Miracle-dz/UniFAR-FTUs huggingface dataset:
Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide

We consider an inverse medium scattering problem for the Helmholtz equation in a closed cylindrical waveguide with penetrable compactly supported scattering objects. We develop novel monotonicity relations for the eigenvalues of an associated modified near field operator, and we use them to establish linearized monotonicity tests that characterize the support of the scatterers in terms of near field observations of the corresponding scattered waves. The proofs of these shape characterizations rely on the existence of localized wave functions, which are solutions to the scattering problem in the waveguide that have arbitrarily large norm in some prescribed region, while at the same time having arbitrarily small norm in some other prescribed region. As a byproduct we obtain a uniqueness result for the inverse medium scattering problem in the waveguide with a simple proof. Some numerical examples are presented to document the potentials and limitations of this approach.
Modeling the Rapid Part of the Pressure-Diffusion Process in the Reynolds Stress Transport Equation

Modeling the pressure-diffusion process is discussed to improve the prediction of turbulent recirculating flows by a second moment closure. Since the recent DNS research of a turbulent recirculating flow by Yao et al. suggested that the pressure-diffusion process of the turbulence energy was significant in the recirculating region, the present study focuses on the rapid part of the process consisting of the mean shear. This rapid pressure-diffusion model is developed for the Reynolds stress equation using the two-component-limit turbulence condition and added to a low Reynolds number two-component-limit full second moment closure for evaluation. Its effects are discussed through applications of turbulent recirculating flows such as a trailing-edge and a back-step flows
Robust Stochastic Stability for a Class of Singular Systems with Uncertain Markovian Jump and Time‐Varying Delay

This paper deals with the problem of the robust stochastic stability for a class of singular systems with uncertain Markovian jump and time‐varying delay. Sufficient conditions on the stochastic stability are presented. The obtained results are formulated in terms of strict linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed approaches.
Thermal Distortion of Stiffened Plate due to Fillet Welds Computational and Experimental Investigation

ABSTRACT Prediction and control of thermal distortion is particularly important for the design and manufacture of multiply stiffened welded structures. This study aimed to develop and experimentally validate a comprehensive simulation tool to predict distortion, with particular emphasis on out-of-plane deformation generated in double-sided fillet-welded attachments. Simulation was used to optimise the relative positions of a twin-arc configuration, to give minimum out-of-plane deformation consistent with reasonable production time for single stiffener, double-fillet attachments. The critical buckling load of the structure was approached and exceeded as the arcs were brought closer and simulation allowed the influence of this factor to be determined.
The southern oscillation and long-range forecasting of the summer monsoon rainfall over India

Abstract The Indian summer monsoon rainfall and the Darwin pressure anomalies are examined for the 81-year period 1901–81. It is found that the tendency of the Darwin pressure anomaly before the monsoon season is a good indicator of the monsoon rainfall anomaly. During the 81-year period, there were only two instances (1901, 1941) when a negative tendency of winter (December, January, February) to spring (March, April, May) Darwin pressure anomaly was followed by a monsoon rainfall anomaly of less than minus one standard deviation; and only three instances (1916, 1933, 1961) when a positive tendency was followed by a rainfall anomaly of more than one standard deviation. Therefore, if the Darwin pressure anomaly during March, April and May is below normal, and if the Darwin seasonal pressure anomaly has been falling a non-occurrence of drought over India can be predicted with a very high degree of confidence. Similarly, above normal Darwin pressure during March, April and May, and increasing seasonal press.
Dynamic cohesive fracture: Models and analysis

Our goal in this paper is to initiate a mathematical study of dynamic cohesive fracture. Mathematical models of static cohesive fracture are quite well understood, and existence of solutions is known to rest on properties of the cohesive energy density ψ, which is a function of the jump in displacement. In particular, a relaxation is required (and a relaxation formula is known) if ψ′(0+) ≠ ∞. However, formulating a model for dynamic fracture when ψ′(0+) = ∞ is not straightforward, compared to when ψ′(0+) is finite, and especially compared to when ψ is smooth. We therefore formulate a model that is suitable when ψ′(0+) = ∞ and also agrees with established models in the more regular case. We then analyze the one-dimensional case and show existence when a finite number of potential fracture points are specified a priori, independent of the regularity of ψ. We also show that if ψ′(0+) < ∞, then relaxation is necessary without this constraint, at least for some initial data.
High Risk Scenarios and Extremes

Quantitative Risk Management (QRM) has become a field of research of considerable importance to numerous areas of application, including insurance, banking, energy, medicine, reliability. Mainly motivated by examples from insurance and finance, the authors develop a theory for handling multivariate extremes. The approach borrows ideas from portfolio theory and aims at an intuitive approach in the spirit of the Peaks over Thresholds method. The point of view is geometric. It leads to a probabilistic description of what in QRM language may be referred to as a high risk scenario: the conditional behaviour of risk factors given that a large move on a linear combination (portfolio, say) has been observed. The theoretical models which describe such conditional extremal behaviour are characterized and their relation to the limit theory for coordinatewise maxima is explained. The first part is an elegant exposition of coordinatewise extreme value theory; the second half develops the more basic geometric theory. Besides a precise mathematical deduction of the main results, the text yields numerous discussions of a more applied nature. A twenty page preview introduces the key concepts; the extensive introduction provides links to financial mathematics and insurance theory. The book is based on a graduate course on point processes and extremes. It could form the basis for an advanced course on multivariate extreme value theory or a course on mathematical issues underlying risk. Students in statistics and finance with a mathematical, quantitative background are the prime audience. Actuaries and risk managers involved in data based risk analysis will find the models discussed in the book stimulating. The text contains many indications for further research.
Some Remark on Optimal Stochastic Control with Partial Information

Abstract We are interested in the control problem of a partially observable diffusion process, which is initialized at a fixed point of ℝ n , and we want to characterize the associated value function. To resort to the theory of viscosity solutions depends on the possibility to translate such a problem on Hilbert spaces like L 2(ℝ n ), and so it can not be used here. Nevertheless, a result of N. Bouleau and F. Hirsch allows us to introduce a broadened problem which fulfills the condition. The fact remains to link these two control problems.
Recovery Guarantees For Quadratic Tensors With Sparse Observations

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a triple product, have emerged from applications such as recommendation systems. Non-convex methods are the method of choice for learning quadratic models, and this work examines their sample complexity and error guarantee. Our main result is that with the number of samples being only linear in the dimension, all local minima of the mean squared error objective are global minima and recover the original tensor. We substantiate our theoretical results with experiments on synthetic and real-world data, showing that quadratic models have better performance than CP models where there are a limited amount of observations available.
Coherence resonance in a Hodgkin-Huxley neuron

We study the nonlinear response of the Hodgkin-Huxley model without external periodic signal to the noisy synaptic current near the saddle-node bifurcation of limit cycles. The coherence of the system, estimated from the interspike interval histogram and from the power spectra of membrane potentials and spike trains, is maximal at a certain noise intensity, so that the coherence resonance occurs. The mechanism of this phenomenon is found to be different from previously studied models of coherence resonance and explained in terms of rigid excitations of periodic oscillations, and the combined effect of amplitude and phase fluctuations.
The structure of rational and ruled symplectic 4-manifolds

This paper investigates the structure of compact symplectic 4-manifolds (V, w) which contain a symplectically embedded copy C of S2 with nonnegative self-intersection number. Such a pair (V, C, w) is called minimal if, in addition, the open manifold V C contains no exceptional curves (i.e., symplectically embedded 2-spheres with self-intersection -1) . We show that every such pair (V, C, w) covers a minimal pair (V, C, c() which may be obtained from V by blowing down a finite number of disjoint exceptional curves in V C. Further, the family of manifold pairs (V, C, w) under consideration is closed under blowing up and down. We next give a complete list of the possible minimal pairs. We show that V is symplectomorphic either to ? p2 with its standard form, or to an S2-bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class. Moreover, this symplectomorphism may be chosen so that it takes C either to 2 a complex line or quadric in CP2, or, in the case when V is a bundle, to a fiber or section of the bundle. DEPARTMENT OF MATHEMATICS, STATE UNIVERSITY OF NEW YORK AT STONY BROOK, STONY BROOK, NEW YORK 11794-3651 E-mail address: dusa@math.sunysb. edu This content downloaded from 207.46. 13.145 on Wed, 27 Apr 2016 05:10:07 UTC All use subject to http://about.jstor. org/terms
Evolution of fission-fragment mass distributions in the neutron-deficient lead region

Low-energy ? -delayed fission of 194,196At and 200,202Fr was studied in detail at the mass separator ISOLDE at CERN. The fission-fragment mass distributions of daughter nuclei 194,196Po and 202Rn indicate a triple-humped structure, marking the transition between asymmetric fission of 178,180 Hg and symmetric fission in the light Ra-Rn nuclei. Comparison with the macroscopic-microscopic finite-range liquid-drop model and the self-consistent approach employing the Gogny D1S energy density functional yields discrepancies. This demonstrates once more the need for dynamical fission calculations, because for both models the potential-energy surfaces lack pronounced structures, in contrast to those for the actinide region.
Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10

Experiments were performed to measure the velocities of both phases in a monodispersed bubbly flow in a vertical column. Using water and water-glycerin mixtures, measurements were obtained for a range of Reynolds numbers from 10 to 500. For all cases, the Weber number was below 2. To generate a uniform stream of bubbles, an array of identical capillaries was used. To avoid coalescence, a small amount of salt was added to the interstitial fluid, which did not affect the fluid properties significantly. Measurements of the bubble phase velocity were obtained using a dual impedance probe and through high-speed digital video processing. A measurement of the vertical component of the fluctuating liquid velocity was obtained using a flying hotwire technique, which resolved the deficiency of this technique for flows with zero-mean velocity. To the best of our knowledge, this technique has not been used to study bubbly liquids in the past. It was found that for all cases, the bubble velocity decreases as the mean .
Measurement and modeling of homogeneous axisymmetric turbulence

A new method for modeling the unknown correlations in Reynolds stress transport equations is developed taking the kinematic relationship of turbulence tensors in homogeneous axisymmetric turbulence. Both the rapid-straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. The partition of the stress dissipation is also studied to assess the possible existence of local isotropy for turbulence at small scales. Homogeneous, axisymmetric turbulence is a simple flow, where the axes of anisotropy of the Reynolds stresses and dissipation tensor are found to be aligned. Using the theory of barycentric coordinates, the relationship between the Reynolds stress and dissipation tensors is derived, satisfying restrictions for the limiting states of turbulence and its assumed behavior for large Reynolds number and arbitrary anisotropy. The role of the anisotropy in constraining models for the turbulent dissipation rate and the pressure–strain correlations is discussed. Comparisons of the resulting closure based on barycentric coordinates with the experimental data for axisymmetric flow measurements of Ertunç and Durst (On the high contraction ratio anomaly of axisymmetric contraction of grid-generated turbulence, Phys. Fluids. 20, February 2008) are good within the limitations of the data.
Rotational excitation of molecular ions in interstellar clouds: HCO+ and HCS+

On a calcule les surfaces d'energie potentielle pour les systemes HCO + /He et HCS + /He. On en deduit les sections efficaces collisionnelles et les coefficients de vitesse pour l'excitation rotationnelle de HCO + et HCS + par collision avec l'helium. On discute des implications astrophysiques des resultats
A Multilevel Nonlinear Profile Analysis Model for Dichotomous Data

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than relying on the choice of different dissimilarity measures that produce different results, (b) item and person parameters are computed during the same estimation step with an appropriate distribution for dichotomous variables, (c) the model estimates profile coordinate standard errors, and (d) additional individual-level variables can be included to model relationships with the profile parameters. An application examined experimental differences in topographic map comprehension among 288 subjects. The model produced a measure of overall test performance or comprehension in addition to pattern variables that measured the correspondence between subject response profiles and an item difficulty profile and an item-discrimination profile. The findings suggested that subjects who used 3-dimensional maps tended to correctly answer more items in addition to correctly answering items that were more discriminating indicators of map comprehension. The NPA analysis was also compared with results from a multidimensional item response theory model.
Invisible metal-grid transparent electrode prepared by electrohydrodynamic (EHD) jet printing

Invisible Ag-grid transparent electrodes (TEs) were prepared by electrohydrodynamic (EHD) jet printing using Ag nano-particle inks. Ag-grid width less than 10 µm was achieved by the EHD jet printing, which was invisible to the naked eye. The Ag-grid line-to-line distance (pitch) was modulated in order to investigate the electrical and optical properties of the EHD jet-printed Ag-grid TEs. The decrease in the sheet resistance at the expense of the transmittance was observed as the Ag-grid pitch decreased. The figure of merit of Ag-grid TEs with various Ag-grid pitches was investigated in order to determine the optimum pitch condition for both electrical and optical properties. With the 150 µm Ag-grid pitch, the EHD jet-printed Ag-grid TE has the sheet resistance of 4.87 Ω sq−1 and the transmittance of 81.75% after annealing at 200 °C under near-infrared. Ag filling factor (FF) was defined to predict the electrical and optical properties of Ag-grid TEs. It was found that the measured electrical and optical properties were well simulated by the theoretical equations incorporating FF. The EHD jet-printed invisible Ag-grid TE with good electrical and optical properties implies its promising application to the printed optoelectronic devices.
Conjugated polymer in isolated and aggregated chain environments studied by amplified spontaneous emission

Aggregate formation of a conjugated polymer in solutions containing good and poor solvents is studied by amplified spontaneous emission (ASE). It is proved that ASE originates only from isolated polymer chains. For sufficient quantity of the poor solvent, aggregates are formed at the expense of the isolated chains, reducing substantially the optical gain. The critical polymer concentration for aggregation and the size distribution of the aggregates formed are determined by using a model based on thermodynamic principles. The number of isolated chains involved in aggregates of a specific size decreases as aggregates become larger incorporating up to seven chains.
Trefftz-discontinuous Galerkin methods for time-harmonic wave problems

Computer simulation of the propagation and interaction of linear waves is a core task in computational science and engineering. It is fundamentally important in a wide range of areas such as antenna design, atmospheric particle scattering, noise prediction, radar and sonar modelling, seismic and ultrasound imaging. The finite element method represents one of the most common discretization techniques for Helmholtz and Maxwell’s equations in bounded domains, which model time-harmonic acoustic and electromagnetic wave scattering, respectively. At medium and high frequencies, resolution requirements and the so-called pollution effect entail an excessive computational effort and prevent standard finite element schemes from an effective use. The wave-based methods offer a possible way to deal with this problem: the trial and test functions are built with special solutions of the underlying PDE inside each element, thus the information about the frequency is directly incorporated in the discrete spaces. This dissertation is concerned with a family of those methods: the socalled Trefftz-discontinuous Galerkin (TDG) methods. These include the wellknown ultraweak variational formulation (UWVF) invented by O. Cessenat and B. Després in the 1990’s. We derive a general formulation of the TDG method for Helmholtz and Maxwell impedance boundary value problems posed in bounded polygonal or polyhedral domains. We show the well-posedness of the scheme and its quasi-optimality in a mesh-dependent energy norm; a similar result in a meshindependent norm is obtained by using a duality argument. This leads to convergence estimates for plane and circular/spherical wave finite element spaces; the dependence of the bounds on the wavenumber is always made explicit. Some numerical experiments demonstrate the effectiveness of the method in the case of the Helmholtz equation. Several mathematical tools are needed for the analysis of the TDG method. In particular, we prove new best approximation estimates for the considered discrete spaces with the use of Vekua’s theory for elliptic equations and approximation results for harmonic polynomials. The duality argument used in the convergence analysis of the scheme in the case of the Maxwell equations requires new wavenumber-explicit stability and regularity results for the corresponding boundary value problem: these are proved with the use of a novel vector Rellich-type identity.
Controllability and a Multiplier Rule for Nondifferentiable Optimization Problems

Let K be a compact subset of a normed vector space $\mathcal{X}$, C a convex body in a Banach space $\mathcal{Y}$, $k_0 \in K$, $(\phi ,\Phi ):K \to \mathbb{R}^m \times \mathcal{Y}$ continuous, and $\Phi (k_0 ) \in C$. We introduce the concept of a “directional derivate container” $\Lambda ^\varepsilon (\phi ,\Phi )(k_0 )$ for $(\phi ,\Phi )$ at $k_0 $ whose definition is equivalent to that of a directional derivative in the special case where $(\phi ,\Phi )$ is “finitely $C^1 $,” that is, all the restrictions of $(\phi ,\Phi )$ to finite-dimensional convex subsets of K are continuously differentiable. In general, $(\phi ,\Phi )$ admits a (nonunique) directional derivate container at $k_0 $ if it can be uniformly approximated by finitely $C^1 $ functions $(\phi _i ,\Phi _i )$ whose directional derivatives in some “neighborhood” of $k_0 $ in K, viewed as functions on K to $\mathbb{R}^m \times \mathcal{Y}$, form a bounded and equicontinuous subset of $C(K,\mathbb{R}^m \times \mathcal{Y})$. For a given $\Lam.
Contribution to the nonlinear theory of plasma wave excitation inside the electron foreshock region

The authors study plasma waves generated in the foreshock region of the solar wind, where it impinges on the earth`s bow shock. These waves have been explained as originating from an instability mode of a beam type interaction with the background plasma. Here the authorts look at the nonlinear problem associated with the instability growth rates which result in stabilization of these waves. They show that the stabilization differs for waves propagating along the beam direction, and at a slight angle with respect to the beam direction.
On the scattering of aerodynamic noise

According to the Lighthill acoustic analogy, the sound induced by a region of turbulence is the same as that due to an equivalent distribution of quadrupole sources within the fluid. It is known that the presence of scattering bodies situated near such multipoles can convert some of their intense near field energy into the form of sound waves whose amplitude is far greater than that of the incident field. Calculations are here presented to determine the extent of this conversion, for hard and soft bodies of various shapes, making use of the reciprocal theorem to recast the problem into one of finding the field, near the obstacle, induced by an incident plane wave. If the obstacle is small compared with a wavelength, then its presence is equivalent to an additional dipole (or source) whose greater efficiency as a sound radiator implies that the familiar intensity law I ∝ U8, for far field intensity I against typical turbulence velocity U for an unbounded flow, is replaced by I ∝ U6 (or I ∝ U4) for a hard (or soft) body. For the situation where the scatterer is large compared with wavelength, the prototype problem of a wedge of exterior angle (p/q)π is shown to yield an intensity law I ∝ U4+2q/p for both hard and soft surfaces. This result is shown to hold for the more general ‘wedge-like’ surfaces, whose dimensions are large scale and whose edges may be smoothed out on a small scale, compared with wavelength. The method used involves the matching of an incompressible flow, on the fine scales typical of the edge geometry, to an outer flow determined by the large scale features of the surface. Favourable comparisons are made with previous results pertaining to the two-dimensional semi-infinite duct and to the half-plate of finite thickness.