Finite Jet Research Articles

Microflexiblity and local integrability of horizontal curves

AbstractLet be an analytic bracket‐generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension within the space of germs of smooth curves tangent to . We formalize this as an asymptotic statement about finite jets of tangent curves. This solves, in the analytic setting, a conjecture of Eliashberg and Mishachev regarding an earlier claim by Gromov about the microflexibility of the tangency condition.From these statements it follows, by an argument due to Gromov, that the ‐principle holds for maps and immersions transverse to .

The role of opened fire doors in enhanced heat exchange of long-distance utility tunnels

Due to their distinctive structural attributes, fire compartments in utility tunnels result in regions of increased temperature concentration and thermal dissipation, notably influencing heat exchange phenomena. Investigating airflow diffusion and thermal exchange principles of fire compartments is important when optimizing heat transfer processes in extensive utility tunnels. In this study, we employed numerical simulations and rigorous experimental validation to compare velocity and temperature field attributes between conventional tunnels and those augmented with fire compartments under diverse boundary conditions. The findings revealed that substantial ventilation exchange, reduced cable-based thermal exchange, diminished wall temperatures, and incorporation of opened fire doors are effective measures in improving the thermal environment in utility tunnels. During the summer season, it was observed that the temperature prerequisites were adequately met in a 400-m-long utility tunnel featuring cross-fire compartments at a ventilation rate of 4 air changes per hour (ACH), while tunnels surpassing a length of 600 m required a ventilation rate of 2 ACH, and single-fire compartment tunnels required a ventilation rate of 6 ACH for similar thermal control. Specifically, at a rate of 2 ACH, the temperature in the tunnel exhibited an average reduction of 3.25 °C with the addition of one additional opened fire door. In comparison, a decrease of 1.91 °C was observed when maintaining a rate of 4 ACH. Finally, the airflow characteristics of tunnels with normally opened fire doors were summarized via a finite forced jet model, and the specific ranges of the potential flow core region, characteristic attenuation region and radial attenuation region were obtained.

Unique jet determination of CR maps into Nash sets

Let M⊂CN be a real-analytic CR submanifold, M′⊂CN′ a Nash set and EM′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p∈M, and for every pair of germs of C∞-smooth CR maps f,g:(M,p)→M′, there exists an integer k=kp such that if f and g have the same k-jets at p, and do not send M into EM′, then necessarily f=g. Furthermore, the map p↦kp may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in CN into Nash subsets in CN′ of D'Angelo finite type, for arbitrary N,N′≥2.

Modelling the decay of finite-span starting and stopping wall jets in an external stream

The flow under consideration is a wall jet that results from an inclined jet in cross-flow emitted into a zero-pressure-gradient turbulent boundary layer from a slot-like outlet of width$b=0.5\,\mathrm {mm}$and span$L=20\,\mathrm {mm}$. Despite the finite jet span, the velocity decay and wall-normal spreading rate in the symmetry plane can be described with power laws almost identical to those for the two-dimensional flow determined by Zhou & Wygnanski (AIAA J., vol. 31, 1993, pp. 848–853). This is explained by the lack of significant lateral spreading found in the present configuration due to a self-amplifying inward-directed fluid motion, fundamentally differing from conditions found in the absence of an external stream. Regions with ‘approximately self-similar’ properties also exist in the case of unsteady velocity programmes where the fluid is ejected in a pulsatile fashion. Here, the wall jet is enclosed by a leading vortex structure and a deceleration wave, for which the time-dependent locations can be predicted by means of empirical constants. This yields models for the major properties inside the advancing and diffusing wall jet that only require knowledge regarding the velocity ratio, the ejected momentum flux and the kinematic viscosity, representing an extension to scaling laws for steady wall jets in still ambience established by Narasimhaet al.(Aeronaut. Q., vol. 77, 1973, pp. 355–359).

Two decades of finite jet determination of CR mappings

This is a survey paper discussing the developments around the so-called finite jet determination problem for CR maps over the past twenty years.

Aerodynamic Modelling of the Airfoil Immersed in Two-Dimensional Jet Flow

In order to study the aerodynamic interaction of the airfoil and jet flow, the free streamline model and the panel method are combined to develop a fast calculation method for the airfoil in two-dimensional inviscid jet flow. The vortex strength and position of the jet boundary are determined by using the free streamline model and the constant total pressure difference assumption, the circulation of the airfoil is solved by the vortex panel method, and the whole process is coupled by relaxation iteration. Firstly, the convergence and effectiveness of the present method are verified. Next, the influence of the length ratio of jet height to airfoil chord, the velocity ratio of jet velocity to freestream velocity, and the ground effect on airfoil aerodynamics are studied. The results show that the aerodynamic characteristics of the airfoil in finite width jet flow and in freestream have a large difference, and it is important to consider the jet deflection for jet/airfoil interaction. In jet flow, the velocity ratio can be regarded as an aerodynamic similarity parameter for the airfoil. When the jet flow is deflected, the airfoil will not only generate lift but also drag, and the ground effect can be used to decrease drag. The developed method in this paper can not only capture the jet deflection but also has higher calculation efficiency than Computational Fluid Dynamic (CFD), which is beneficial for the preliminary design of a powered-lift device.

Interaction of synthetic jets with a massively separated three-dimensional flow field

The interaction of an array of finite span synthetic jet actuators with a massively separated flow was explored experimentally over a cantilevered, swept, and tapered model having a deflected control surface. The interaction of one synthetic jet with the local flow led to a flow field associated with formation and advection of vortex rings that bent into the flow, resulting in flow reattachment in their trajectory. Under specific conditions, when multiple jets were actuated, their interaction was either constructive or distractive, depending on the separation severity and spanwise flow magnitude. This work improves control of three-dimensional flow separation using distributed actuators.

The finite jet determination problem for CR maps of positive codimension into Nash manifolds

We prove the first general finite jet determination result in positive codimension for CR maps from real-analytic minimal submanifolds M ⊂ C N $M\subset \mathbb {C}^N$ into Nash (real) submanifolds M ′ ⊂ C N ′ $M^{\prime }\subset \mathbb {C}^{N^{\prime }}$ . For a sheaf S $\mathcal {S}$ of C ∞ $\mathcal {C}^\infty$ -smooth CR maps from M $M$ into M ′ $M^{\prime }$ , we show that the non-existence of so-called 2-approximate CR S $\mathcal {S}$ -deformations from M $M$ into M ′ $M^{\prime }$ implies the following strong finite jet determination property: There exists a map ℓ : M → Z + $\ell \colon M\rightarrow {\mathbb {Z}}_+$ , bounded on compact subsets of M $M$ , such that for every point p ∈ M $p\in M$ , whenever f , g $f,g$ are two elements of S p $\mathcal {S}_p$ with j p ℓ ( p ) f = j p ℓ ( p ) g $j^{\ell (p)}_pf=j^{\ell (p)}_pg$ , then f = g $f=g$ . Applying the deformation point of view allows a unified treatment of a number of classes of target manifolds, which includes, among others, strictly pseudoconvex, Levi–non-degenerate, but also some particularly important Levi-degenerate targets, such as boundaries of classical domains.

Addendum to “Stationary discs and finite jet determination for non-degenerate generic real submanifolds” [Adv. Math. 343 (2019) 910–934

We previously introduced a new notion of non-degeneracy for generic real submanifolds in CN. The definition is however not complete and the purpose of this addendum is to complete it.

Stationary discs and finite jet determination for CR mappings in higher codimension

We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a C2-smooth CR diffeomorphism of two C4-smooth strictly pseudoconvex Levi generating CR manifolds is uniquely determined by its 2-jet at a given point. A new key element of the proof is the existence of non-defective stationary discs.

The automorphism group and limit set of a bounded domain I: The finite type case

For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to Aut(Bk). Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2k−1. As applications we prove a new finite jet determination theorem and a Tits alternative theorem. The geometry of the Kobayashi metric plays an important role in the paper.

A Numerical Model for Heat Transfer in Dry and Wet Grinding Based on the Finite Difference Method and Jet Cooling

AbstractGrinding is a promising machining method for finishing workpieces that need a smooth surface with tight tolerances. Due to the high thermal energy generated in the grinding zone, an accurate prediction of workpiece temperature plays a crucial role in the design and optimization of the grinding process. Finite difference method (FDM) is used for simulating the temperature distribution in a workpiece subjected to shallow grinding using a DuFort–Frankel explicit scheme. Moreover, two simple methods, one for modeling the effect of material removal in shallow grinding and the other for calculating the heat partition, are presented. A semi-empirical correlation of cooling jet is applied to calculate the convection heat transfer coefficient (CHTC) over the grinding surface. Experiments were carried out to verify the simulation results, and a good agreement was observed between the simulation and experimental data. An analysis of the results indicated that the misestimation of workpiece temperature could occur when the effect of the material removal rate is not considered in the simulation. The simulation results showed that the heat flux flow is one-dimensional for a high Peclet number, while a two-dimensional heat flux flow prevails for a low Peclet number. The results revealed that reducing the Peclet number and extending the depth of cut increase the heat partition. The study of wet grinding demonstrated that, for efficient cooling, the coolant should be applied directly to the contact zone. Moreover, using water-based emulsion as a coolant was more effective than palm and sunflower oils.

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.

Local isometric immersions of pseudo-spherical surfaces and kth order evolution equations

We consider the class of evolution equations of the form [Formula: see text], [Formula: see text], that describe pseudo-spherical surfaces. These were classified by Chern and Tenenblat in [Pseudospherical surfaces and evolution equations, Stud. Appl. Math 74 (1986) 55–83.]. This class of equations is characterized by the property that to each solution of such an equation, there corresponds a 2-dimensional Riemannian metric of constant curvature [Formula: see text]. Motivated by the special properties of the sine-Gordon equation, we investigate the following problem: given such a metric, is there a local isometric immersion in [Formula: see text] such that the coefficients of the second fundamental form of the immersed surface depend on a jet of finite order of [Formula: see text]? We extend our earlier results for second-order evolution equations [N. Kahouadji, N. Kamran and K. Tenenblat, Local isometric immersions of pseudo-spherical surfaces and evolution equations, Fields Inst. Commun. 75 (2015) 369–381; N. Kahouadji, N. Kamran and K. Tenenblat, Second-order equations and local isometric immersions of pseudo-spherical surfaces, Comm. Anal. Geom. 24(3) (2016) 605–643.] to [Formula: see text]th order equations by proving that there is only one type of equation that admit such an isometric immersion. More precisely, we prove under the condition of finite jet dependency that the coefficients of the second fundamental forms of the local isometric immersion determined by the solutions [Formula: see text] are universal, i.e. they are independent of [Formula: see text]. Moreover, we show that there exists a foliation of the domain of the parameters of the surface by straight lines with the property that the mean curvature of the surface is constant along the images of these straight lines under the isometric immersion.

Jet determination of smooth CR automorphisms and generalized stationary discs

We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in mathbb {C}^{n+1} by constructing generalized stationary discs glued to such hypersurfaces.

Jet veto resummation with jet rapidity cuts

Jet vetoes are widely used in experimental analyses at the LHC to distinguish different hard-interaction processes. Experimental jet selections require a cut on the (pseudo)rapidity of reconstructed jets, |ηjet| ≤ ηcut. We extend the standard jet-pT (jet-veto) resummation, which implicitly works in the limit ηcut → ∞, by incorporating a finite jet rapidity cut. We also consider the case of a step in the required pTcut at an intermediate value of |η| ≃ 2.5, which is of experimental relevance to avoid the increased pile-up contamination beyond the reach of the tracking detectors. We identify all relevant parametric regimes, discuss their factorization and resummation as well as the relations between them, and show that the phenomenologically relevant regimes are free of large nonglobal logarithms. The ηcut dependence of all resummation ingredients is computed to the same order to which they are currently known for ηcut → ∞. Our results pave the way for carrying out the jet-veto resummation including a sharp cut or a step at ηcut to the same order as is currently available in the ηcut → ∞ limit. The numerical impact of the jet rapidity cut is illustrated for benchmark qoverline{q} and gg initiated color-singlet processes at NLL′+NLO. We find that a rapidity cut at high ηcut = 4.5 is safe to use and has little effect on the cross section. A sharp cut at ηcut = 2.5 can in some cases lead to a substantial increase in the perturbative uncertainties, which can be mitigated by instead using a step in the veto.

Stationary discs and finite jet determination for non-degenerate generic real submanifolds

Let M⊂CN be a generic real submanifold of class C4. In case M is Levi non-degenerate in the sense Tumanov, we construct stationary discs for M. If furthermore M satisfies an additional non-degeneracy condition, we apply the method of stationary discs to obtain 2-jet determination of CR automorphisms of M.

The necessity for boundary corrections in a standard practice for the open-jet wind tunnel testing of automobiles

This paper is intended to provide a summary of the necessary adjustments required for road-representative open-jet wind tunnel measurements on automobiles. The open-jet wind tunnel provides accurate measurements, but they are made in a finite-sized jet that differs from the unconfined open-road conditions. Furthermore, measurements on a given automobile made in different open-jet wind tunnels disagree with each other, and with measurements in closed-wall wind tunnels that were corrected for the influences of their solid boundaries. There appears to be reticence at some company levels to making ‘corrections’ to open-jet measurements. Perhaps non-specialist managers think that the need for a ‘correction’ means an erroneous measurement. It does not! Any high-quality wind tunnel measurement is accurate, but it needs to be ‘calibrated’ to on-road conditions through an appropriate set of procedures. Closed-wall wind tunnels measure higher drag coefficients, in comparison with those in an unconstrained on-road flow. Open-jet wind tunnels frequently measure a lower value. The closed-wall adjustments lower the drag coefficient to the unconstrained value. Open-jet adjustments should also adjust the drag coefficient to the same unconstrained value. This paper explores the range of effects from the finite jet and elucidates the effectiveness of a two-measurement correction procedure. It is shown that not every data point must be measured twice, only a small selected subset. Since approximately 20% of tunnel occupancy is in the fan-on condition, then the additional cost of correct accurate on-road-equivalent data is low.

Complete spelling rules for the Monster tower over three-space

The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projective bundle over the previous. Moreover, each level is a fiber compactified jet bundle equipped with an action of finite jets of the diffeomorphism group. There is a correspondence between points in the tower and curves in the base manifold. These points admit a stratification which can be encoded by a word called the RVT code. Here, we derive the spelling rules for these words in the case of a three dimensional base. That is, we determine precisely which words are realized by points in the tower. To this end, we study the incidence relations between certain subtowers, called Baby Monsters, and present a general method for determining the level at which each Baby Monster is born. Here, we focus on the case where the base manifold is three dimensional, but all the methods presented generalize to bases of arbitrary dimension.

A Compact Autonomous Underwater Vehicle With Cephalopod-Inspired Propulsion

AbstractIn this paper, a bioinspired, compact, cost-effective autonomous underwater vehicle system is presented. Designed to operate in a heterogeneous, multivehicle collaboration hierarchy, the presented vehicle design features 3D printing technology to enable fast fabrication with a complex internal structure. Similar to a previous vehicle prototype, this system generates propulsive forces by expelling unsteady, pulsed jets, inspired by the locomotion of cephalopods and jellyfish. The novel thrusters enable the vehicle to be fully actuated in horizontal plane motions, without sacrificing the low-forward-drag, slender vehicle profile. By successively ingesting water and expelling finite water jets, periodic actuation forces are generated at all possible vehicle velocities, eliminating the need for control surfaces used in many conventional underwater vehicle designs. A semiactive buoyancy control system, inspired by the nautilus, adjusts the vehicle depth by passively allowing water flowing into and actively expelling water out of an internal bladder. A compact embedded system is developed to achieve the control and sensing capabilities necessary for multiagent interactions with the minimum required processing power and at a low energy cost. The new vehicle design also showcases an underwater optical communication system for short-range, high-speed data transmission, supplementing the conventional acoustic communication system. Experimental results show that, with the thruster motors powered at a 60% duty-cycle, the new vehicle is able to achieve a 1/4 zero-radius turn in 3.5 s and one-body-width sway translation in 2.5 s.