Escape rate spectra for hyperbolic $\mathbb {Z}$ -covers of Schottky surfaces

Investigation of the influence of heat source orientation on the transient flow behavior during PCM melting using particle image velocimetry

Effects of rolling motion on transient flow behaviors of gas-liquid two-phase flow in horizontal pipes

This research is aimed to study the transient behavior of air flow through the intake manifold of a heavy duty diesel engine according to the step of valve opening. The numerical study of air flow through the intake manifold was done on the 6SD-1 Isuzu engine. Two numerical techniques, finite element and finite volume methods were used in comparison and tendency confirmation of air flow characteristics inside the manifold. The transient air flow was studied at the engine speed of 1,000 rpm, 1,500 and 2,000 rpm. The numerical results from both numerical techniques agree exceptionally well with each other. The transient behavior of air flow according to the step of valve opening is well illustrated.

Modeling transient flow behavior with the high velocity non-Darcy effect in composite naturally fractured-homogeneous gas reservoirs

The present study reports the characterization of the transient flow behavior in the liquid PCM domain during the melting process, initiated by a planer heat source. Experiments were conducted at three angles of inclination of the heat source (0, 8 and 18-degrees) from the vertical. Paraffin wax was used as the PCM and was enclosed in an insulated, optically clear, thin rectangular chamber. Particle image velocimetry (PIV) was used during the melting process to measure the instantaneous velocity of the PCM and obtain two-dimensional velocity fields within the liquid domain. Results clearly show the presence of a dominant recirculation zone occurring at all angles. This recirculation zone was enhanced by an increase in the inclination of the heat source, supporting a direct correlation between the tilt angle and the bulk fluid flow in the melted region. The melting rate decreased with the progression of time for all investigated cases. A growing region of stagnant fluid flow within the center of the recirculation zone contributed to the reduction in the melt rate. The size of this stagnant region decreased with increases in the tilt angle due to the enhancement of natural convection. The data demonstrates significant changes in transient flow behavior with orientation in the liquid PCM domain. These results further our understanding of the phase change and associated heat transfer processes in PCM and have wide applicability to PCM-based thermal energy storage.

Zero boil-off (ZBO) storage technology that integrates passive insulation with active refrigeration, serves as the fundamental technical basis for the long-term and stable storage of cryogenic liquids. To explore the transient thermodynamic behavior of the gas-liquid flow within the storage tank and research the optimal coupling forms between the refrigerator and the tank during ZBO storage process, a ZBO experimental setup was constructed. Initially, the mechanisms of thermal stratification and the tank pressurization during the self-pressurization phase were investigated. Subsequently, a comparative analysis was carried out regarding the power consumption of the refrigerator and the internal transient thermodynamic behavior under various coupling forms between the refrigerator and the tank. The results indicated that the refrigerator power consumption under cooling liquid form was decreased by 29.4% in comparison to that under the recondensing gas form. Moreover, the cooling liquid form significantly enhanced the convection of the fluids, effectively alleviating the thermal stratification phenomenon. Furthermore, the effects of storage pressure and initial filling rate on the refrigerator power consumption and the internal thermodynamic behavior were analyzed. The setup provides valuable insights for the development of a measuring device that couples multiple parameters of temperature and pressure.

The transient behavior of oil flow under negative pressure is studied experimentally. To observe the negative pressure, three types of pipe models with different boundary conditions are used. The pipe used in experiment is 20 m in length, and 8 mm or 12 mm in diameter. Quick operation of a valve mounted at the end of pipe causes fluid transients. The negative pressure is measured mainly using strain gauges set on the outer surface of the pipe. By applying the principle of pressure difference meter, the relation between strain and negative pressure was tested equivalently. The negative pressure below absolute zero was observed experimentally. The numerical computation by means of characteristics method showed a good agreement with the experimental results. The condition of inner surface of the pipe has a great influence on the transient behavior under negative pressure.

The transient behavior of oil flow under negative pressure is studied experimentally. To observe negative pressure, three types of oil flow models are used. The pipe is 20 m in length, and 8 mm or 12 mm in diameter. The boundary conditions of three types are different from each other. Quick oparation of a valve mounted at the end of pipe causes a fluid transient. Negative pressure is measured using strain gauges on the outer surface of the pipe. By applying the principle of pressure difference meter, the relation between strain and negative pressure was tested equivalently. Negative absolute pressure was observed experimentally. The numerical calculation by means of characteristics method showed a good agreement with the experimental results. The condition of inner surface of the pipe has a great influence on the transient behavior under negative pressure.

Transient two-phase flow behavior in pipelines-experiment and modeling

We describe all connected components of the space of hyperbolic Gorenstein\nquasi-homogeneous surface singularities. We prove that any connected component\nis homeomorphic to a quotient of R^d by a discrete group.\n

The real :1-dimensional Euclidean space JR3 is given a sense of reality by being considered as a model of the physical world and most of its elementary properties are well known. Mathematically, the hyperbolic space, which is one type of non-Euclidean geometry, has the same right to claim its own existence as the Euclidean space, but few of its properties have been established as common knowledge. In the present volume, we give a glimpse into the charms of hyperbolic manifolds, which are generalizations of the hyperbolic space in the sense that they can be regarded as the hyperbolic space in a “neighborhood” of any point on it.

In [ECHLPT] and [S] it is shown that if the fundamental group of a Seifert fibred 3manifold is not virtually nilpotent then it has an automatic structure. In the unpublished 1992 preprint [G2] Gersten constructs a biautomatic structure on the fundamental group of any circle bundle over a hyperbolic surface. He asks if the same can be done for the above Seifert fibered 3-manifold. We show the existence of such a biautomatic structure. We do this in the context of a general discussion of biautomatic structures on virtually central extensions of finitely generated groups. A virtually central extension is an extension of a group by an abelian group for which the induced action of on is finite, that is, given by a map with finite image. The fundamental group of a Seifert fibered 3-manifold as above is a virtually central extension of a Fuchsian group by . (For convenience we are using the term “Fuchsian group” for any discrete finitely generated subgroup of — orientable or not.) We use a concept of “regular 2-cocycles” on a group which was suggested by Gersten’s work. Here “regularity” is with respect to a (poss ibly asynchronously) automatic structure on . If is a biautomatic structure on we show that any virtually central extension of defined by an -regular cocycle also has a biautomatic structure. As an application we show that any virtually central extension of a Fuchsian group by a finitely generated abelian group is biautomatic. In fact, if is a geodesic language on , we show that all of is represented by -regular cocycles . In case is torsion free and with trivial -action this is implicit in Gersten’s work (loc. cit. — we give an independent treatment here that is mor e geometric; alternatively, it follows from his result about biautomaticity plus Theorem A below). The general case follows easily from this using Corollary 2.7 below, which says that a cohomology class for a group is regular if its restriction to some finite index subgroup of is regular. The converse to the fact that regular cocycles lead to biautomatic structures is also true. Theorem A. Let be a virtually central extension of the group by a finitely generated abelian group . Then carries a biautomatic structure if and only if has a biautomatic structure for which the cohomology class of the extension is represent ed by an -regular cocycle.

We apply a study of orders in quaternion algebras, to the differential geometry of Riemann surfaces. The least length of a closed geodesic on a hyperbolic surface is called its systole, and denoted sysπ 1 . P. Buser and P. Sarnak constructed Riemann surfaces X whose systole behaves logarithmically in the genus g(X). The Fuchsian groups in their examples are principal congruence subgroups of a fixed arithmetic group with rational trace field. We generalize their construction to principal congruence subgroups of arbitrary arithmetic surfaces. The key tool is a new trace estimate valid for an arbitrary ideal in a quaternion algebra. We obtain a particularly sharp bound for a principal congruence tower of Hurwitz surfaces (PCH), namely the 4/3bound sysπ1(XPCH) ≥ 4 log(g(XPCH)). Similar results are obtained for the systole of hyperbolic 3-manifolds, relative to their simplicial volume.

The present study focuses the effects of Reynolds number Re and magnetic Reynolds number Rm on the transient behavior of the MHD flow. The incompressible, electrically conducting and viscous fluid flows through a long pipe subjected to magnetic field B0(t)=B0f(t). B0 is the intensity and f(t) is the time varying function of the magnetic field which is chosen as polynomial, trigonometric, exponential and logarithmic function to illustrate the problem parameters effects. The Re and Rm effects on the behavior of the flow at transient levels are studied with these functions by taking Hartmann number Ha value as 20. The unsteady MHD equations in coupled form are treated by using the dual reciprocity boundary element method (DRBEM). The study reveals that, when Re or Rm increases the time level where the flow elongates is postponed to a further time level. Moreover, the increase in Re flattens the flow as in the increase of Hartmann number. However, the increase in Rm increases the flow magnitude. The transient flow and induced current contours are demonstrated for several Re and Rm values. After the flow elongates, the flow and induced current lines preserve the behavior for polynomial, exponential and logarithmic type f(t) while trigonometric type f(t) causes the flow to show periodic behavior.

Rheological properties of heavy & light crude oil mixtures for improving flowability