Three-dimensional Partition Research Articles

A quasi-three-dimensional distributed parameter model of micro-channel separated heat pipe applied for cooling telecommunication cabinets

Micro-channel separated heat pipes (micro-channel SHPs), which may cycle without inputting additional electrical power, have shown their advantages of energy saving and compact structure, and they are preferred in the cooling of electronic equipment with narrow inner space. The non-uniformly distributed refrigerant flow among multiple flat tubes and air flow among multiple fins of micro-channel heat exchangers may have a significant effect on the performance of SHPs. In this study, a quasi-three-dimensional distributed parameter model of micro-channel SHPs is proposed for predicting the effects of non-uniformly distributed refrigerant and air flows on the performance. The model is developed by modeling all the components of a micro-channel SHP, i.e. an evaporator, an ascending tube, a condenser and a descending tube, respectively. In the model, the refrigerant flow is described as uneven flow among tubes and the flow direction is fixed inside each tube; the air flow is modelled as the flow with two-dimensional uneven distribution at the windward of heat exchanger and with the fixed direction across the heat exchanger; the three-dimensional partition method is applied to the control volume partition of flat tubes and fins. The proposed model is validated by experiments, and the results show that the deviations between simulated and experimental data of the heat transfer capacity, the temperature difference of micro-channel SHP, the outlet air temperature of evaporator and the outlet air temperature of condenser are 4.6%, 0.9 °C, 1.1 °C and 0.4 °C, respectively.

Holographic microstate counting for AdS4 black holes in massive IIA supergravity

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS4 × S6 from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional mathcal{N}=2 Chern-Simons-matter gauge theories in the large N limit. The I-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic mathcal{N}=2 gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on S6. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.

Predicting crystal growth via a unified kinetic three-dimensional partition model.

Understanding and predicting crystal growth is fundamental to the control of functionality in modern materials. Despite investigations for more than one hundred years, it is only recently that the molecular intricacies of these processes have been revealed by scanning probe microscopy. To organize and understand this large amount of new information, new rules for crystal growth need to be developed and tested. However, because of the complexity and variety of different crystal systems, attempts to understand crystal growth in detail have so far relied on developing models that are usually applicable to only one system. Such models cannot be used to achieve the wide scope of understanding that is required to create a unified model across crystal types and crystal structures. Here we describe a general approach to understanding and, in theory, predicting the growth of a wide range of crystal types, including the incorporation of defect structures, by simultaneous molecular-scale simulation of crystal habit and surface topology using a unified kinetic three-dimensional partition model. This entails dividing the structure into 'natural tiles' or Voronoi polyhedra that are metastable and, consequently, temporally persistent. As such, these units are then suitable for re-construction of the crystal via a Monte Carlo algorithm. We demonstrate our approach by predicting the crystal growth of a diverse set of crystal types, including zeolites, metal-organic frameworks, calcite, urea and l-cystine.

A new pentagon identity for the tetrahedron index

Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N=2 supersymmetric theories and give a mathematical proof of it.

BPS states and their reductions

Abstract We develop a method to identify the BPS states in the Hilbert space of a supersymmetric field theory on a generic curved space which preserves at least two real supercharges. We also propose a one-to-one map between BPS states in d-dimensional field theories and states that contribute to the supersymmetric partition function of a corresponding (d − 1)-dimensional field theory. As an application we obtain the superconformal index on rounded and squashed three spheres, and we show a natural reduction of the respective indices to the three-dimensional exact partition functions. We discuss the validity of the correspondence both at the perturbative and at the non-perturbative level and exploit the idea to uplift the computation of the exact supersymmetric partition function on a general manifold to a higher dimensional index.

Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods

A known problem of partition of unity-based generalized finite element methods is the linear dependence of the approximation space, which leads to singular stiffness matrix. Up to now, the linear dependence problem has not been fully understood and an efficient way to alleviate it is not available. In our previous paper “Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes” [Comput. Methods Appl. Mech. Engrg. 200 (2011) 665–674], the origin of the linear dependence problem was first dissected and then a method was proposed to reliably predict the rank deficiency of the linearly dependent global approximations of two-dimensional partition of unity-based generalized finite element methods. This paper extends the previous work to three-dimensional cases. The linear dependence problem is first investigated at an element level and then extended to the whole mesh. Derivation of general formulations in a three-dimensional setting is undoubtedly more challenging than a two-dimensional setting because of the complicated element topology. The principle of the increase of rank deficiency is once more applied. The methodology of summing up the added rank deficiency of each element as that of the whole mesh is further proved to be valid in three-dimensional cases. This work together with the previous work is regarded as the essential step to successfully and completely solve the linear dependence problem in partition of unity-based finite element methods.

Practical solvent system selection for counter-current separation of pharmaceutical compounds

Counter-current chromatography (CCC) is a technique that shows a lot of potential for large scale purification. Its usefulness in a “research and development” pharmaceutical environment has been investigated, and the conclusions are shown in this article. The use of CCC requires the development of an appropriate solvent system (a parameter of critical importance), a process which can be tedious. This article presents a novel strategy, combining a statistical approach and fast HPLC to generate a three-dimensional partition coefficient map and rapidly predict an optimal solvent system. This screen is performed in half a day and involves 9 experiments per solvent mixture. Test separations were performed using that screen to ensure the validity of the method.

The three-dimensional assignment and partition problems. New lower bounds

For the three-dimensional assignment problem, new sharp lower bounds are derived from its relationship with the partition problem. The new sharp lower bounds derived for the partition problem from optimal control theory are of great value not only for the three-dimensional assignment problem, but also for the partition problem itself.

Three-Dimensional Partition and Registration of Subsurface Land Space

AbstractTraditional legal doctrine pictures land ownership in the form of a cone down to the center of the earth. This article suggests that it is desirable for the law to enable subsurface subdivision into separate, three-dimensional property units, constituting separate subjects for title and transactions. Thus the law would contribute to the public interest in recognizing the subsurface space as a separate property unit from both the functional and the planning aspects.Before three-dimensional registration can begin, it is necessary to create an infrastructure of professional standards for three-dimensional survey for registration purposes. The creation of such standards constitutes one of the main goals of the world survey profession.It may be assumed that there is a downward limit below which the subsurface has no effect on the surface space and vice versa. In this case, the traditional doctrine may be seriously contested by the argument that those deep levels of the earth should be defined as a collective property. However, it is not practical to establish a fixed downward limit upon ownership of subsurface space. When expropriating the subsurface, it is necessary to compensate the landowner for the consequential damage, as well as for the direct damage incurred. There is some doubt whether compensation should be paid for subsurface area that the landowner could not reasonably and practically exploit. As soon as the axiomatic impediment to three-dimensional subdivision is removed, the importance of long-term planning for subsurface use will increase.

Massively parallel finite volume computation of three-dimensional thermal convective flows

A parallel implementation of the finite volume method for three-dimensional, time-dependent, thermal convective flows is presented. The algebraic equations resulting from the finite volume discretization are solved by a parallel multigrid method. A flexible parallel code has been implemented on distributed-memory systems, by using domain decomposition techniques and the MPI communication software. The code uses one-, two- or three-dimensional partition according to different geometries. It currently runs on the Intel Paragon, the Cray T3D, T3E, the IBM SP2 and the Beowulf systems, which can be ported easily to other parallel systems. A comparison of the wallclock time of the code between these systems is made, and code performances with respect to different numbers of processors are presented.

Applicability of Aboav's rule to a three-dimensional Voronoi partition

Abstract Data on mF , the average number of faces in cells adjacent to cells with F faces, obtained by Kumar, Kurtz, Banavas and Sharma in 1992 for a three-dimensional (3D) Poisson-Voronoi partition can be fitted to a linear relation with 1/F. This suggests that Aboav's rule, valid for two-dimensional networks, is likely to be also of general applicability to 3D random tetravalent networks, for example polycrystals and soap froths.

Three-dimensional analysis of scattered P waves on the basis of the PP single isotropic scattering model.

Wave trains immediately following the initial motion of P waves are analyzed assuming that they are scattered P waves by heterogeneities in the earth medium. Three-dimensional partition of the energy density of scattered P waves is theoretically studied, where PP single isotropic scattering and homogeneous and random distribution of scatterers are assumed. The theoretical analysis shows that the three-dimensional mean trajectory for scattered P waves in velocity space is represented by a spheroid, which is prolate to the propagation direction of the direct P wave, and the spheroid tends to become spherical as time goes on. This model is applied to an analysis of short-period (1-30Hz) records of small local earthquakes observed by a three-component velocity seismometer installed at the bottom of a deep borehole. The three-dimensional partition of energy density is calculated by using the covariance tensor for particle velocity observed. The observed horizontal component of energy density of scattered P waves agrees well with the theoretical one, although the observed vertical component is larger than and the observed radial component is smaller than the theoretical one. Our theoretical model is proved to be good in accounting for horizontal component. In order to explain changes in vertical plane, it is suggested that refraction and reflection at horizontal lateral boundaries and the earth's surface, and/or PS conversion scattering should be considered.