Jet Space Research Articles

上流境界層内に設置した噴流の設置間隔がキャビティ音に及ぼす影響

This work presents an experimental investigation for effects of the spanwise spacing of small-jets placed in the approaching boundary layer on cavity tone. The sound and velocity fields of a flow around a cavity were measured with a low noise wind tunnel. The freestream velocity was changed from U0 = 10 - 45 m/s. The depth-to-length ratio of the cavity was D/L = 0.5. The upstream boundary layer is laminar, and the boundary layer thickness is δ/L = 0.065 at U0 = 30 m/s. The effects of the jets from the wall in the upstream boundary layer with various spanwise spacing p/L = 0.1, 0.25, 0.4, 0.5, 0.6 and 1.0 on the cavity tone were investigated. The jet velocity was Uj = 3.0 m/s. The results show the cavity tone can be reduced by control of blowing jets. The control effect on the cavity tone depends on the spanwise spacing and velocity of blowing jets. In this experiment, the most effective spanwise spacing of jets for noise reduction was p/L = 0.4 - 0.6. The three-dimensional spanwise velocity field was induced by blowing jets. As a result, the spanwise coherence of the vortices inducing intense sound became weak, and the radiating sound became weak.

Natural Boundary Conditions in Geometric Calculus of Variations

Abstract In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of Y - the manifold of dependent and independent variables underlying a given problem - as well as the order of its Lagrangian. Our result follows from the natural behavior, under boundary-friendly transformations, of an operator, similar to the Euler map, constructed in the context of relative horizontal forms on jet bundles (or Grassmann fibrations) over Y . Explicit examples of natural boundary conditions are obtained when Y is an (n + 1)-dimensional domain in ℝn+1, and the Lagrangian is first-order (in particular, the hypersurface area).

Slanted vector fields for jet spaces

Low pole order frames of slanted vector fields are constructed on the space of vertical k-jets of the universal family of complete intersections in \(\mathbb {P} ^n\) and, adapting the arguments, low pole order frames of slanted vector fields are also constructed on the space of vertical logarithmic k-jets along the universal family of projective hypersurfaces in \(\mathbb {P} ^n\) with several irreducible smooth components. Both the pole order (here \(=5k-2\)) and the determination of the locus where the global generation statement fails are improved compared to the literature (previously \(=k^{2}+2k\)), thanks to three new ingredients: we reformulate the problem in terms of some adjoint action, we introduce a new formalism of geometric jet coordinates, and then we construct what we call building-block vector fields, making the problem for arbitrary jet order \(k\geqslant 1\) into a very analog of the much easier case where \(k=0\), i.e. where no jet coordinates are needed.

Numerical simulation of oxy-coal MILD combustion with high-velocity oxygen jets

For achieving efficient oxy-coal combustion in a MILD state, the optimum operating conditions with high-velocity jets in a lab-scale cylindrical furnace was determined. The flow characteristics, combustion temperature, ignition characteristics, emissions under different oxygen jet design and jet spacing were simulated and compared. The results show that the ignition temperature is 517 °C for Datong bituminous coal with an averaged particle size of 60 um; the ignition delay is approximately 10–15 ms under co-flow jets conditions and only 4 ms under coaxial jets condition. Under co-flow jets conditions, except for the case L = 75 mm, as the jet spacing increases, the oxidizer flow could be internally diluted to a lower concentration and preheated to a higher temperature, at least 1200 K. The maximum temperature increase in furnace is approximately 915 °C for L = 75 mm and 880 °C for coaxial jets, both are not MILD combustion. Co-flow jets with L = 30–60 mm are recommended, taking L = 30 mm condition as example, the combustion temperature fluctuated no more than 15%, and almost no CO and 50–70 ppm NO emission exist in the outlet of the furnace.

Partial extensions of jets and the polar distribution on Grassmannians of non-maximal integral elements

We study an intrinsic distribution, called polar, on the space of l-dimensional integral elements of the higher order contact structure on jet spaces. The main result establishes that this exterior differential system is the prolongation of a natural system of PDEs, named pasting conditions, on sections of the bundle of partial jet extensions. Informally, a partial jet extension is a kth order jet with additional (k+1)st order information along l of the n possible directions. A choice of partial extensions of a jet into all possible l-directions satisfies the pasting conditions if the extensions coincide along pairwise intersecting l-directions.We further show that prolonging the polar distribution once more yields the space of (l,n)-dimensional integral flags with its double fibration distribution. When l>1 the exterior differential system is holonomic, stabilizing after one further prolongation.The proof starts form the space of integral flags, constructing the tower of prolongations by reduction.

Automatic disruption classification in JET with the ITER-like wall

The new full-metal ITER-like wall at JET was found to have a deep impact on the physics of disruptions at JET. In order to develop disruption classification, the 10D operational space of JET with the new ITER-like wall has been explored using the generative topographic mapping method. The 2D map has been exploited to develop an automatic disruption classification of several disruption classes manually identified. In particular, all the non-intentional disruptions have been considered, that occurred in JET from 2011 to 2013 with the new wall. A statistical analysis of the plasma parameters describing the operational spaces of JET with carbon wall and JET ITER-like wall has been performed and some physical considerations have been made on the difference between these two operational spaces and the disruption classes which can be identified. The performance of the JET- ITER-like wall classifier is tested in real-time in conjunction with a disruption predictor presently operating at JET with good results. Moreover, to validate and analyse the results, another reference classifier has been developed, based on the k-nearest neighbour technique. Finally, in order to verify the reliability of the performed classification, a conformal predictor based on non-conformity measures has been developed.

The Latitudinal Dependence of Atmospheric Jet Scales and Macroturbulent Energy Cascades

Abstract The latitudinal width of atmospheric eddy-driven jets and scales of macroturbulence are examined latitude by latitude over a wide range of rotation rates using a high-resolution idealized GCM. It is found that for each latitude, through all rotation rates, the jet spacing scales with the Rhines scale. These simulations show the presence of a “supercriticality latitude” within the baroclinic zone, where poleward (equatorward) of this latitude, the Rhines scale is larger (smaller) than the Rossby deformation radius. Poleward of this latitude, a classic geostrophic turbulence picture appears with a − spectral slope of inverse cascade from the deformation radius up to the Rhines scale. A shallower slope than the −3 slope of enstrophy cascade is found from the deformation radius down to the viscosity scale as a result of the broad input of baroclinic eddy kinetic energy. At these latitudes, eddy–eddy interactions transfer barotropic eddy kinetic energy from the input scales of baroclinic eddy kinetic energy up to the jet scale and down to smaller scales. For the Earth case, this latitude is outside the baroclinic zone and therefore an inverse cascade does not appear. Equatorward of the supercriticality latitude, the − slope of inverse cascade vanishes, eddy–mean flow interactions play an important role in the balance, and the spectrum follows a −3 slope from the Rhines scale down to smaller scales, similar to what is observed on Earth. Moreover, the length scale of the energy-containing zonal wavenumber is equal to (larger than) the jet scale poleward (equatorward) of the supercriticality latitude.

Non-global logarithms, factorization, and the soft substructure of jets

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.

Feature extraction on local jet space for texture classification

The proposal of this study is to analyze the texture pattern recognition over the local jet space looking forward to improve the texture characterization. Local jets decompose the image based on partial derivatives allowing the texture feature extraction be exploited in different levels of geometrical structures. Each local jet component evidences a different local pattern, such as, flat regions, directional variations and concavity or convexity. Subsequently, a texture descriptor is used to extract features from 0th, 1st and 2nd-derivative components. Four well-known databases (Brodatz, Vistex, Usptex and Outex) and four texture descriptors (Fourier descriptors, Gabor filters, Local Binary Pattern and Local Binary Pattern Variance) were used to validate the idea, showing in most cases an increase of the success rates.

DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE INTERNALITY TO THE CONSTANTS

AbstractSuppose p is the generic type of a differential-algebraic jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown that p satisfies a certain strengthening of almost internality to the constants. This strengthening, which was originally called “being Moishezon to the constants” in [9] but is here renamed preserving internality to the constants, is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry. An example is given showing that only a generic analogue holds in the differential-algebraic case: there is a finite dimensional differential-algebraic variety X with a subvariety Z that is internal to the constants, such that the restriction of the differential-algebraic tangent bundle of X to Z is not almost internal to the constants.

Symmetries in Lagrangian Field Theory

By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first order jet bundles $J^1\pi$ of a fiber bundle $\pi:E\to {\mathbb R}^k$ where ${\mathbb R}^k$ is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.

Jacobi multipliers, non-local symmetries, and nonlinear oscillators

Constants of motion, Lagrangians, and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil’shchik, Vinogradov, and coworkers. Finally, the existence of non-local symmetries for such two nonlinear oscillators is proved.

Experimental and Numerical Investigations on Steady and Unsteady Jet Impingement Cooling for High-Power Electronics

Effective cooling of electronic equipment has emerged as a challenging and constraining problem of the 21st century. This paper reports the experimental and numerical investigations carried out to study the feasibility and effectiveness of steady and unsteady air jet impingement cooling used in high-power electronics. The results obtained from numerical studies are validated with the values obtained from experimental studies. Studies have been conducted to see the effects of parameters such as the Reynolds number, the period of pulse, and the ratio of jet spacing to diameter (Z/D) on the heat transfer characteristics. The Reynolds number is varied between 10000 and 20000 and the period of pulse is varied between 2 and 10 s. It is found that in both steady and unsteady jets, an optimum cooling is obtained when the Z/D ratio is 5. For a Reynolds of 20000, the stagnation heat transfer coefficient increases by 25% when an unsteady jet is used instead of a steady jet. A correlation is proposed for the Nusselt number in terms of the Reynolds number and this is valid for air as the cooling medium.

LES of density ratio effects on film cooling under rotating frame

A numerical study was conducted to investigate the performance of film cooling injection from a row of multiple square holes spaced laterally across a flat plate. LES with the standard Smagorinsky–Lilly model was used to investigate the dynamic mixing process between the coolant jet stream and the mainstream flows. The finite volume method and the unsteady PISO algorithm on a non-uniform staggered grid were applied. The values of rotation number (Ro) examined were 0.0, 0.03021, 0.06042, and 0.12084, jet spacing to jet width ratio (P/D) was 3.0, and a jet Reynolds number (Re) of 4700, which based on the hole width and the jet exit velocity. The effects of the coolant to mainstream density ratio (DR) on the film cooling effectiveness were investigated by injecting either nitrogen (DR = 0.98) or carbon dioxide (DR = 1.55) as the coolant streams. The effect of DR on the film-cooling effectiveness is coupled with varying velocity ratio (VR = 0.5 and 1.0). The coolant gas was injected at 90° to the mainstream flow. The flow fields of the present study were compared with experimental data in order to validate the reliability of the LES technique. It was shown that rotation has a strong impact on the jet trajectory behaviour and the film cooling effectiveness. In all cases, as the rotation number increases, the film effectiveness increases; this effect is increased as the velocity ratio increases. The results also showed the strong influence of velocity ratio on the flow field behaviour and the film cooling where the jet penetrates further into the cross flow as VR increases and the wake region increases with increasing VR. Furthermore, it was concluded that DR has only a minor effect on flow field and heat transfer at a constant velocity ratio.

The Dolbeault dga of the formal neighborhood of the diagonal

A well-known theorem of Kapranov states that the Atiyah class of the tangent bundle TX of a complex manifold X makes the shifted tangent bundle TX[-1] into a Lie algebra object in the derived category D(X) . Moreover, he showed that there is an L_\infty -algebra structure on the shifted Dolbeault resolution (\mathcal A^{\bullet-1}_X(TX),\overline{\partial}) of TX and wrote down the structure maps explicitly in the case when X is Kähler. The corresponding Chevalley-Eilenberg complex is isomorphic to the Dolbeault resolution (\mathcal A^{0,\bullet}_X(\mathcal{J}^\infty_X),\overline{\partial}) of the jet bundle \mathcal{J}^\infty_X via the construction of the holomorphic exponential map of the Kähler manifold. In this paper, we show that (\mathcal A^{0,\bullet}_X(\mathcal{J}^\infty_X),\overline{\partial}) is naturally isomorphic to the Dolbeault dga (\mathcal A^\bullet(X_{X \times X}\scriptscriptstyle {(\infty)},\overline{\partial}) associated to the formal neighborhood of the diagonal of X \times X which we introduced in [15]. We also give an alternative proof of Kapranov's theorem by obtaining an explicit formula for the pullback of functions via the holomorphic exponential map, which allows us to study the general case of an arbitrary embedding later.

Hyperbolicity of generic high-degree hypersurfaces in complex projective space

We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet differentials on the complex projective space to a hypersurface. The other is slanted vector fields of low vertical pole order on the vertical jet space of the universal hypersurface. We also present a number of related results, obtained by the same methods, such as: (i) a Big-Picard-Theorem type statement concerning extendibility, across the puncture, of holomorphic maps from a punctured disk to a generic hypersurface of high degree, (ii) nonexistence of nontrivial sets of entire functions satisfying certain polynomial equations with slowly varying coefficients, and (iii) Second Main Theorems for jet differentials and slowly moving targets.

Formula omitted]-algebras from multicontact geometry

I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I define higher codimensional versions of pre-contact structures as distributions on manifolds whose characteristic symmetries span a constant dimensional distribution. I call them pre-multicontact structures. Every distribution is almost everywhere, locally, a pre-multicontact structure. After showing that the standard symplectization of contact manifolds generalizes naturally to a (pre-)multisymplectization of (pre-)multicontact manifolds, I make use of results by C. Rogers and M. Zambon to associate a canonical L∞-algebra to any (pre-)multicontact structure. Such L∞-algebra is a multicontact version of the Jacobi bracket on a contact manifold. Unlike the multisymplecticL∞-algebra of Rogers and Zambon, the multicontactL∞-algebra is always a homological resolution of a Lie algebra. Finally, I describe in local coordinates the L∞-algebra associated to the Cartan distribution on jet spaces.

Robust global identifiability theory using potentials—Application to compartmental models

This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input–output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve.

Temperature field measurement of an array of laminar premixed slot flame Jets using Mach-Zehnder interferometry

An experimental study was performed to investigate the influence of Reynolds number (Re) and non-dimensional jet-to-jet spacing (S/Dh) on flame shape, structure and temperature field of an array of laminar premixed slot flame jets. Mach-Zehnder interferometry technique is used to obtain an insight to the overall temperature field between single, twin and triple slot flame jets. The slot jets with large aspect ratio (L/W), length of L=60mm and width of W=6mm were used to eliminate the three-dimensional effect of temperature field. The effect of jet-to-jet spacing was investigated on flame characteristics under the test conditions of 200≤Re≤400 and equivalence ratio (φ) of unity. The present measurement reveals that the variation of maximum flame temperature with increment of Reynolds number is mainly due to heat transfer effects and is negligible while the flame height is increased. For the cases of twin and triple flame jets by increasing Reynolds number and decreasing non-dimensional jet-to-jet spacing (S/Dh), the interferences between the jets are increased and the jets attracted each other. Strong interference was observed at S/Dh=1.15. For the case of triple jets at this S/Dh, the central jet was suppressed while the side jets deflected towards the inner jet. The interference between jets was found to reduce the heat flux in the jet-to-jet interacting zone due to incomplete combustion. Also the optimum jet-to-jet spacing of triple flame jets is obtained at each Reynolds number to enhance the heat transfer performance of the jets.

Exact renormalization group and higher-spin holography

In this paper, we revisit scalar field theories in $d$ space-time dimensions possessing $U(N)$ global symmetry. Following our recent work arXiv:1402.1430v2, we consider the generating function of correlation functions of all $U(N)$-invariant, single-trace operators at the free fixed point. The exact renormalization group equations are cast as Hamilton equations of radial evolution in a model space-time of one higher dimension, in this case $AdS_{d+1}$. The geometry associated with the RG equations is seen to emerge naturally out of the infinite jet bundle corresponding to the field theory, and suggests their interpretation as higher-spin equations of motion. While the higher-spin equations we obtain are remarkably simple, they are non-local in an essential way. Nevertheless, solving these bulk equations of motion in terms of a boundary source, we derive the on-shell action and demonstrate that it correctly encodes all of the correlation functions of the field theory, written as `Witten diagrams'. Since the model space-time has the isometries of the fixed point, it is possible to construct new higher spin theories defined in terms of geometric structures over other model space-times. We illustrate this by explicitly constructing the higher spin RG equations corresponding to the $z=2$ non-relativistic free field theory in $D$ spatial dimensions. In this case, the model space-time is the Schr\"odinger space-time, $Schr_{D+3}$.