Manifold Research Articles

The joint probability density function of mixture fraction, reaction progress variable, and total enthalpy in a stratified, swirl-stabilized turbulent flame

The three-condition version of the uniform conditional state combustion model makes use of the mixture fraction, progress variable, and normalized total enthalpy as conditioning variables to build a three-dimensional conditional manifold for chemistry. In order to map the solution in conditional space into the flow domain, the joint Probability Density Function (PDF) of the conditioning variables needs to be modeled. In simulations, presumed functions (i.e., β-PDF for the mixture fraction and progress variable and δ-PDF for total enthalpy) are often used for modeling the marginal PDFs. In this work, the measurements from the Cambridge/Sandia burner are employed to obtain the marginal PDFs for the conditioning variables at various points in the reacting domain. The measurements are then combined from all positions in space to form conditional PDFs of the normalized total enthalpy for various values of the other two variables. In the vicinity of the flame brush, the marginal PDF of the normalized total enthalpy resembles a bimodal Gaussian distribution; nonetheless, the conditional PDFs for this variable are nearly Gaussian distributions. The correlation coefficients between the conditioning variables are also investigated, and the assumption of their statistical independence is examined. To consider the association between the conditioning variables for modeling, the copula concept is introduced, and the performances of three different copulas are tested. Furthermore, the statistical moments of the conditioning variables are computed from the experimental data at different points and are utilized for modeling the joint PDF of the conditioning variables from two different approaches that are compared.

Factorization of Dirac Operators on Almost-Regular Fibrations of Spinc Manifolds

Factorization of Dirac Operators on Almost-Regular Fibrations of Spinc Manifolds

Action and perception manifolds have gradients that may play a role in learning: Comment on "Laws of nature that define biological action and perception" By M. Latash.

Action and perception manifolds have gradients that may play a role in learning: Comment on "Laws of nature that define biological action and perception" By M. Latash.

Contact geometry in superconductors and New Massive Gravity

The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.

New examples of stably ergodic diffeomorphisms in dimension 3

We prove that in the isotopy class of any volume preserving partially hyperbolic diffeomorphism in a three-dimensional manifold, there is a non-partially hyperbolic stably ergodic diffeomorphism. In particular, we provide new examples of stably ergodic diffeomorphisms in three-dimensional manifolds with respect to a smooth volume measure.

Covariant Derivative of the Curvature Tensor of Kenmotsu Manifolds

In this paper, we define a (1, 3)-tensor field T(X, Y)Z on Kenmotsu manifolds and give a necessary and sufficient condition for T to be a curvature-like tensor. Next, we present some properties related to the curvature-like tensor T and prove that $$M^{2m+1}$$ is an $$\eta $$ -Einstein–Kenmotsu manifold if and only if $$\sum ^{m}_{j=1}T( \varphi (e_j), e_j) X = 0$$ . Besides, we define a (1, 4)-tensor field t on the Kenmotsu manifold M which determines when M is a Chaki T-pseudo-symmetric manifold. Then, we obtain a formula for the covariant derivative of the curvature tensor of Kenmotsu manifold M. We also find some conditions under which an $$\eta $$ -Einstein–Kenmotsu manifold is a Chaki T-pseudo-symmetric. Finally, we give an example to verify our results and prove that every three-dimensional Kenmotsu manifold is a generalized pseudo-symmetric manifold.

On a class of generalized recurrent $(k,\mu)$-contact metric manifolds

On a class of generalized recurrent $(k,\mu)$-contact metric manifolds

О тензоре кручения аффинной связности на двумерном и трехмерном многообразиях

The basis for this study of affine connections in linear frame bundle over a smooth manifold is the structure equations of the bundle. An affine connection is given in this bundle by the Laptev — Lumiste method. The differential equations are written for components of the deformation ten­sor from an affine connection to the symmetrical canonical one. The ex­pressions for the components of the torsion tensor for two-dimensional and three-dimensional manifolds were found. For a two-dimensional manifold, the affine torsion is a fraction, in the numerator there is a linear combination of two fiber coordinates which coefficients are two functions depending on the base coordinates (the co­ordinates on the base), and in the denominator there is the determinant composed of the fiber coordinates (the coordinates in a fiber). For a three-dimensional manifold, the arbitrariness of the numerator is determined by nine functions depending on the base coordinates.

Topological spines of 4–manifolds

We show that infinitely many of the simply connected 4-manifolds constructed by Levine and Lidman that do not admit PL spines actually admit topological spines.

On Embedding of the Morse-Smale Diffeomorphisms in a Topological Flow

This review presents the results of recent years on solving of the Palis problem on finding necessary and sufficient conditions for the embedding of Morse-Smale cascades in topological flows. To date, the problem has been solved by Palis for Morse-Smale diffeomorphisms given on manifolds of dimension two. The result for the circle is a trivial exercise. In dimensions three and higher new effects arise related to the possibility of wild embeddings of closures of invariant manifolds of saddle periodic points that leads to additional obstacles for Morse-Smale diffeomorphisms to embed in topological flows. The progress achieved in solving of Paliss problem in dimension three is associated with the recently obtained complete topological classification of Morse-Smale diffeomorphisms on three-dimensional manifolds and the introduction of new invariants describing the embedding of separatrices of saddle periodic points in a supporting manifold. The transition to a higher dimension requires the latest results from the topology of manifolds. The necessary topological information, which plays key roles in the proofs, is also presented in the survey.

Watercore Identification of Xinjiang Fuji Apple Based on Manifold Learning Algorithm and Near Infrared Transmission Spectroscopy

Watercore Identification of Xinjiang Fuji Apple Based on Manifold Learning Algorithm and Near Infrared Transmission Spectroscopy

Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold

A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii. We consider a contact structure with singularities as a $$G$$ -structure with singularities, we find some topological and differential invariants of singularities of contact structure and establish their relation to the invariants found by B. Jakubczyk and M. Zhitomirskii.

Jeff Derksen's Citational Poetics

This paper investigates Jeff Derksen’s citational poetics in The Vestiges, and how this text’s creative practice critically examines the processes of neoliberalization in the present. With citational poetics, I see Derksen’s writing copy and comment on multiple textual forms in order to depict the poem’s role in social observation alongside its ability mobilize and array these textual forms against structures that far exceed the structure of the poem itself. The Vestiges in turn displays how the disparate materials of the long neoliberal moment and the traces of its manifold processes—from critical theory and chart topping hits to overthrown governments—can be brought to bear on the present, and specifically how mobilizing these different kinds of textual and historical matter locate citational poetics within a wider project of anti-capitalist research.

A geometric look at MHD and the Braginsky dynamo

ABSTRACT This paper considers magnetohydrodynamics (MHD) and some of its applications from the perspective of differential geometry, considering the dynamics of an ideal fluid flow and magnetic field on a general three-dimensional manifold, equipped with a metric and an induced volume form. The benefit of this level of abstraction is that it clarifies basic aspects of fluid dynamics such as how certain quantities are transported, how they transform under the action of mappings (e.g. the flow map between Lagrangian labels and Eulerian positions), how conservation laws arise, and the origin of certain approximations that preserve the mathematical structure of classical mechanics. First, the governing equations for ideal MHD are derived in a general setting by means of an action principle and making use of Lie derivatives. The way in which these equations transform under a pull back by the map taking the position of a fluid parcel to a background location is detailed. This is then used to parameterise Alfvén waves using concepts of pseudomomentum and pseudofield, in parallel with the development of Generalised Lagrangian Mean theory in hydrodynamics. Finally non-ideal MHD is considered with a sketch of the development of the Braginsky -dynamo in a general setting. Expressions for the α-tensor are obtained, including a novel geometric formulation in terms of connection coefficients, and related to formulae found elsewhere in the literature.

New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Three-Dimensional Manifolds

The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of three-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.

Constant mean curvature spheres in homogeneous three-manifolds

We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

On hypersurfaces with Kirichenko–Uskorev structure in Kählerian manifolds

On hypersurfaces with Kirichenko–Uskorev structure in Kählerian manifolds

Submanifolds of a conformal Sasakian manifold

In the present paper, some results on geometry of conformal Sasakian manifolds and their associated submanifolds are provided. Besides this an example of a three-dimensional conformal Sasakian manifold is constructed for illustration that is not Sasakian manifold.

Numerical investigation of flow boiling in manifold microchannel-based heat exchangers

Microchannel heat sinks have the potential to achieve the physical limit of phase change heat transfer. With advances in nano-/microscale fabrication techniques, important progress on microchannel heat exchangers has been made in recent years. However, the two-phase flow evolution and its influence on flow boiling at microscale remains ambiguous. Detailed information on transport process in microchannel and underlying mechanism are required for the fully understanding and further optimization of the microchannel heat sink. Here, we constructed a three-dimensional manifold microchannel-based heat exchanger model to study the two-phase flow pattern and heat transfer performance using the Phase-field method. The dynamics of vapor bubbles in microchannels of 80 μm, 150 μm, and 300 μm in depth was carefully investigated with respect to Reynolds number and thermal boundary conditions. Parameters and underlying mechanism that influence the two-phase flow evolution and heat transfer performance in the manifold microchannels are systematically analyzed. Finally, mechanism of heat transfer crisis and critical heat flux (CHF) in microchannel is studied, and strategies to optimize the flow field to delay the CHF are discussed. Our study provides detailed information on the transport process at microscale and offers opportunities for the design and fabrication of next generation microscale heat sinks.

Examples of Integrable Systems with Dissipation on the Tangent Bundles of Three-Dimensional Manifolds

In this paper, we prove the integrability of certain classes of dynamical systems on the tangent bundles of four-dimensional manifolds (systems with four degrees of freedom). The force field considered possessed so-called variable dissipation; they are generalizations of fields studied earlier. This paper continues earlier works of the author devoted to systems on the tangent bundles of two- and three-dimensional manifolds.