Simulation of Fluid Phase Equilibria in Square-Well Fluids: From Three to Two Dimensions

2008 ◽  
Vol 73 (4) ◽  
pp. 518-532 ◽  
Author(s):  
Horst L. Vörtler
Keyword(s):  
Critical Temperature ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Critical Density ◽  
Fluid Phase ◽  
Two Dimensions ◽  
Slit Width ◽  
Virtual Particle ◽  
Square Well ◽  
Coexistence Densities

We study the influence of geometric restrictions on vapour/liquid coexistence properties and critical data of square-well fluids. Starting with three-dimensional bulk systems, we model the confinement by slit-like pores with decreasing slit widths arriving finally at planar (two-dimensional) fluid layers. For both bulk and confined fluids, we use a uniform approach performing series of canonical ensemble Monte Carlo simulations with Widom-like (virtual) particle insertions to estimate chemical potential versus density isotherms. By estimating the corresponding vapour/liquid coexistence densities using a Maxwell-like equal area rule for the subcritical chemical potential isotherms, we are able to study the influence of the confinement not only on chemical potentials but also on the coexistence properties. Critical point data are calculated from the coexistence densities by means of scaling relations. In particular, we study the change of the critical temperature and critical density varying the slit width and including the two- and three-dimensional bulk fluids as limiting cases. While the difference between the bulk and the slit critical temperature is found to decay exponentially with an exponent reciprocal to a linear function in the slit width, no comparable simple relation describing the influence of the confinement on the critical density is found.

scholarly journals Influence of diffusion and viscosity on the field asymmetry of the effect of gravity in the critical fluid

2021 ◽  
pp. 8-16
Author(s):  
A.D. Alekhin
Keyword(s):  
Critical Temperature ◽  
Light Intensity ◽  
Density Gradient ◽  
Critical Field ◽  
Chemical Potential ◽  
Scattered Light ◽  
Critical Density ◽  
Scattered Light Intensity ◽  
Gravity Effect ◽  
Critical Temperature Tc

A brief review of the results of studies of the effect of gravity in inhomogeneous substance near a critical state of a critical fluid (CF) has been presented in paper, based on the data of light scattering, refractometry, and slow neutron transmission methods.Based on these data, the field-altitude asymmetry of various properties of an inhomogeneous substance has been analyzed, namely order parameter Dr(z), scattered light intensity I(z), density gradient dr(z)/dz of the substance. It had been shown that the field-altitude asymmetries of the scattered light intensity I(z)~dr/dm(h) and the density gradient dr(z)/dz~dr/dh(h) of the substance are diametrically opposite. The different altitudinal asymmetry of these quantities dr/dh(h) and dr/dm(h) is explained in paper by the altitude asymmetry of the derivative of the chemical potential dm/dh, and hence with the altitude asymmetry of the chemical potential Dm(h)>>h in the external field h.To the present time, the physical mechanism of the altitude asymmetry of the gravity effect has not been studied. In this regard the mechanism of the formation of the vertical asymmetry of the internal critical field Dm(h) has proposed in paper to be associated with the kinetic characteristics of the inhomogeneous critical fluid: the diffusion coefficients D (h) and viscosity coefficients h(h), when the system passes from a homogeneous state to an inhomogeneous one under the action of an internal asymmetric fields |DU(z)|= |Dm(z)|>>|h=rcgz/Pc|. For this purpose, a high-pressure cell with a height L, with a critical filling density of the substance is considered in paper.It has been shown that when the system is under critical density filling by substance =rc  the critical level of substance z = 0 with the critical density rc  at the critical temperature Tc is realized above the middle of the sample with an inhomogeneous substance. Based on the literature data of P-V-T-measurements and the gravity effect in benzene and ethane, the values of the altitudinal change in the internal critical field have been found. It has been shown that the value of the critical internal inhomogeneous field in the inhomogeneous critical fluid significantly exceeds the variable of the Earth's gravity |DU(h,Tc)|= |Dm(h,Tc)>>|h|  It has been also shown that the magnitude of this field according to the cubic law depends on the critical temperature Tc of the substance: |Dm(z,Tc1)/|Dm(z,Tc2) » (Tc1/Tc2)3.

Investigation in the Vicinity of the Critical Point

1988 ◽  
Vol 43 (8-9) ◽  
pp. 734-740
Author(s):  
I. R. Yukhnovskii
Keyword(s):  
Critical Temperature ◽  
Partition Function ◽  
Critical Point ◽  
Explicit Form ◽  
Reference System ◽  
Chemical Potential ◽  
Critical Density ◽  
Collective Variables ◽  
Potential Surfaces

Abstract It is shown that the events occuring in the vicinity of the critical point can be described in full by means of the collective variables with the appropriate reference system. The partition function containing the explicit form for the quartic measure density is obtained and integrated. Expressions for the critical temperature, critical density and critical chemical potential surfaces are calculated.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

Critical constants and density dependence of the Lorenz–Lorentz coefficient for germane

1978 ◽  
Vol 56 (9) ◽  
pp. 1140-1141 ◽  
Author(s):  
P. Palffy-Muhoray ◽  
D. Balzarini
Keyword(s):  
Critical Temperature ◽  
Density Dependence ◽  
Experimental Error ◽  
Critical Density ◽  
Coexistence Curve ◽  
Index Of Refraction ◽  
Density Range ◽  
Temperature Range ◽  
Critical Constants

The index of refraction at 6328 Å has been measured for germane in the density range 0.15 to 0.9 g/cm3. The temperature and density ranges over which measurements are made are near the coexistence curve. The coefficient in the Lorenz–Lorentz expression, [Formula: see text], is constant to within 0.5% within experimental error for the temperature range and density range studied. The coefficient is slightly higher near the critical density. The critical density is measured to be 0.503 g/cm3. The critical temperature is measured to be 38.92 °C.

scholarly journals Three-dimensional quantification of twisting in the Arabidopsis petiole

2021 ◽  
Author(s):  
Yuta Otsuka ◽  
Hirokazu Tsukaya
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Light Sheet ◽  
Underlying Mechanism ◽  
Two Dimensions ◽  
Observation Angle ◽  
Differential Growth ◽  
Light Sheet Microscopy ◽  
Definition Of ◽  
Twisting Angle

AbstractOrganisms have a variety of three-dimensional (3D) structures that change over time. These changes include twisting, which is 3D deformation that cannot happen in two dimensions. Twisting is linked to important adaptive functions of organs, such as adjusting the orientation of leaves and flowers in plants to align with environmental stimuli (e.g. light, gravity). Despite its importance, the underlying mechanism for twisting remains to be determined, partly because there is no rigorous method for quantifying the twisting of plant organs. Conventional studies have relied on approximate measurements of the twisting angle in 2D, with arbitrary choices of observation angle. Here, we present the first rigorous quantification of the 3D twisting angles of Arabidopsis petioles based on light sheet microscopy. Mathematical separation of bending and twisting with strict definition of petiole cross-sections were implemented; differences in the spatial distribution of bending and twisting were detected via the quantification of angles along the petiole. Based on the measured values, we discuss that minute degrees of differential growth can result in pronounced twisting in petioles.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

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