Uniform Cone Research Articles

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator models from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than 50% reduction in the resource usage required to achieve the same level of accuracy as uniform and user-constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

Tuning up catalytical properties of electrochemically prepared nanoconical Co-Ni deposit for HER and OER

Catalysts can be successfully prepared by a simple electrochemical process. Their surface composition distinguishes catalytic activity toward hydrogen and oxygen evolution reactions. In this work, uniform Co-Ni cones were synthesized using the one-step method from an electrolyte containing a crystal modifier. Electrodeposited layers were oxidized and/or reduced in the furnace at 100 °C. Freshly electrodeposited coating was stored in air atmosphere for seven days. This results in an oxide layer forming on the surface of the catalyst. Changes in the surface composition, confirmed by the XPS method, strongly influenced the wettability, catalytic performance, and size of evolved hydrogen bubbles. The conical Co-Ni surface oxidized in a controlled way possesses the best catalytic activity towards hydrogen and oxygen evolution. Conversely, the spontaneously formed oxide layer decreases the catalytic performance in mentioned reactions compared with the fresh sample. The proper storage of synthesized samples is essential due to their desired catalytic applications. Proposed controlled oxidation can be an accessible way to increase nanomaterials catalytic performance.

Special uniform Vinberg cones and their applications

Special uniform Vinberg cones and their applications

Electric field simulation for uniform and FGM cone type spacer with adhering spherical conducting particle in GIS

Small spherical conducting particles which may be generated due to mechanical abrasion or arcing during switching of isolators and circuit breakers strongly affect the distribution of the electric field especially if they are very adjacent or adhering to the spacer surface. The simulation of the electric field depends on the location, the size of the contaminating particle and the spacer relative permittivity. This paper studies the effect of the presence of the adhering spherical conducting particles with different sizes and locations on the electric field distribution at solid/gas interface surface and around the spacer. Cone type spacer model with uniform and function grading material (FGM) permittivity distributions has been introduced to study the effect of the presence of the spherical conducting particles on the characteristics of the electric field along and around the spacer surface. The effect of the FGM spacer with its different arrangements on the insulation characteristics along and around the spacer surface will be discussed. The electric field simulation is performed by the concept of Finite Element Method (FEM) using three-dimension simulation model.

Microstructure and trapped field of YBCO bulk single-grain superconductors prepared by interior seeding

The microstructural analyses of YBCO bulk single-grain superconductors grown by interior seeding with taller and shorter upper pellets have shown that a suitable upper pellet height can lower the porosity in the upper part of the sample, produce a more appropriate distribution of pinning centres in the form of Y-211 particles and suppress subgrain formation with a higher crystal misalignment in the c-growth sector (c-GS), which can lead to a higher measured trapped magnetic field and a more uniform cone of the trapped-field profile. The observed bulging of the sample surface at the c-GS can be explained by the edge melt distribution model, which shows that macroscopic mass transport to the growth sector occurs with higher growth rates.

Stray light in cone beam optical computed tomography: II. Reduction using a convergent light source

Optical cone beam computed tomography (CBCT) using a broad beam and CCD camera is a fast method for densitometry of 3D optical gel dosimeters. However, diffuse light sources introduce considerable stray light into the imaging system, leading to underestimation of attenuation coefficients and non-uniformities in CT images unless corrections are applied to each projection image. In this study, the light source of a commercial optical CT scanner is replaced with a convergent cone beam source consisting of almost exclusively image forming primary rays. The convergent source is achieved using a small isotropic source and a Fresnel lens. To characterize stray light effects, full-field cone beam CT imaging is compared to fan beam CT (FBCT) using a 1 cm high fan beam aperture centered on the optic axis of the system. Attenuating liquids are scanned within a large 96 mm diameter uniform phantom and in a small 13.5 mm diameter finger phantom. For the uniform phantom, cone and fan beam CT attenuation coefficients agree within a maximum deviation of (1 ± 2)% between mean values over a wide range from 0.036 to 0.43 cm−1. For the finger phantom, agreement is found with a maximum deviation of (4 ± 2)% between mean values over a range of 0.1–0.47 cm−1. With the convergent source, artifacts associated with refractive index mismatch and vessel optical features are more pronounced. Further optimization of the source size to achieve a balance between quantitative accuracy and artifact reduction should enable practical, accurate 3D dosimetry, avoiding time consuming 3D scatter measurements.

Une inégalité de Korn non linéaire dans [formula omitted], [formula omitted

Let Ω be a bounded and connected open subset of Rn that satisfies the uniform interior cone property and let p>n. We establish a nonlinear Korn inequality in W2,p, which provides an upper bound of the ‖⋅‖W2,p(Ω)-norm of the difference between two immersions φ∈W2,p(Ω) and φ˜∈W2,p(Ω) in terms of the ‖⋅‖W1,p(Ω)-norm of the difference between their associated metric tensors ∇φT∇φ∈W1,p(Ω) and ∇φ˜T∇φ˜∈W1,p(Ω).Second, let Ω be a bounded, simply-connected, open subset of Rn with a Lipschitz boundary, the set Ω being locally on the same side of its boundary. Using the above nonlinear Korn inequality in W2,p, we establish the local Lipschitz-continuity of the mapping C∈W1,p(Ω)→φ∈W2,p(Ω), which is well-defined when the components of the Riemann curvature tensor associated with C vanish in D′(Ω), the immersion φ∈W2,p(Ω) being the solution, unique up to an isometry of En, of the equation ∇φT∇φ=C in Ω.

Continuity of eigenvalues of the Laplace operator according to domain

A new proof of the following fact is proposed. The eigenvalues of the Laplace-Dirichlet operator are continuous as functions in the corresponding space in domains satisfying the uniform cone condition. The author’s approach to this problem is based on a topological version of the upper (lower) limit for sequences of sets.

Minimal Failure Probability for Ceramic Design Via Shape Control

We consider the probability of failure for components made of brittle materials under one time application of a load, as introduced by Weibull and Batdorf-Crosse. These models have been applied to the design of ceramic heat shields of space shuttles and to ceramic components of the combustion chamber in gas turbines, for example. In this paper, we introduce the probability of failure as an objective functional in shape optimization. We study the convexity and the lower semi-continuity properties of such objective functionals and prove the existence of optimal shapes in the class of shapes with a uniform cone property. We also shortly comment on shape derivatives and optimality conditions.

Influence of selected variables on trihalomethane removals by spray aeration

The widespread use of chlorine and the reluctance of drinking water providers to alter their disinfection systems have sparked increased investigation into posttreatment removal of trihalomethanes (THMs). One posttreatment method is spray aeration, in which water is sprayed through showerheads in storage tanks. In this research the influence of various parameters on THM removals was evaluated using a mass balance–based model and sensitivity analysis. THM formation and the configuration (droplet size, travel distance, and spray pattern) and magnitude (percent recycle) of the sprayed water flow were determined to be the most influential parameters, whereas temperature, spray angle for uniform cone flow distribution, and THM species were the least influential factors. Practitioners should find these results helpful in determining the most important design parameters for spray aeration systems. In addition, the study elucidates the advantages of spray aeration in removing brominated THM species.

The study on formation mechanism of novel ZnO cone prepared by using pulsed current electrodeposition

The ZnO cones were grown on the indium tin oxide (ITO) substrates using the pulsed current electrodeposition (PCE) method. The influences of concentration of Zn(NO3)2 and reaction time on morphological evolution of ZnO cones were investigated for obtaining uniform ZnO cones. Based on scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analysis, a possible growth process of homogeneous nucleation and subsequent coalescent growth was proposed as plausible mechanistic interpretation for formation of the novel conical ZnO.

Theory of Transitional Universe (New Model of Space-Time)

This is a theory that makes macroscopic predictions based on the principle of duality as universal constant in space-time continuum, which is finite in its infinity due to integrated horizon and inherent reverse polarity.It implies that there is an absolute frame of reference in our uniform double cone space-time model (as observed in cosmos) which shows that the state of our universe is a deterministic function of its previous state of a primordial universe where the rotating mass of first order extended in our universe to second order in the angular momentum. Locality assumes that the current state of space-time is determined by the states of a fixed number of previous time steps. Discretized difference equations use at least the current and previous time steps if they are second order systems like the wave equation. Physical quantities come in pairs which are called conjugate quantities. According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually.It means that space-time is not flat per Einstein-Minkowski and that there couldn’t be a singular event of a Big Bang due to a single, primitive force (“primeval atom”), which allegedly caused a sudden “birth’ of space-time without a preceding event -- past “conception” of our universe in a primordial universe. Accordingly, our 4D time-space model comprises a cross-like string structure with an integrated spiral timeframe that enables no analogy spacecrafts to traverse space unimpeded, as described in this article.

Shy couplings, $\operatorname{CAT} ({0})$ spaces, and the lion and man

Two random processes X and Y on a metric space are said to be $\varepsilon$-shy coupled if there is positive probability of them staying at least a positive distance $\varepsilon$ apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity conditions; we remove these conditions by showing the nonexistence of shy co-adapted couplings of reflecting Brownian motion in any bounded CAT(0) domain with boundary satisfying uniform exterior sphere and interior cone conditions, for example, simply-connected bounded planar domains with $C^2$ boundary. The proof uses a Cameron-Martin-Girsanov argument, together with a continuity property of the Skorokhod transformation and properties of the intrinsic metric of the domain. To this end, a generalization of Gauss' lemma is established that shows differentiability of the intrinsic distance function for closures of CAT(0) domains with boundaries satisfying uniform exterior sphere and interior cone conditions. By this means, the shy coupling question is converted into a Lion and Man pursuit-evasion problem.

XPS studies on surface reduction of tungsten oxide nanowire film by Ar+ bombardment

WO3 nanowire film was bombarded by Ar ion beam in the analysis chamber of an X-ray photoelectron spectroscopy (XPS) system to produce uniform tungsten cone arrays. The WO3 nanowire film itself served as an etching mask during the Ar+ bombardment. The changes of surface chemical states and electronic structures during bombardment were monitored by in situ XPS. The morphological evolution with different Ar+ bombardment time was observed by ex situ scanning electron microscopy (SEM). At the start of Ar+ bombardment partial W6+ in WO3 was reduced to W5+ immediately, subsequently to W4+ and then to Wx+ (intermediate chemical state between W4+ and W0), finally to W0. Multiple oxidation states of tungsten coexisted until finally only W0 left. SEM images showed that the nanowires were broken and then fused together to be divided into clusters with a certain orientation after long-time high-energy ion beam bombardment. The mechanism of the ion-induced reduction during bombardment and the reason of the orientated cone arrays formation were discussed respectively.

Electronic states in heterostructures with piece-wise uniform Dirac cones

We discuss graphene physics that are associated with Fermi velocity rather than bandgap or external potential. Such physics are illustrated with a simple junction that is comprised of two uniform electrodes bridged by a central uniform channel. The main difference between these components is supposed to come at their Fermi velocities (Dirac cone slopes), which take different values: ν0 in the electrodes and v in the channel. This junction can be fabricated, for example, by depositing a single-layer graphene on prepatterned substrate. Both scattering states and localized states have been explored. Making full analog with optics, the discussions have been focused on these aspects: refraction, total internal reflection (TIR), and transmission. Regarding them, Snell’s law and the TIR critical angle have been derived and the TIR impacts on transmission have been calculated. Potential applications of this junction have been discussed. In particular, we found that, an electrical switch and an electron box can be made of it.

On the regularity of domains satisfying a uniform hour–glass condition and a sharp version of the Hopf–Oleinik boundary point principle

We prove that an open, proper, nonempty subset of ${\mathbb{R}}^n$ is a locally Lyapunov domain if and only if it satisfies a uniform hour-glass condition. The limiting cases are as follows: Lipschitz domains may be characterized by a uniform double cone condition, and domains of class may be characterized by a uniform two-sided ball condition. We discuss a sharp generalization of the Hopf–Oleinik boundary point principle for domains satisfying an interior pseudoball condition, for semi-elliptic operators with singular drift and obtain a sharp version of the Hopf strong maximum principle for second order, nondivergence form differential operators with singular drift. Bibliography: 66 titles. Illustrations: 7 figures.

Brownian Dynamics of Globules

We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and a center moving according to a diffusion process. The spheres are hard, hence non-intersecting, which induces in the equation a reflection term with a local (collision-)time. A smooth interaction is considered too and, in the particular case of a gradient system, the reversible measure of the dynamics is given. In the proofs, we analyze geometrical properties of the boundary of the set in which the process takes its values, in particular the so-called Uniform Exterior Sphere and Uniform Normal Cone properties. These techniques extend to other hard core models of objects with a time-dependent random characteristic: we present here an application to the random motion of a chain-like molecule.

Sobolev embeddings for unbounded domain with variable exponent having values across N

We study Sobolev embeddings for unbounded domain with variable exponent having values across N. A main result of this paper is the following theorem: Let Omega be an unbounded domain in RN satisfying the uniform cone condition. Suppose that p : Omega -> R is Lipschitz and 1 L-q(.) (Omega) for any q is an element of L-infinity(Omega) satisfying condition p(x) = N. In this theorem the usual condition sup p(x) < N is not required.

Uniqueness results for nonlocal Hamilton–Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh–Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.

Exit Time, Green Function and Semilinear Elliptic Equations

Let $D$ be a bounded Lipschitz domain in $R^n$ with $n\geq 2$ and $\tau_D$ be the first exit time from $D$ by Brownian motion on $R^n$. In the first part of this paper, we are concerned with sharp estimates on the expected exit time $E_x [ \tau_D]$. We show that if $D$ satisfies a uniform interior cone condition with angle $\theta \in ( \cos^{-1}(1/\sqrt{n}), \pi )$, then $c_1 \varphi_1(x) \leq E_x [\tau_D] \leq c_2 \varphi_1 (x)$ on $D$. Here $\varphi_1$ is the first positive eigenfunction for the Dirichlet Laplacian on $D$. The above result is sharp as we show that if $D$ is a truncated circular cone with angle $\theta < \cos^{-1}(1/\sqrt{n})$, then the upper bound for $E_x [\tau_D]$ fails. These results are then used in the second part of this paper to investigate whether positive solutions of the semilinear equation $\Delta u = u^{p}$ in $ D,$ $p\in R$, that vanish on an open subset $\Gamma \subset \partial D$ decay at the same rate as $\varphi_1$ on $\Gamma$.