Laird et al., Phys. Rev. E 86, 060602 (2012)], allowing us to estimate the size of deviations from the predictions of Morphometric Thermodynamics (MT). We compare our results to the analytical expressions for the surface energy as a function of wall radius R and fluid density derived from the White Bear II variant of the density functional theory, as well as to the leading terms of the Virial Expansion. For the cylindrical wall, we observe deviations from MT proportional to R−2 and R−3, which are consistent with the available Virial expressions. For the spherical wall, while the precision is not sufficient to detect statistically significant deviations from MT, the MD results indicate the range of densities for which the truncated Virial Expansions are applicable.We report molecular-dynamics (MD) simulation results for the surface free energy of a hard-sphere fluid at cylindrical and spherical hard walls of different radii. The precision of the results is much higher than that in our previous study [B. B. Laird et al., Phys. Rev. E 86, 060602 (2012)], allowing us to estimate the size of deviations from the predictions of Morphometric Thermodynamics (MT). We compare our results to the analytical expressions for the surface energy as a function of wall radius R and fluid density derived from the White Bear II variant of the density functional theory, as well as to the leading terms of the Virial Expansion. For the cylindrical wall, we observe deviations from MT proportional to R−2 and R−3, which are consistent with the available Virial expressions. For the spherical wall, while the precision is not sufficient to detect statistically significant deviations from MT, the MD results indicate the range of densities for which the truncated Virial Expansions are applicable.
G Ropke - One of the best experts on this subject based on the ideXlab platform.
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cluster Virial Expansion of the equation of state for hydrogen plasma with e h 2 contributions
Physical Review E, 2015Co-Authors: Y A Omarbakiyeva, H Reinholz, G RopkeAbstract:The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ interaction. Traditional semiempirical concepts such as the excluded volume are improved using microscopic approaches to treat the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ problem. Within a cluster Virial Expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature-dependent second Virial coefficient. The scattering states are calculated using the phase Expansion method for the polarization interaction that incorporates experimental data for the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, and the second Virial coefficient due to the $e\text{\ensuremath{-}}{\mathrm{H}}_{2}$ interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the ${\mathrm{H}}_{2}$ and the free-electron components are abundant.
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cluster Virial Expansion for the equation of state of partially ionized hydrogen plasma
Physical Review E, 2010Co-Authors: Y A Omarbakiyeva, C Fortmann, T S Ramazanov, G RopkeAbstract:We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-Virial Expansion. We use the Beth-Uhlenbeck approach to calculate the second Virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-Virial Expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the Virial Expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second Virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.
Alexey O Ivanov - One of the best experts on this subject based on the ideXlab platform.
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free energy of dipolar hard spheres the Virial Expansion under the presence of an external magnetic field
Physica A-statistical Mechanics and Its Applications, 2014Co-Authors: Ekaterina A Elfimova, Tatyana E Karavaeva, Alexey O IvanovAbstract:Abstract A method for calculation of the free energy of dipolar hard spheres under the presence of an applied magnetic field is presented. The method is based on the Virial Expansion in terms of density as well as the dipolar coupling constant λ , and it uses diagram technique. The formulas and the diagrams, needed to calculate the second B 2 and third B 3 Virial coefficients, are derived up to the order of ∼ λ 3 , and compared to the zero-field case. The formula for B 2 is the same as in the zero-field case; the formula for B 3 , however, is different in an applied field, and a derivation is presented. This is a surprising result which is not emphasized in standard texts, but which has been noticed before in the Virial Expansion for flexible molecules (Caracciolo et al., 2006; Caracciolo et al., 2008). To verify the correctness of the obtained formulas, B 2 and B 3 were calculated within the accuracy of λ 2 , which were applied to initial magnetic susceptibility. The obtained expression fully coincides with the well-known theories (Morozov and Lebedev, 1990; Huke and Lucke, 2000; Ivanov and Kuznetsova, 2001), which used different methods to calculate the initial magnetic susceptibility.
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thermodynamics of ferrofluids in applied magnetic fields
Physical Review E, 2013Co-Authors: Ekaterina A Elfimova, Alexey O Ivanov, Philip J CampAbstract:Thethermodynamicpropertiesofferrofluidsinappliedmagneticfieldsareexaminedusingtheoryandcomputer simulation. The dipolar hard sphere model is used. The second and third Virial coefficients (B2 and B3 )a re evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B3 for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ 2. The analytical formulas for the Virial coefficients are incorporated in to various forms of Virial Expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the Virial Expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the Virial Expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.
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magnetophoresis sedimentation and diffusion of particles in concentrated magnetic fluids
Journal of Chemical Physics, 2011Co-Authors: A F Pshenichnikov, Ekaterina A Elfimova, Alexey O IvanovAbstract:A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a Virial Expansion with accuracy to the terms quadratic in particle concentration. The Virial Expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentra...
