Jet Space Research Articles

On the Diverio-Trapani conjecture

In this paper we establish effective lower bounds on the degrees of the Debarre and Kobayashi conjectures. Then we study a more general conjecture proposed by Diverio-Trapani on the ampleness of jet bundles of general complete intersections in complex projective spaces.

Morphology and internal structure of soot particles under the influence of jet–swirl and jet–jet interactions in a diesel combustion environment

A new multi-location soot sampling method is used to enhance the knowledge about the structural evolution of in-flame particles in a light-duty optical diesel engine. Through thermophoresis-based particle sampling performed at multiple in-bowl locations, the soot structures are shown for both early formation stage and later stage from the same combustion event. Three different jet-spacing angles of 45°, 90° and 180° were studied to analyse how different levels of jet–jet interaction impact the soot particle morphology and internal structure. One selected jet–jet interaction condition was further analysed to show differences in soot structures between the up-swirl side and down-swirl side of the wall jets. From transmission electron microscopes (TEM) images of the sampled soot particles and their statistical size analysis, it was found soot particles initially formed within 45∘ separated jet–jet interaction region have un-solidified premature aggregates due to limited carbonisation in the locally fuel-rich mixtures. When these soot particles travelled on the down-swirl side of the jets, they became solidified and carbonised while the oxidation was evident from the smaller soot primary particle and longer carbon-layer fringe and lower tortuosity. The higher mixing on the up-swirl side of the jets further enhanced the soot oxidation, resulting in even smaller soot primary particle, fragmentation of large soot aggregates, and even longer and less curved carbon-layer fringes. Regarding jet–jet interaction, the 180° jet spacing angle created no jet–jet interaction condition on the soot sampler locations. For smaller jet-spacing angles, the increase in jet–jet interaction promoted the soot formation as evidenced by larger and more complex soot aggregates formed due to more active soot aggregation and agglomeration. The soot oxidation became limited at higher jet–jet interaction conditions, which led to more amorphous soot internal structures.

Numerical Simulation of Swirling Impinging Jet Issuing from a Threaded Hole under Inclined Condition.

There are some inclined jet holes in the cooling structure of the leading edge region of gas turbine blades. In order to improve the cooling effect of traditional round holes, this paper proposes to replace the round holes with threaded holes, and studies the complex flow and heat transfer performance of the swirling impinging jet (SIJ) issuing from the 45° threaded holes in the inclined condition by numerical simulation. The influencing factors include jet inclination angle α (45°–90°), jet-to-plate distance (H/d = 2, 4, 6), and Reynolds number (6000–24,000). The results show that the inclination angle and jet-to-plate distance have a great influence on the size, shape, and position of vortices in the jet space, while the Reynolds number has little effect on the vortices. In the inclined state, the impinging cooling effect of the swirling impinging jet is better than that of the circular impinging jet (CIJ), both heat transfer coefficients will degrade significantly when the inclination angle is 45°. When the inclination angle is greater than 45°, compared with the round hole, the enhanced heat transfer region for the swirling jet is in the region of r/d < 3, while both of the Nusselt numbers in the wall jet region are weak, with a value of just 20. At the same time, with the increasing of the inclination angle (α > 45°), the average Nusselt number on target surface holds a constant value. Under the inclined conditions, the heat transfer coefficient on the target surface for the swirling jet is increased totally with the increasing of the Re, but when the Re is larger than 18,000, the rate of enhanced heat transfer gradually weakens.

Principal parts of a vector bundle on projective line and the fractional derivative

This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic geometric parallel.

Unconstrained texture classification using efficient jet texton learning

This paper proposes a simple and effective texture recognition method that uses a new class of jet texton learning. In this approach, first a Jet space representation of the image is derived from a set of derivative of Gaussian (DtGs) filter responses upto 2nd order (R6), so called local jet vector (Ljv), which satisfies the scale space properties, where the combinations of local jets preserve the intrinsic local structure of the image in a hierarchical way and are invariant to image translation, rotation and scaling. Next, the jet textons dictionary is learned using K-means clustering algorithm from DtGs responses, followed by a contrast Weber law normalization pre-processing step. Finally, the feature distribution of jet texton is considered as a model which is utilized to classify texture using a non-parametric nearest regularized subspace (Nrs) classifier. Extensive experiments on three large and well-known benchmark database for texture classification like KTH-TIPS, Brodatz and CUReT show that the proposed method achieves state-of-the-art performance, especially when the number of available training samples is limited. The source code of complete system is made publicly available at https://github.com/swalpa/JetTexton.

Two-dimensional numerical study of two-phase rotating detonation wave with different injections

Two-dimensional numerical simulations on the two-phase rotating detonation wave of a stoichiometric ratio of the air-octane mixture by the discrete phase model are performed. The propagation process and stable flow field of the rotating detonation wave under nonpremixed and nonuniform injection conditions are analyzed. The effects of air injection total temperature and fuel injection inhomogeneity on the gas-liquid two-phase rotating detonation wave are investigated. The results show that under the same conditions, with the increase in the total temperature of air injection, the peak temperature, height, and propagation velocity of the detonation wave increase, but the peak pressure of the detonation wave decreases. The larger the jet spacing, the more pronounced the detonation wave is disturbed by the fuel jet. As the fuel jet spacing increases, the detonation wave propagation velocity decreases, but the peak temperature and peak pressure of the detonation wave increase. For the case of a jet spacing of 10 mm, the detonation wave cannot propagate when the air total temperature is 300 K, but the detonation wave can be stably propagated when the air total temperature is increased to 600 K. The stable propagation boundary of the rotating detonation wave with the combined action of the air total temperature and the jet spacing is obtained.

Lepage forms in Finsler geometry: Second-order generalization

Projectability of Lepage forms, defined on higher-order jet spaces, onto the corresponding Grassmann fibrations, is a basic requirement for the extension of the theory of Lepage forms to integral variational functionals for submanifolds. In this paper, projectability of second-order Lepage forms is considered for variational functionals of the Finsler type. Underlying geometric concepts such as regular 2-velocities, contact elements and second-order Grassmann fibrations of rank 1 are discussed. It is shown that a Lepage form is projectable if and only if its Hamiltonian vanishes identically. In this case, explicit formulas for the Lagrange functions and the projected Lepage forms are given in terms of the adapted coordinates.

A machine learning approach based on generative topographic mapping for disruption prevention and avoidance at JET

The need for predictive capabilities greater than 95% with very limited false alarms are demanding requirements for reliable disruption prediction systems in tokamaks such as JET or, in the near future, ITER. The prediction of an upcoming disruption must be provided sufficiently in advance in order to apply effective disruption avoidance or mitigation actions to prevent the machine from being damaged.In this paper, following the typical machine learning workflow, a generative topographic mapping (GTM) of the operational space of JET has been built using a set of disrupted and regularly terminated discharges. In order to build the predictive model, a suitable set of dimensionless, machine-independent, physics-based features have been synthesized, which make use of 1D plasma profile information, rather than simple zero-D time series. The use of such predicting features, together with the power of the GTM in fitting the model to the data, obtains, in an unsupervised way, a 2D map of the multi-dimensional parameter space of JET, where it is possible to identify a boundary separating the region free from disruption from the disruption region. In addition to helping in operational boundaries studies, the GTM map can also be used for disruption prediction exploiting the potential of the developed GTM toolbox to monitor the discharge dynamics. Following the trajectory of a discharge on the map throughout the different regions, an alarm is triggered depending on the disruption risk of these regions. The proposed approach to predict disruptions has been evaluated on a training and an independent test set and achieves very good performance with only one tardive detection and a limited number of false detections. The warning times are suitable for avoidance purposes and, more important, the detections are consistent with physical causes and mechanisms that destabilize the plasma leading to disruptions.

Cellular Legendrian contact homology for surfaces, part II

This paper is a continuation of [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)]. For Legendrian surfaces in [Formula: see text]-jet spaces, we prove that the Cellular DGA defined in [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)] is stable tame isomorphic to the Legendrian contact homology DGA, modulo the explicit construction of a specific Legendrian surface. In [Cellular computation of Legendrian contact homology for surfaces, to appear in Internat. J. Math.], we construct this surface, thereby completing Theorem 5.1 and the proof of the isomorphism.

Restriction and dimensional reduction of differential operators

We consider the restriction of a differential operator (DO) [Formula: see text] acting on the sections [Formula: see text] of a vector bundle [Formula: see text] with base [Formula: see text], in the language of jet bundles. When the base of [Formula: see text] is restricted to a submanifold [Formula: see text], all information about derivatives in directions that are not tangent to [Formula: see text] is lost. To restrict [Formula: see text] to a DO [Formula: see text] acting on sections [Formula: see text] of the restricted bundle [Formula: see text] (with [Formula: see text] the natural embedding), one must choose an auxiliary DO [Formula: see text] and express the derivatives non-tangent to [Formula: see text] from the kernel of [Formula: see text]. This is equivalent to choosing a splitting of certain short exact sequence of jet bundles. A property of [Formula: see text] called formal integrability is crucial for restriction’s self-consistency. We give an explicit example illustrating what can go wrong if [Formula: see text] is not formally integrable.As an important application of this methodology, we consider the dimensional reduction of DOs invariant with respect to the action of a connected Lie group [Formula: see text]. The splitting relation comes from the Lie derivative of the action, which is formally integrable. The reduction of the action of another group is also considered.

A Jet Bundle Approach to the Variational Structure of Nonholonomic Mechanical Systems

The aim of this paper is to study the geometry of nonholonomic mechanical systems in the realms of geometric mechanics and geometric analysis. This work was intended as an attempt at bringing together these two areas, in which geometric methods play the major role, in the study of nonholonomic systems. In this paper, we explore the geometry of Lagrangian mechanical systems subject to nonholonomic constraints using various bundle and variational structures intrinsically present in the nonholonomic setting. We consider the constrained Hamel equations of motion in a way that aids the analysis and helps to highlight the variational structure of such equations. To illustrate results of this work and as an application of the constrained Hamel formalism discussed in this paper, we conclude with taking the balanced Tennessee racer into consideration.

Isocrystals associated to arithmetic jet spaces of abelian schemes

Using Buium's theory of arithmetic differential characters, we construct a filtered F-isocrystal H(A)K associated to an abelian scheme A over a p-adically complete discrete valuation ring with perfect residue field. As a filtered vector space, H(A)K admits a natural map to the usual de Rham cohomology of A, but the Frobenius operator comes from arithmetic differential theory and is not the same as the usual crystalline one. When A is an elliptic curve, we show that H(A)K has a natural integral model H(A), which implies an integral refinement of a result of Buium's on arithmetic differential characters. The weak admissibility of H(A)K depends on the invertibility of an arithmetic-differential modular parameter. Thus the Fontaine functor associates to suitably generic A a local Galois representation of an apparently new kind.

BiLipschitz embeddings of spheres into jet space Carnot groups not admitting Lipschitz extensions

For all $k,n\ge 1$, we construct a biLipschitz embedding of $\mathbb{S}^n$ into the jet space Carnot group $J^k(\mathbb{R}^n)$ that does not admit a Lipschitz extension to $\mathbb{B}^{n+1}$. We begin with a smooth, positive function $f:\mathbb{B}^n\to \mathbb{R}$ with $k^{th}$-order derivatives that are approximately linear near $\partial \mathbb{B}^n$. Realizing $\mathbb{S}^n$ as two copies of $\mathbb{B}^n$, the embedding is given by taking the jet of $f$ on the upper hemisphere and the jet of $-f$ on the lower hemisphere. To prove the lack of a Lipschitz extension, we modify an argument of Haj{\l}asz, Schikorra, and Tyson for the case $n=1$ and generalize an argument of Rigot and Wenger for $n\ge 2$.

On geometric objects, the non-existence of a gravitational stress-energy tensor, and the uniqueness of the Einstein field equation

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a “geometric object”, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy. The main theorem proven underlying all the arguments is considerably stronger than the standard result in the literature used for the same purposes (Lovelock's theorem of 1972): it holds in all dimensions (not only in four); it does not require an assumption about the differential order of the desired concomitant of the metric; and it has a more natural physical interpretation.

Analysis of intermittently controlled multiple jets using DNS

Jet is one of the most basic flow used in the industrial field, and improvement of mixing and diffusion by jet is required in industrial equipment. Characteristics such as mixing and diffusion of the jet strongly depend on the large scale vortex structure formed near the outlet, and the mixing performance of the jet can be improved by controlling the vortex structure near the jet outlet with appropriate inflow conditions. In the case of mixing and diffusion in a wide space, a multiple jets are used in many fields in practice. Multiple jets are, unlike jets issued from single nozzle, interfere with each other downstream and strongly influence mixing performance such as entrainment of surrounding fluid and diffusion to surrounding environment. In this study, in order to reduce interference between jets or to use interference actively, intermittent control of jets with varying control frequency and jet spacing was studied using DNS (Direct Numerical Simulation). Statistical mechanical entropy is evaluated to quantify the mixing characteristics of intermittent control. It is confirmed that the mixing efficiency is significantly improved as compared to the non-controlled jet, which suggests that the intermittent control can be expected to help improve the mixing performance of multiple jets.

Quasi-phase-matched high harmonic generation in structured plasmas

Structured plasmas are employed in order to realize the quasi-phase-matched generation of high harmonics. The plasma originates from laser ablated solids leading to the appearance of multiple separated jets. By altering the shape of the solid the dimensions of the plasma structure are easily optimized. Combining optimal jet widths and spacing the maximum enhancement of the harmonic intensity by a factor of 16 is observed after four plasma jets.

Branched Projective Structures on a Riemann Surface and Logarithmic Connections

We study the set \mathcal{P}_S consisting of all branched holomorphic projective structures on a compact Riemann surface X of genus g \geq 1 and with a fixed branching divisor S := \sum_{i=1}^d n_i\cdot x_i , where x_i \in X . Under the hypothesis that n_i,=1 , for all i , with d a positive even integer such that d \neq 2g-2 , we show that \mathcal{P}_S coincides with a subset of the set of all logarithmic connections with singular locus S , satisfying certain geometric conditions, on the rank two holomorphic jet bundle J^1(Q) , where Q is a fixed holomorphic line bundle on X such that Q^{\otimes 2}= TX \otimes \mathcal{O}_X(S) . The space of all logarithmic connections of the above type is an affine space over the vector space H^0(X, K^{\otimes 2}_X \otimes\mathcal{O}_X(S)) of dimension 3g-3+d . We conclude that \mathcal{P}_S is a subset of this affine space that has codimenison d at a generic point.

Influence of jet spacing on flow and heat transfer characteristics in intermittently controlled multiple impinging jets

Influence of jet spacing on flow and heat transfer characteristics in intermittently controlled multiple impinging jets

The influence of pulse parameters on the downstream uniformity of linear-field jet array in argon

The nanosecond (ns) pulse excited plasma jet array shows merits of large treatment area and high chemical reactivity, while the pulse parameters influence the downstream uniformity of the ns pulse excited jet array significantly. In this paper, the downstream uniformity of the ns pulsed jet array with linear-field electrode structure is investigated by discharge image measurement at different amplitude of applied voltage, rising time and pulse repetition frequency (PRF). The voltage-current waveform and Schlieren image are measured and the electrical field distribution of the jet array is simulated to reveal the interaction mechanisms. The experimental results show that the divergence of side plumes becomes severer and the plume length of all three jet units becomes longer at higher applied voltage, which is caused by the enhancement of the electron energy and density. The shorter rising time also increases the transported charge and input energy and extends the length of the plasma plumes. At 0.5 L/min Ar flow rate, all of the lengths of plumes increase with PRF although the laminar regimes of the gas flows are reduced. At Ar flow rate of 1, 2, and 4 L/min, the middle jet is suppressed, which is analyzed by the electrical field distribution simulation. It is shown that the highest electric fields at the outside walls of side jet units, which suppress the propagation of ionization front from the orifice to the outer space of the middle jet. At lower Ar flow rate, there are severe depletion of electrons in the side jets by oxygen and penning ionization in the middle jet by background molecules, which result in the enhancement of the jet array downstream uniformity. The results are of importance to optimize pulse parameters for the realization of controllable and scalable pulse excited jet array for various applications.

Local jet pattern: a robust descriptor for texture classification

Methods based on locally encoded image features have recently become popular for texture classification tasks, particularly in the existence of large intra-class variation due to changes in illumination, scale, and viewpoint. Inspired by the theories of image structure analysis, this work proposes an efficient, simple, yet robust descriptor namely local jet pattern (Ljp) for texture classification. In this approach, a jet space representation of a texture image is computed from a set of derivatives of Gaussian (DtGs) filter responses up to second order, so-called local jet vectors (Ljv), which also satisfy the Scale Space properties. The Ljp is obtained by using the relation of center pixel with its’ local neighborhoods in jet space. Finally, the feature vector of a texture image is formed by concatenating the histogram of Ljp for all elements of Ljv. All DtGs responses up to second order together preserves the intrinsic local image structure, and achieves invariance to scale, rotation, and reflection. This allows us to design a discriminative and robust framework for texture classification. Extensive experiments on five standard texture image databases, employing nearest subspace classifier (Nsc), the proposed descriptor achieves 100%, 99.92%, 99.75%, 99.16%, and 99.65% accuracy for Outex_TC10, Outex_TC12, KTH-TIPS, Brodatz, CUReT, respectively, which are better compared to state-of-the-art methods.