Geometric Criteria Research Articles

Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant

We consider an obliquely reflected Brownian motion Z with positive drift in a quadrant stopped at time T, where T≔inf{t>0:Z(t)=(0,0)} is the first hitting time at the origin. Such a process can be defined even in the non-standard case in which the reflection matrix is not completely-S. We show in this case that the process has two possible behaviors: either it tends to infinity or it hits the corner (origin) in finite time. Given an arbitrary starting point (u,v) in the quadrant, we consider the escape (resp. absorption) probabilities P(u,v)[T=∞] (resp. P(u,v)[T<∞]). We establish the partial differential equations and the oblique Neumann boundary conditions which characterize the escape probability and provide a functional equation satisfied by the Laplace transform of the escape probability. Asymptotics for the absorption probability in the simpler case in which the starting point in the quadrant is (u,0) are then given. We proceed to show a geometric criterion on the parameters which characterizes the case in which the absorption probability has a product form and is exponential. We call this new criterion the dual skew symmetry condition due to its natural connection with the skew symmetry condition for the stationary distribution. We then obtain an explicit integral expression for the Laplace transform of the escape probability and conclude by presenting exact asymptotics for the escape probability at the origin.

Reallocation model in land consolidation using multi‐objective particle swarm optimization dealing with landowners' rights

AbstractIn conventional reallocation, farmers' preferences are used to determine the location of their new parcels in predetermined blocks. The most common conflict that can arise during this process is that demand may be high for some blocks. The manner of resolving such disputes, which deal directly with landowners' rights, can affect the success or failure of land consolidation projects. In this study, a novel model for land reallocation is proposed which is based on the principle that the initial situation of the landowner's parcels before land consolidation will be comparable with the new situation that includes all of his/her rights. For this, a spatial similarity‐based approach was proposed, taking into account geometric, ownership, physical, and locational criteria. Then, the agricultural land reallocation model (LR‐MOPSO) was developed using the multi‐objective particle swarm algorithm. Three objectives were defined: (1) simultaneous consideration of farmers' priority and spatial similarity criteria; (2) pooling of farmers' fragmented parcels; and (3) optimal placement of parcels within the block. The LR‐MOPSO model was applied to an Iranian case study and results were compared with a conventional approach. With this model decision‐makers in land consolidation projects will be able to redistribute parcels in a more transparent way, while dealing with landowners' rights.

Local $$L^p$$ norms of Schrödinger eigenfunctions on $${\mathbb {S}}^2$$

On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every \(p\ne 6\), Sogge’s estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.

Математическая модель безлопаточного диффузора центробежного компрессора на основе CFD-расчетов

The centrifugal compressor design involves the use of approximate engineering techniques based on mathematical modeling. One of such techniques is the universal modeling method, which proves to be practically applicable. Having generalized a series of CFD calculations, we used a mathematical model in the latest version of the compressor model to calculate flow parameters in vaneless diffusers. The diffuser model was identified based on the results of experimental studies of average-flow model stages carried out at SPbPU. The model is also used to calculate Clark low-flow centrifugal compressor stages with narrow diffusers with a relative width in the range of 0.5--2.0 %. For these stages, the developed mathematical model showed insufficient efficiency, since the dimensions of the diffusers go beyond the limits of its applicability. To solve this problem, we calculated a series of vaneless diffusers with a relative width in the range of 0.6--1.2 % in the ANSYS CFX software package. Relying on the results of CFD calculations, we plotted the gas dynamic characteristics of the loss coefficients and changes in the flow angle depending on the flow angle at the inlet to the vaneless diffuser. To process the calculated data, the method of regression analysis was applied, with the help of which a system of algebraic equations was developed that connects geometric, gas-dynamic parameters and similarity criteria. The obtained equations are included in a new mathematical model of the universal modeling method for calculating the flow parameters of vaneless diffusers. Comparison of the calculated gas-dynamic characteristics according to the new model with experimental data showed the average error of modeling the calculated (maximum) efficiency equal to 1.08 %

Topological and geometric hyperbolicity criteria for polynomial automorphisms of

AbstractWe prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of $\mathbb {C}^2$ . Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.

Geometric construction of auxetic metamaterials

AbstractThis paper is devoted to a category of metamaterials called auxetics, identified by their negative Poisson's ratio. Our work consists in exploring geometrical strategies to generate irregular auxetic structures. More precisely we seek to reduce the Poisson's ratio ν, by pruning an irregular network based solely on geometric criteria. We introduce a strategy combining a pure geometric pruning algorithm followed by a physics‐based testing phase to determine the resulting Poisson's ratio of our structures. We propose an algorithm that generates sets of irregular auxetic networks. Our contributions include geometrical characterization of auxetic networks, development of a pruning strategy, generation of auxetic networks with low Poisson's ratio, as well as validation of our approach. We provide statistical validation of our approach on large sets of irregular networks, and we additionally laser‐cut auxetic networks in sheets of rubber. The findings reported here show that it is possible to reduce the Poisson's ratio by geometric pruning, and that we can generate irregular auxetic networks at lower processing times than a physics‐based approach.

Presenting a Semi-Automatic, Statistically-Based Approach to Assess the Sharpness Level of Optical Images from Natural Targets via the Edge Method. Case Study: The Landsat 8 OLI–L1T Data

Developing reliable methodologies of data quality assessment is of paramount importance for maximizing the exploitation of Earth observation (EO) products. Among the different factors influencing EO optical image quality, sharpness has a relevant role. When implementing on-orbit approaches of sharpness assessment, such as the edge method, a crucial step that strongly affects the final results is the selection of suitable edges to use for the analysis. Within this context, this paper aims at proposing a semi-automatic, statistically-based edge method (SaSbEM) that exploits edges extracted from natural targets easily and largely available on Earth: agricultural fields. For each image that is analyzed, SaSbEM detects numerous suitable edges (e.g., dozens-hundreds) characterized by specific geometrical and statistical criteria. This guarantees the repeatability and reliability of the analysis. Then, it implements a standard edge method to assess the sharpness level of each edge. Finally, it performs a statistical analysis of the results to have a robust characterization of the image sharpness level and its uncertainty. The method was validated by using Landsat 8 L1T products. Results proved that: SaSbEM is capable of performing a reliable and repeatable sharpness assessment; Landsat 8 L1T data are characterized by very good sharpness performance.

Variational approximation of interface energies and applications

Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with such interface energies. The considered approach is based on a \Gamma -convergence approximation combined with convex analysis techniques.

Effect of the Hydration Shell on the Carbonyl Vibration in the Ala-Leu-Ala-Leu Peptide.

The vibrational spectrum of the Ala-Leu-Ala-Leu peptide in solution, computed from first-principles simulations, shows a prominent band in the amide I region that is assigned to stretching of carbonyl groups. Close inspection reveals combined but slightly different contributions by the three carbonyl groups of the peptide. The shift in their exact vibrational signature is in agreement with the different probabilities of these groups to form hydrogen bonds with the solvent. The central carbonyl group has a hydrogen bond probability intermediate to the other two groups due to interchanges between different hydrogen-bonded states. Analysis of the interaction energies of individual water molecules with that group shows that shifts in its frequency are directly related to the interactions with the water molecules in the first hydration shell. The interaction strength is well correlated with the hydrogen bond distance and hydrogen bond angle, though there is no perfect match, allowing geometrical criteria for hydrogen bonds to be used as long as the sampling is sufficient to consider averages. The hydrogen bond state of a carbonyl group can therefore serve as an indicator of the solvent’s effect on the vibrational frequency.

Fractional-order delay differential equations for the dynamics of hepatitis C virus infection with IFN-[formula omitted] treatment

Herein, we propose a fractional-order delay differential model for the dynamics of Hepatitis-C Virus (HCV), with interferon-α(IFN-α) treatment. A fractional-order derivative is considered to represent the long-run immune memory required for intermediate cellular interactions. A discrete time-delay τ is also incorporated to represent the intracellular delay between initial infection of a cell by HCV and the release of new virions. By using time-delay τ as a bifurcation parameter, the stability of infection-free and infected steady states is investigated. The coefficients of the corresponding characteristic equation depend on τ, and geometric stability switch criteria is used to study the stability switching properties. The fractional-order delay differential model has been verified with real observations. Incorporating fractional-order and immune memory, in the model, greatly enriches the dynamics of the system and improves the consistency of the model with the observations.

Element activation method and non-conformal dynamic remeshing strategy to model additive manufacturing

Modeling of Additive Manufacturing (AM) at the part scale involves non-linear thermo-mechanical simulations. Such a process also imposes a very fine discretization and requires altering the geometry of the models during the simulations to model the addition of matter, which is a computational challenge by itself. The first focus of this work is the addition of an additive manufacturing module in the fully implicit in-house Finite Element code Metafor [1] which is developed at the University of Liège. The implemented method to activate elements and to activate and deactivate boundary conditions during a simulation is adapted from the element deletion algorithm implemented in Metafor in the scope of crack propagation [2]. This algorithm is modified to allow the activation of elements based on a user-specified criterion (e.g. geometrical criterion, thermal criterion, etc.). The second objective of this work is to improve the efficiency of the AM simulations, in particular by using a dynamic remeshing strategy to reduce the computational cost of the simulations. This remeshing is done using non-conformal meshes, where hanging nodes are handled via the use of Lagrange multiplier constraints. The mesh data transfer used after remeshing is based on projection methods involving finite volumes [3]. The presented model is then compared against a 2D numerical simulation of Direct Energy Deposition of a High-Speed Steel thick deposit from the literature [4].

Lebesgue spectrum of countable multiplicity for conservative flows on the torus

We study the spectral measures of conservative mixing flows on the 2 2 -torus having one degenerate singularity. We show that, for a sufficiently strong singularity, the spectrum of these flows is typically Lebesgue with infinite multiplicity. For this, we use two main ingredients: (1) a proof of absolute continuity of the maximal spectral type for this class of non-uniformly stretching flows that have an irregular decay of correlations, (2) a geometric criterion that yields infinite Lebesgue multiplicity of the spectrum and that is well adapted to rapidly mixing flows.

Nanodevices Tend to Be Round.

Under several circumstances, a nanowire transistor with a square cross-section behaves as a circular. Taking the Gate-All-Around junctionless transistor as a primary example, we investigate the transition of the conductive region from square to circle-like. In this case, the metamorphosis is accentuated by smaller size, lower doping, and higher gate voltage. After defining the geometrical criterion for square-to-circle shift, simulation results are used to document the main consequences. This transition occurs naturally in nanowires thinner than 50 nm. The results are rather universal, and supportive evidence is gathered from inversion-mode Gate-All-Around (GAA) MOSFETs as well as from thermal diffusion process.

3.2.1] and [4.1.1] isomers of Lehn's [2.2.2] Cryptand: Prediction of ion selectivity by quantum chemical calculations XV**

AbstractSelective alkaline and earth alkaline metal ion encapsulation by two different Lehn‐type cryptands, noted as [3.2.1] and [4.1.1], was predicted and between them compared on the DFT (B3LYP/LANL2DZp) basis set. Since these cryptands are isomers to the well‐known [2.2.2] cryptand, the cation encapsulation selectivity of all three cages were compared. The ion selectivity and ability of the host to adjust their structure to successfully accommodate the metal ions, were based on energy and geometric criteria. Different lengths of O‐Et‐O‐bridging arms provide an unsymmetrical cryptand host with great flexibility to accommodate large alkali and alkaline earth metal cations.

Theoretical and Mechanistic Validation of Global Kinetic Parameters of the Inactivation of GABA Aminotransferase by OV329 and CPP-115

((S)-3-Amino-(difluoromethylenyl)cyclopent-1-ene-1-carboxylic acid (OV329) is a recently discovered inactivator of γ-aminobutyric acid aminotransferase (GABA-AT), which has 10 times better inactivation efficiency than its predecessor, CPP-115, despite the only structural difference being an endocyclic double bond in OV329. Both compounds are mechanism-based enzyme inactivators (MBEIs), which inactivate GABA-AT by a similar mechanism. Here, a combination of a variety of computational chemistry tools and experimental methods, including quantum mechanical (QM) calculations, molecular dynamic simulations, progress curve analysis, and deuterium kinetic isotope effect (KIE) experiments, are utilized to comprehensively study the mechanism of inactivation of GABA-AT by CPP-115 and OV329 and account for their experimentally obtained global kinetic parameters kinact and KI. Our first key finding is that the rate-limiting step of the inactivation mechanism is the deprotonation step, and according to QM calculations and the KIE experiments, kinact accurately represents the enhancement of the rate-limiting step for the given mechanism. Second, the present study shows that the widely used simple QM models do not accurately represent the geometric criteria that are present in the enzyme for the deprotonation step. In contrast, QM cluster models successfully represent both the ground state destabilization and the transition state stabilization, as revealed by natural bond orbital analysis. Furthermore, the globally derived KI values for both of the inactivators represent the inhibitor constants for the initial binding complexes (Kd) and indicate the inactivator competition with the substrate according to progress curve analysis and the observed binding isotope effect. The configurational entropy loss accounts for the difference in KI values between the inactivators. The approach we describe in this work can be employed to determine the validity of globally derived parameters in the process of MBEI optimization for given inactivation mechanisms.

Characteristic Cohomology I: Singularities of Given Type

Abstract For a germ of a variety $\mathcal{V}, 0 \subset \mathbb C^N, 0$, a singularity $\mathcal{V}_0$ of ‘type $\mathcal{V}$’ is given by a germ $f_0 : \mathbb C^n, 0 \to \mathbb C^N, 0$ which is transverse to $\mathcal{V}$ in an appropriate sense so that $\mathcal{V}_0 = f_0^{\,-1}(\mathcal{V})$. If $\mathcal{V}$ is a hypersurface germ, then so is $\mathcal{V}_0 $, and by transversality ${\operatorname{codim}}_{\mathbb C} {\operatorname{sing}}(\mathcal{V}_0) = {\operatorname{codim}}_{\mathbb C} {\operatorname{sing}}(\mathcal{V})$ provided $n \gt {\operatorname{codim}}_{\mathbb C} {\operatorname{sing}}(\mathcal{V})$. So $\mathcal{V}_0, 0$ will exhibit singularities of $\mathcal{V}$ up to codimension n. For singularities $\mathcal{V}_0, 0$ of type $\mathcal{V}$, we introduce a method to capture the contribution of the topology of $\mathcal{V}$ to that of $\mathcal{V}_0$. It is via the ‘characteristic cohomology’ of the Milnor fiber (for $\mathcal{V}, 0$ a hypersurface), and complement and link of $\mathcal{V}_0$ (in the general case). The characteristic cohomology of the Milnor fiber $\mathcal{A}_{\mathcal{V}}(\,f_0; R)$, and respectively of the complement $\mathcal{C}_{\mathcal{V}}(\,f_0; R)$, are subalgebras of the cohomology of the Milnor fibers, respectively the complement, with coefficients R in the corresponding cohomology. For a fixed $\mathcal{V}$, they are functorial over the category of singularities of type $\mathcal{V}$. In addition, for the link of $\mathcal{V}_0$ there is a characteristic cohomology subgroup $\mathcal{B}_{\mathcal{V}}(\,f_0, \mathbf{k})$ of the cohomology of the link over a field $\mathbf{k}$ of characteristic 0. The cohomologies $\mathcal{C}_{\mathcal{V}}(\,f_0; R)$ and $\mathcal{B}_{\mathcal{V}}(\,f_0, \mathbf{k})$ are shown to be invariant under the $\mathcal{K}_{\mathcal{V}}$-equivalence of defining germs f0, and likewise $\mathcal{A}_{\mathcal{V}}(\,f_0; R)$ is shown to be invariant under the $\mathcal{K}_{H}$-equivalence of f0 for H the defining equation of $\mathcal{V}, 0$. We give a geometric criterion involving ‘vanishing compact models’ for both the Milnor fibers and complements which detect non-vanishing subalgebras of the characteristic cohomologies, and subgroups of the characteristic cohomology of the link. Also, we consider how in the hypersurface case the cohomology of the Milnor fiber is a module over the characteristic cohomology $\mathcal{A}_{\mathcal{V}}(\,f_0; R)$. We briefly consider the application of these results to a number of cases of singularities of a given type. In part II, we specialize to the case of matrix singularities and using results on the topology of the Milnor fibers, complements and links of the varieties of singular matrices obtained in another paper allow us to give precise results for the characteristic cohomology of all three types.

Cross-Talk between Overlap Interactions in Biomolecules: A Case Study of the β-Turn Motif.

Noncovalent interactions play a pivotal role in regulating protein conformation, stability and dynamics. Among the quantum mechanical (QM) overlap-based noncovalent interactions, is the best understood with studies ranging from small molecules to -turns of model proteins such as GB1. However, these investigations do not explore the interplay between multiple overlap interactions in contributing to local structure and stability. In this work, we identify and characterize all noncovalent overlap interactions in the -turn, an important secondary structural element that facilitates the folding of a polypeptide chain. Invoking a QM framework of natural bond orbitals, we demonstrate the role of several additional interactions such as and that are energetically comparable to or larger than . We find that these interactions are sensitive to changes in the side chain of the residues in the -turn of GB1, suggesting that the may not be the only component in dictating -turn conformation and stability. Furthermore, a database search of and in the PDB reveals that they are prevalent in most proteins and have significant interaction energies (∼1 kcal/mol). This indicates that all overlap interactions must be taken into account to obtain a comprehensive picture of their contributions to protein structure and energetics. Lastly, based on the extent of QM overlaps and interaction energies, we propose geometric criteria using which these additional interactions can be efficiently tracked in broad database searches.

Planar Hexacoordinate Carbons: Half Covalent, Half Ionic.

Herein, the first global minima containing a planar hexacoordinate carbon (phC) atom are reported. The fifteen structures belong to the CE3 M3 + (E=S-Te and M=Li-Cs) series and satisfy both geometric and electronic criteria to be considered as a true phC. The design strategy consisted of replacing oxygen in the D3h CO3 Li3 + structure with heavy and less electronegative chalcogens, inducing a negative charge on the C atom and an attractive electrostatic interaction between C and the alkali-metal cations. The chemical bonding analyses indicate that carbon is covalently bonded to three chalcogens and ionically connected to the three alkali metals.

Planar Hexacoordinate Carbons: Half Covalent, Half Ionic

AbstractHerein, the first global minima containing a planar hexacoordinate carbon (phC) atom are reported. The fifteen structures belong to the CE3M3+ (E=S–Te and M=Li–Cs) series and satisfy both geometric and electronic criteria to be considered as a true phC. The design strategy consisted of replacing oxygen in the D3h CO3Li3+ structure with heavy and less electronegative chalcogens, inducing a negative charge on the C atom and an attractive electrostatic interaction between C and the alkali‐metal cations. The chemical bonding analyses indicate that carbon is covalently bonded to three chalcogens and ionically connected to the three alkali metals.

Contact dynamics analysis of the single-pin meshing pair of a tracked vehicle

Single-pin meshing pairs are widely used in light-tracked vehicles. The purpose of this paper is to establish a nonlinear contact algorithm between the sprocket and track for multibody dynamics simulation. Based on the actual configuration, the tooth groove profile is discretized into three cambered surfaces, and the track pin is modeled as a cylinder with a protrusion. A body-fixed frame is introduced for each contact surface to facilitate the geometric contact criteria and contact force evaluation. Then the features of equal-pitch, sub-pitch and extra-pitch meshing are described with multibody dynamics analysis. It indicates that track pitch and sprocket pitch are the critical process parameters. A field test was performed to excavate the cause of chassis vibration. Compared with simulation results, the proposed contact model can effectively simulate the high-frequency excitation applied on a tracked vehicle. To improve its service life, a suggestion for the sprocket and track design is developed to fully use the sub-pitch meshing.