Miracle-dz/UniFAR-FTUs huggingface dataset:
On fluid flows in precessing narrow annular channels: asymptotic analysis and numerical simulation

We consider a viscous, incompressible fluid confined in a narrow annular channel rotating rapidly about its axis of symmetry with angular velocity Ω that itself precesses slowly about an axis fixed in an inertial frame. The precessional problem is characterized by three parameters: the Ekman number E, the Poincaré number ε and the aspect ratio of the channel Γ. Dependent upon the size of Γ, precessionally driven flows can be either resonant or non-resonant with the Poincaré forcing. By assuming that it is the viscous effect, rather than the nonlinear effect, that plays an essential role at exact resonance, two asymptotic expressions for ε ≪ 1 and E ≪ 1 describing the single and double inertial-mode resonance are derived under the non-slip boundary condition. An asymptotic expression describing non-resonant precessing flows is also derived. Further studies based on numerical integrations, including two-dimensional linear analysis and direct three-dimensional nonlinear simulation, show a satisfactory quantitative agreement between the three asymptotic expressions and the fuller numerics for small and moderate Reynolds numbers at an asymptotically small E. The transition from two-dimensional precessing flow to three-dimensional small-scale turbulence for large Reynolds numbers is also investigated.
Physics of Airfoil Clocking in Axial Compressors

Axial compressors have inherently unsteady flow fields because of relative motion between rotor and statnr airfnils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead in progressively more complex wake/wake and wake/airfnil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. The current study uses an unsteady, two-dimensional thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of stator clocking in a low-speed 2 ½-stage compressor. Relative motion between rotors and stators is made possible by the use of systems of patched and overlaid grids. Results include surface pressures instantaneous forces and efficiencies for a 2 ½-stage compressor configuration.Copyright © 1997 by ASME
Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions

We present a Lyapunov-type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature, most results concerning existence and uniqueness are obtained under regularity assumptions of the coefficients with respect to the Wasserstein distance. Some existence and uniqueness results for irregular coefficients have been obtained by considering the total variation distance. Here, we extend this approach to the control of the solution in some weighted total variation distance, that allows us now to derive a rather general weak uniqueness result, merely assuming measurability and certain integrability on the drift coefficient and some non-degeneracy on the dispersion coefficient. We also present an abstract weak existence result for the solution of law-dependent stochastic differential equations with merely measurable coefficients, based on an approximation with law-dependent stochastic differential equations with regular coefficients under Lyapunov-type assumptions.
Stochastic Distributed Learning with Gradient Quantization and Variance Reduction

We consider distributed optimization where the objective function is spread among different devices, each sending incremental model updates to a central server. To alleviate the communication bottleneck, recent work proposed various schemes to compress (e.g.\ quantize or sparsify) the gradients, thereby introducing additional variance $\omega \geq 1$ that might slow down convergence. For strongly convex functions with condition number $\kappa$ distributed among $n$ machines, we (i) give a scheme that converges in $\mathcal{O}((\kappa + \kappa \frac{\omega}{n} + \omega)$ $\log (1/\epsilon))$ steps to a neighborhood of the optimal solution. For objective functions with a finite-sum structure, each worker having less than $m$ components, we (ii) present novel variance reduced schemes that converge in $\mathcal{O}((\kappa + \kappa \frac{\omega}{n} + \omega + m)\log(1/\epsilon))$ steps to arbitrary accuracy $\epsilon > 0$. These are the first methods that achieve linear convergence for arbitrary quantized updates. We also (iii) give analysis for the weakly convex and non-convex cases and (iv) verify in experiments that our novel variance reduced schemes are more efficient than the baselines.
Existence of a persistent hub in the convex preferential attachment model

A class of convex preferential attachment models is introduced. In this class a vertex of degree $k$ gets a new edge with probability proportional to some convex function of $k$, so this class includes many common generalizations of the Barab\'asi-Albert random graph. For this class we prove the existence with probability one of a vertex (called persistent hub) such that at all but finitely many moments of time it has the maximal degree in the graph.
Large deviation eigenvalue density for the soft edge Laguerre and Jacobi β-ensembles

We analyze the eigenvalue density for the Laguerre and Jacobi β-ensembles in the cases that the corresponding exponents are extensive. In particular, we obtain the asymptotic expansion up to terms o(1), in the large deviation regime outside the limiting interval of support. As found in recent studies of the large deviation density for the Gaussian β-ensemble, and Laguerre β-ensemble with fixed exponent, there is a scaling from this asymptotic expansion to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.
A link invariant related to Khovanov homology and knot Floer homology

In this paper we introduce a chain complex $C_{1 \pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of resolutions with differential d=d_0+d_1. We show that the E_2 page of the associated spectral sequence is isomorphic to the Khovanov homology of K, and that the total homology is a link invariant which we conjecture is isomorphic to \delta-graded knot Floer homology. The complex can be refined to a tangle invariant for braids on 2n strands, where the associated invariant is a bimodule over an algebra A_n. We show that A_n is isomorphic to B'(2n+1, n), the algebra used for the DA-bimodule constructed by Ozsvath and Szabo in their algebraic construction of knot Floer homology.
On the transposition anti-involution in real Clifford algebras II: stabilizer groups of primitive idempotents

In the first article [R. Abłamowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras I: The transposition map, Linear Multilinear Algebra, to appear] we showed that real Clifford algebras Cℓ(V, Q) possess a unique transposition anti-involution . The map reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of associated matrix of that element in the left regular representation of the algebra. In this article we show that, depending on the value of (p − q) mod 8, where ϵ = (p, q) is the signature of Q, the anti-involution gives rise to transposition, Hermitian complex and Hermitian quaternionic conjugation of representation matrices in spinor representations. We realize spinors in minimal left ideals S = Cℓ p,q f generated by a primitive idempotent f. The map allows us to define a dual spinor space S*, and a new spinor norm on S, which is different, in general, from two spinor norms known to exist. We study a transitive action of generalized Salingaros' multiplicative vee groups G p,q on complete sets of mutually annihilating primitive idempotents. Using the normal stabilizer subgroup G p,q (f), we construct left transversals, spinor bases and maps between spinor spaces for different orthogonal idempotents f i summing up to 1. We classify the stabilizer groups according to the signature in simple and semisimple cases.
Scaling of hydrogenic atoms and ions interacting with laser fields: Positronium in a laser field

Scaling laws are derived for hydrogenlike atoms and ions interacting with laser fields. In particular, the scaling of (appearance) intensities is derived. This scaling is independent of the physical mechanism responsible for the ionization process, be it tunneling or multiphoton ionization. It provides a firm basis and explanation for the validity of earlier models for the estimation of appearance intensities and of the extrapolation into the tunneling regime of scaling laws obtained through lowest-order perturbation theory. As an example of the applicability of the scaling laws, we calculate two-, three-, and six-photon generalized cross sections and ionization rates for positronium at laser frequencies of current experimental interest.
On $(N(k),\xi)$-semi-Riemannian manifolds: Semisymmetries

N (k), ξ)-semi-Riemannian manifolds are defined. Examples and properties of (N (k), ξ)-semi-Riemannian manifolds are given. Some basic re- lations involving Ta-curvature tensor in (N (k), ξ)-semi-Riemannian manifolds are proved. It is proved that if M is an n-dimensional ξ-Ta-flat (N (k), ξ)-semi- Riemannian manifold, then it is η-Einstein under an algebraic condition. It is also proved that a semi-Riemannian manifold, which is T -recurrent or T - symmetric, is always T -semisymmetric, where T is any tensor of type (1, 3). (Ta, Tb)-semisymmetric semi-Riemannian manifold is defined and studied. Sev- eral interesting results for Ta-semisymmetric, Ta-symmetric and Ta-recurrent (N (k), ξ)-semi-Riemannian manifolds are obtained. The definition of (Ta, STb )- semisymmetric semi-Riemannian manifold is given. (Ta, STb )-semisymmetric (N (k), ξ)-semi-Riemannian manifolds are classified. Some results for Ta-Ricci- semisymmetric (N (k), ξ)-semi-Riemannian manifolds are obtained.
COMPLEXITY OF LARGE TIME BEHAVIOUR OF EVOLUTION EQUATIONS WITH BOUNDED DATA

The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.
Natural weathering of oak (Quercus petrae) and chestnut (Castanea sativa) coated with various finishes

Weathering performance of Oak (Quercus petrae) and Chestnut (Castanea sativa) as well as various exterior coatings were investigated. Alkyd primer + alkyd paint and alkyd primer + alkyd resin varnish increased the glossiness in chestnut and oak, respectively. Besides, alkyd primer and acrylic stain had little effect on the change of the glossiness for both species. However, alkyd stain significantly decreased the glossiness not only for chestnut but also oak after weathering. Acrylic stain receded the total color change (ΔE*) compared with the alkyd paint or stain. Alkyd-based stain showed much better performance against atmospheric conditions compared with other coatings. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011
Continuous approximation of $ M_t/M_t/ 1 $ distributions with application to production

A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by a continuous drift-diffusion process a Smoluchowski equation on the half space is derived approximating the forward Kolmogorov equations. The approximate model is analyzed and validated, showing excellent agreement for the probabilities of all queue lengths and for all queuing utilizations, including ones that are very small and some that are significantly larger than one. Having an excellent approximation for the probability of an empty queue generates an approximation of the expected outflow of the queueing system. Comparisons to several well-established approximation from the literature show significant improvements in several numerical examples.
A Generalisation of Isomorphisms with Applications

In this paper, we study the behaviour of TF-isomorphisms, a natural generalisation of isomorphisms. TF-isomorphisms allow us to simplify the approach to seemingly unrelated problems. In particular, we mention the Neighbourhood Reconstruction problem, the Matrix Symmetrization problem and Stability of Graphs. We start with a study of invariance under TF-isomorphisms. In particular, we show that alternating trails and incidence double covers are conserved by TF-isomorphisms, irrespective of whether they are TF-isomorphisms between graphs or digraphs. We then define an equivalence relation and subsequently relate its equivalence classes to the incidence double cover of a graph. By directing the edges of an incidence double cover from one colour class to the other and discarding isolated vertices we obtain an invariant under TF-isomorphisms which gathers a number of invariants. This can be used to study TF-orbitals, an analogous generalisation of the orbitals of a permutation group.
Moving Boundary Problems for Quasi-Steady Conduction Limited Melting

The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that the crystal melts completely, extending previous results that hold for a special class of initial and boundary conditions. These new results, together with predictions for whether the crystal pinches off and breaks into two, are supported by numerical calculations using the level set method. The effects of surface tension are subsequently considered, leading to a canonical problem for near-complete-melting which is studied in linear stability terms and then solved numerically. A kinetic undercooling-type boundary condition is also considered. Our study is motivated in part by experiments undertaken as part of the Isothermal Dendritic Growth Experiment, in which dendritic crystals of pivalic acid were melted in an microgravity environment: these crystals were found to be prolate spheroidal in shape, with an aspect ratio initially increasing with time then rather abruptly decreasing to unity. Our asymptotic and numerical investigation sheds some light on these processes.
Faà di Bruno for operads and internal algebras

For any coloured operad R , we prove a Faà di Bruno formula for the ‘connected Green function’ in the incidence bialgebra of R . This generalises on one hand the classical Faà di Bruno formula (dual to composition of power series), corresponding to the case where R is the terminal reduced operad, and on the other hand the Faà di Bruno formula for P ‐trees of Gálvez–Kock–Tonks ( P a finitary polynomial endofunctor), which corresponds to the case where R is the free operad on P . Following Gálvez–Kock–Tonks, we work at the objective level of groupoid slices, hence all proofs are ‘bijective’: the formula is established as the homotopy cardinality of an explicit equivalence of groupoids, in turn derived from a certain two‐sided bar construction. In fact we establish the formula more generally in a relative situation, for algebras of one polynomial monad internal to another. This covers in particular nonsymmetric operads (for which the terminal reduced case yields the noncommutative Faà di Bruno formula of Brouder–Frabetti–Krattenthaler).
Faraday Rotation Measurements Using Incoherent Scatter

A complete description is given of the method used at the Jicamarca Radar Observatory to derive Faraday rotation information (and hence absolute electron density profiles that do not require subsequent normalization or correction for the effects of Te/Ti) from incoherent scatter data. Similar techniques which could be used at other observatories with radars not having the unusual properties of the Jicamarca radar are discussed. At temperate and polar latitudes the optimum frequencies for incoherent scatter Faraday measurements in most of the ionosphere are roughly 100–200 MHz. Somewhat higher frequencies should give acceptable daytime results, however. A slight modification of the Faraday measurement, used at Jicamarca to obtain the autocorrelation function of the scattered signal, is also briefly described.
A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces

Abstract The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H_{p}} to the Lebesgue space L p {L_{p}} for all 0 < p ≤ 1 {0<p\leq 1} . We also prove that the result is sharp in a particular sense.
There always is a variational source condition for nonlinear problems in Banach spaces

Variational source conditions proved useful for deriving convergence rates for Tikhonov's regularization method and also for other methods. Up to now such conditions have been verified only for few examples or for situations which can be handled by classical techniques, too. Here we show that for almost every ill-posed inverse problem variational source conditions are satisfied. Whether linear or nonlinear, whether Hilbert or Banach spaces, whether one or multiple solutions, variational source conditions are a universal tool for proving convergence rates.
Three-Dimensional Modeling of a Helixchanger® Heat Exchanger Using CFD

Abstract Detailed three-dimensional computational fluid dynamics (CFD) simulations have been performed to explore the performance of a helically baffled heat exchanger, commercially referred to as the Helixchanger ® heat exchanger. The CFD simulations employ the HEATX computer simulation program, which is designed for the simulation of shell-and-tube heat exchangers. The simulation accounts for the complex helical geometry of baffles, leakages, and nozzle entrance and exit. Three cases are presented that correspond to helix angles of 10°, 25°, and 40°, defined with respect to the radial axis. Inspection of the computed flows reveals distinct inner and outer regions, with the outer region showing a very desirable plug flow characteristic. The inner region, however, displays recirculation zones due to back mixing at the small helix angle, which suggests potential vibration problems but also creates a desirable temperature uniformity. A comparison with plug flow showed that the helically baffled heat exchanger had a fluid turn ratio of 0.64, 0.78, and 0.77 for the 10°, 25°, and 40° helix angles, indicating more overall plug-like flow for the higher helix angles. Computed pressure drops compare reasonably well with ABB Lummus Heat Transfer correlation results, although nozzle entrance and exit losses require further study.
Thermally driven hydromagnetic convection in a rapidly rotating sphere

Buoyancy-induced convection is investigated in a rapidly rotating, self-gravitating fluid sphere internally heated by a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance ϖ* from the rotation axis. Attention is restricted to relatively small magnetic field strengths (as measured by the parameter ∧) such that the dominant force balance remains geo-strophic. Convection is then confined to a thin cylindrical annulus, radius ϖ0*, about the rotation axis. A linear analysis is used to find the state of marginal stability together with the corresponding minimum critical value of the modified Rayleigh number, Rc (a measure of the buoyancy force required to maintain convective motions). Two distinct modes of instability are found to operate: ‘Rossby’ and ‘magnetic’. When no magnetic field is applied (∧ = 0), and when the Prandtl number σ ≪ 1, the instability takes the form of a thermally driven Rossby wave propagating eastward but with group velocity westward. Modifications to this mode due to a non-zero magnetic field result in Rc being a complicated function Rc(∧, q, σ), where q = k/η and σ = v/k with v, k and η denoting the viscous, thermal and magnetic diffusivities. When it has a significant effect [σ ≤ O(1)], the magnetic field inhibits the Rossby mode and convection moves towards the axis where the field is weaker (ϖ0*→ 0). The presence of the magnetic field also permits new modes of instability which are facilitated by increasing field strength, with Rc ∝ ∧─1. These magnetic modes propagate eastwards (westwards) when q < qm (q > qm) with qm ≈ 2.8. Of particular interest to the Earth is the limit q ≪ 1 where the marginally stable magnetic mode takes the form of an undamped buoyancy wave in an unstably stratified fluid. No diffusive processes are operating at leading order and the only effect opposing convection is the geostrophic constraint.
Trapped modes for periodic structures in waveguides

The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N‐1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly general hypotheses, including the special case where the obstacles consist of line segments placed parallel to the waveguide walls. Copyright © 2004 John Wiley & Sons, Ltd.
Points with finite orbits for trace maps

We study an action of ${\rm Aut}(F_n)$ on $\mathbb{R}^{2^n-1}$ by trace maps, defined using the traces of $n$-tuples of matrices in $\mathrm{SL}(2,\mathbb{C})$ having real traces. We determine the finite orbits for this action. These orbits essentially come from (i) the finite subgroups of $\mathrm{SL}(2,\mathbb C)$, and (ii) a dense set of (rational) points in an embedded quotient of an $n$-torus.
Digit Repetition Effect in Two-Digit Number Comparison

Previous data from two-digit number naming show that when target and prime numbers share one digit at different positions (e.g., target 28 and prime 86 or 72) an inhibition effect may be observed (Ratinckx, Brysbaert, & Fias, 2005). Such an effect has been ascribed to the mechanism of morpho-phonological transcoding from Arabic to verbal format. We evaluate the alternative hypothesis of an inhibition effect arising during the Arabic form processing when two different syntactic values have to be assigned to the same single digit. In Experiments 1 and 3, a digit repetition effect was observed in number comparison tasks, even when phonological transcoding is blocked by an articulatory suppression task. Conversely, Experiment 2 showed that no digit repetition effect can be found with number comparison of verbal written numbers. Results are compatible with an Arabic-syntactic processing stage, where units and decades are decomposed and where each single digit is activated and recognized.