Tilted Fluid Research Articles

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated 1+3 threading congruence, used jointly with the 3+1 foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.

Ultrasonic manipulation of particles in an open fluid film

Ultrasonic manipulation is a noncontact method of trapping and holding particles in suspension, and has found many applications in microfluidic systems. Typically, ultrasonic standing waves are used; this approach is well established in fully enclosed microfluidic systems consisting of channels or chambers with an attached piezoelectric actuator. In this work, we examine the use of ultrasonic manipulation in open fluid films, which offer a high degree of accessibility. A piezoelectric actuator is presented which can be lowered into a separate fluid tray. This two-part system offers a high degree of flexibility; indeed the actuator can be removed with little disturbance to the particle patterns, so manipulation could potentially be periodically applied as required. Particle manipulation is shown to be possible over a distance many times the size of the actuator. Furthermore, particle manipulation can also be achieved in a tilted fluid film, so alignment between the two parts of the system is not critical to its operation.

Instabilities of Bianchi type IX Einstein static universes

We investigate the stability of the Einstein static universe as a non-LRS Bianchi type IX solution of the Einstein equations in the presence of both non-tilted and tilted fluids. We find that the static universe is unstable to homogeneous perturbations of Bianchi type IX to the future and the past.

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.

KINEMATIC SELF-SIMILAR CYLINDRICALLY SYMMETRIC SOLUTIONS

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in the perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.

CHIRAL LIPID BILAYERS WITH CYLINDRICAL SYMMETRY

In this paper, we have studied the chiral lipid bilayers with the tilted fluid phase where the orientation of the molecular tilt varies as a function of the cylindrical coordinates. The rigorous solution of the equation related to the orientation of the long molecular axis is obtained, which describes the property of the tubules with a modulation in the tilt. When the angle of the molecular director is independent of the cylindrical coordinates θ, z, the patterns formed by chiral molecules can be degenerated to the right-handed helix, the left-handed helix, the straight lines, and the circles. The curvature and torsion of the corresponding curves are given explicitly, which denotes the winding of the molecules around the cylinder. We find also that the angle between the director of the molecule and the local normal direction of the cylinder increases if the radius of the cylinder reduces when the tilted angle ϕ from the equator of the cylinder is uniform.

Self-similar Bianchi models: II. Class B models

In a companion article (referred to hereafter as paper I) a detailed study of the simply transitive spatially homogeneous (SH) models of class A concerning the existence of a simply transitive similarity group has been given. The present work (paper II) continues and completes the above study by considering the remaining set of class B models. Following the procedure of paper I we find all SH models of class B subjected only to the minimal geometric assumption to admit a proper homothetic vector field (HVF). The physical implications of the obtained geometric results are studied by specializing our considerations to the case of vacuum and γ-law perfect fluid models. As a result, we regain all the known exact solutions regarding vacuum and non-tilted perfect fluid models. In the case of tilted fluids, we find the general self-similar solution for the exceptional type VI−1/9 model and we identify it as an equilibrium point in the corresponding dynamical state space. It is found that this new exact solution belongs to the subclass of models nαα = 0, is defined for , and although it has a five-dimensional stable manifold there always exist two unstable modes in the restricted state space. Furthermore, the analysis of the remaining types guarantees that tilted perfect fluid models of types III, IV, V and VIIh cannot admit a proper HVF, strongly suggesting that these models either may not be asymptotically self-similar (type V) or may be extreme tilted at late times. Finally, for each Bianchi type, we give the extreme tilted equilibrium points of their state space.

Bianchi cosmologies: a tale of two tilted fluids

We use a dynamical systems approach to study Bianchi type VI0 cosmological models containing two tilted γ-law perfect fluids. The full state space is 11-dimensional, but the existence of a monotonic function simplifies the analysis considerably. We restrict attention to a particular, physically interesting, invariant subspace and find all equilibrium points that are future stable in the full 11-dimensional state space; these are consequently local attractors and serve as late-time asymptotes for an open set of tilted type VI0 models containing two tilted fluids. We find that if one of the fluids has an equation of state parameter , the stiffest fluid will be dynamically insignificant at late times. For the value there is a two-dimensional bifurcation set and, if both fluids are stiffer than , both fluids will have extreme tilt asymptotically. We investigate in detail the case in which one fluid is extremely tilted. We also consider the case with one stiff fluid close to the initial singularity and find that the chaotic behaviour which occurs in general Bianchi models with is suppressed.

Vacuum plane waves in 4+1 D and exact solutions to Einstein's equations in 3+1 D

In this paper, we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalize the vacuum plane-wave solutions in 3+1 dimensions to the (4+1)-dimensional case. By doing a Kaluza–Klein reduction we obtain solutions to the Einstein–Maxwell equations in 3+1 dimensions. The solutions generalize the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain (3+1)-dimensional solutions to the Einstein equations with a scalar field.

Fluctuation Forces Stabilizing Two Kinds of Staircases in Chiral Tilted Fluid Smectics Frustrated between Ferro- and Antiferro-Electricity

Conventional dispersion and steric interactions between mesogenic molecules generally promote SmC*, while the interlayer orientational correlation between transverse molecular dipoles stabilizes anticlinic SmC A *. Ferroelectric and antiferroelectric orders thus produced are frustrated because of the X-Y freedom and the low-energy barrier between them. We can naturally explain not only a series of subphases between SmC A * and SmC* but also the staircase character of SmC f * emerging just below SmA by using the Casimir type long-range interaction due to polarization fluctuations, if we take account of the discrete flexoelectric polarization appropriately in addition to the ordinary one.

2A09 離散フレクソエレクトリック分極とカシミール力による2つの悪魔の階段(物理・物性)

2A09 離散フレクソエレクトリック分極とカシミール力による2つの悪魔の階段(物理・物性)

Isotropization of two-component fluids

We consider the problem of late-time isotropization in spatially homogeneous but anisotropic cosmological models when the source of the gravitational field consists of two noninteracting perfect fluids—one tilted and one nontilted. In particular, we study irrotational Bianchi type V models. By introducing appropriate dimensionless variables, a full global understanding of the state space of the gravitational field equations becomes possible. The issue of isotropization can then be addressed in a simple fashion. We also discuss implications for the cosmic “no-hair” theorem for Bianchi models when part of the source is a tilted fluid.

Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes

Lipid bilayer membranes below their main transition have two tilt order parameters, corresponding to the two monolayers. These two tilts may be strongly coupled to membrane shape but only weakly coupled to each other. We discuss some implications of this observation for rippled and saddle phases, bilayer tubules, and bicontinuous phases. Tilt difference introduces a length scale into the elastic theory of tilted fluid membranes. It can drive an instability of the flat phase; it also provides a simple mechanism for the spontaneous breaking of inversion symmetry seen in some recent experiments.

On the thermodynamics of tilted and collisionless gases in Friedmann-Robertson-Walker spacetimes

Some features of the thermodynamics of tilted fluids, as witnessed by observers comoving with the fluid, are analysed. The Gibbs equation, expressed in terms of quantities measured by preferred observers comoving with the metric, is obtained and the role played by the entropy production discussed. The results of Bedran and Calvão are analysed from the the point of view of kinetic theory. We focus our attention on a collisionless gases model proposed by Ellis et al and show that for the latter is a conformal Killing vector in accordance with Bedran and Calvão.

NATURAL CONVECTION HEAT TRANSFER IN INCLINED ENCLOSURES WITH MULTIPLE CONDUCTING SOLID PARTITIONS

ABSTRACT Laminar natural convection heat transfer is studied in a tilted fluid system consisting of multiple layers of fluid separated by solid partitions with finite thickness and conductivity. A closed form solution is derived in the limit of a thin-layered system subject to a uniform heat flux from the sides and adiabatic boundary conditions at two ends. Results are obtained in terms of overall Nusselt number Nu as a function of Rayleigh number Ra, angle of inclination of the system φ solid to fluid conductivity ratio K, thickness of the fluid layers Z,-, thickness of the solid partitions t;, and number of partitions Z ϑ. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with limiting cases of the problem and are in agreement. A numerical study of the same phenomenon is obtained by solving the complete system of governing equations using a finite difference formulation and a volume control method. Good agreement is found...

Theory of chiral lipid tubules.

We present a continuum theory for the self-assembly of cylindrical tubules from chiral lipid bilayers in any tilted fluid phase. This theory shows that tubule formation is driven by an intrinsic bending force due to molecular chirality, and gives the radius in terms of the continuum parameters. The radius diverges as an untilted phase is approached. The theory also predicts that the tilt direction is modulated in a helical striped pattern on the tubule. This striped pattern is consistent with helical patterns observed in electron micrographs of lipid tubules.

Geological-Engineering Evaluation: Castilla and Chichimene Fields, Cubarral Association Contract, Colombia

A multidisciplinary geological and engineering evaluation project was undertaken for fields within the Chevron Colombia operated Cubarral Association Contract. The goal of the project was to combine geological and engineering evaluations to form a strategy for maximizing the efficiency of ongoing field development, recompletion, and production procedures. The Association Contract is located in the Llanos basin about 100 km southeast of Bogota. The fields: Castilla, Chichimene NE and Chichimene SW contain approximately 2200, 100, and 65 MMBO in place, respectively. The Guadalupe sandstone produces 14-21[degrees] API oil. The geological evaluation consisted of three phases: (1) revision of the structural interpretations, (2) detailed stratigraphic analyses, and (3) delineation of tilted fluid contacts and determination of original-oil-in-place. Structural interpretations show that reservoir properties and continuity are strongly affected by depositional environment which varies between the fields. A major facies change between massive, braided-stream sandstones at Castilla and deltaic to shallow marine sandstones at Chichimene northeast is reflected in production characteristics. The fields show strongly tilted oil-water contacts due to regional hydrodynamic gradients. Geometrical and hydrodynamic calculations were used to delineate the direction and magnitude of the tilts to assess original oil-in-place.

Effect of the I*phase temperature range on the nature of the tilted fluid to hexatic transition

Abstract High precision layer spacing measurements have been carried out in the C* and I* phases of a number of compounds. The results suggest that the temperature range of the I* phase influences the nature of the tilted fluid to hexatic transition. For smaller ranges of I*, the C* phase evolves continuously to I*. The curves for the temperature variation of the layer spacing indicate that with increasing range of I* one may expect to observe a critical point followed by a line of first-order transitions. The presence of a second hexatic phase, viz., F* below I* also appears to play an important role in determining the nature of the C*-I* transition. A comparison between this scenario and a similar one proposed by Aharony et. al.,1 is also presented.

Tilted Fluid Contacts in Mid-Continent Region

Equations are given for tilted fluid contacts tilted by moving water, and for those tilted by moving oil with stationary water. The equations describe the relations between the angle of tilt, the horizontal gradients in head or pressure, the speed of flow, the permeability, and the viscosity. These equations may be used to analyze the field data to determine the cause of the tilts in given cases. Although some laboratory data suggest that capillary phenomena may produce tilted or irregular contacts, the field data suggest that the effect of variations in pore size is in most cases unimportant. However, in some fields, such as Wasson, West Texas, capillary relations may cause the tilts of the oil-water contacts. Some tilted contacts appear to be produced by structural tilt ng of level contacts which have been sealed or made immobile by chemical reactions that produce solids. Tilted fluid contacts produced by moving water are termed dynamic, and those produced by all other causes, including moving oil, static. East of a line from Corpus Christi to the middle of the north border of Kansas, the tilted fluid contacts appear to be of static origin. West of this line, some of the tilts in the Mid-Continent region may be static, some dynamic. The tilted fluid contacts most likely to be caused by moving water are in the Carrizo and Wilcox sandstones of South Texas.

Some Theoretical Considerations of Tilted Water Tables

Abstract An analysis has been made of the factors responsible for tilted fluidcontacts in petroleum reservoirs. The factors are static and dynamic with theformer being controlled by those variables responsible for the capillary riseof fluids, and the latter include rate of formation tilt and hydrauliccirculation. The explanation that rate of formation tilt may be responsible fortilted contacts appears untenable. The role of some of these factors in themigration, fractionation, accumulation, and possibly the prospecting for oil isindicated. Introduction While it is generally considered that the segregation of gas, oil, and waterin a petroleum reservoir results in approximately horizontal planes separatingthese phases, there are factors which modify this simplified picture to a verygreat extent. Some of these factors are static, and the departure of the fluidinterfaces from horizontal may represent a static equilibrium. Some of thesefactors may be dynamic and the interface positions may be non-equilibrium andrepresent a steady state condition. Of course combinations of these twosituations may also exist. The reasons most commonly given for this behaviorare hydraulic circulation of fluids, change in character of the formation, anda rate of tilt of the formations more rapid than the rate at which the fluidsmay re-establish an equilibrium. Russell's Principles of Petroleum Geologycontains an extensive discussion of tilted fluid interfaces and theirimportance in the migration and accumulation of petroleum. Russell citesexamples of tilted water tables at Lance Creek, Wyo.; Rock River, Wyo.; CutBank, Mont.; Cushing, Okla.; and Graham, Okla. Also given was the Wasson Fieldof West Texas which has saucer shaped oil-water and gas-oil interfaces with thesaucer being deeper in the case of the oil-water contact. The Bradford Field inPennsylvania has a tilted water table. San Ardo, Coalinga Nose and some otherCalifornia fields have tilted contacts. A recent paper by King Hubbertdiscusses the effect of hydraulic circulation of the water underlying the oilin a given stratum and its implications in the accumulation of and drilling forthe oil. The foregoing would indicate that tilted fluid interfaces are not uncommonand that it would be of importance to understand the forces which areresponsible. Further, it would be of interest to examine certain idealizedmodels of situations which may cause tilting with the thought in mind ofderiving relationships between the important variables. These relationships mayonly hold exactly for the models assumed but the results may applysemi-quantitatively to actual formations and at least indicate trends. Thediscussion will be divided into the effect of static factors and the effect ofdynamic factors. T.P. 3564