Parabolic Region Research Articles

Magnetic properties of the amorphous Co-Fe-Cr-Si-B alloy after annealing in unsaturated magnetic field

The regularities of influence of temperature and intensity of a longitudinal magnetic field significantly less than the saturation field during annealing on the magnetic properties of an amorphous soft magnetic alloy based on Co have been studied. The possibility of the effectiveness of such treatment in comparison with traditional annealing without a field due to partial or complete suppression of stabilization of domain boundaries because of directional ordering is demonstrated. Annealing at temperatures below the Curie point with the application of unsaturated field exceeding the saturation field of the residual induction of an amorphous alloy in as-quenched state (40 A/m) showed the greatest efficiency compared with annealing without a field in terms of simultaneously reducing the coercive force Hc and increasing the low-field permeability µ0.3 and maximum permeability µmax. In comparison with non-field annealing, depending on the conditions of unsaturated magnetic field annealing, the possibility of reducing Hc by 39 %, increasing µmax by 4.5 times and µ0.3 by 3.8 times is shown. After annealing in unsaturated field on the magnetization curve of the alloy Co69Fe3.7Cr3.8Si12.5B11, the perminvar region, as well as the parabolic region where Rayleigh's law is fulfilled, end in lower fields than after annealing without a field. The results obtained are discussed taking into account the occurrence of various physical processes in the alloy during heat treatment.

From spectral cluster to uniform resolvent estimates on compact manifolds

It is well known that uniform resolvent estimates imply spectral cluster estimates. We show that the converse is also true in some cases. In particular, Sogge's universal spectral cluster estimates for the Laplace–Beltrami operator on closed Riemannian manifolds directly imply uniform resolvent estimates outside a parabolic region, without any reference to parametrices. The method is purely functional analytic and takes full advantage of the known spectral cluster bounds. This yields new resolvent estimates for manifolds with boundary or with low-regularity metrics, among other examples. Moreover, we show that the resolvent estimates are stable under perturbations and use this to establish uniform Sobolev and spectral cluster inequalities for Schrödinger operators with singular potentials.

Certain sufficient conditions for phi-like functions in a parabolic region

To obtain the main result of the present paper we use the technique of differential subordination. As special cases of our main result, we obtain sufficient conditions for $f\in\mathcal A$ to be $\phi-$like, starlike and close-to-convex in a parabolic region.

Experimental observation of a confined bubble moving in shear-thinning fluids

The motion of a long gas bubble in a confined capillary tube is ubiquitous in a wide range of engineering and biological applications. While the understanding of the deposited thin viscous film near the tube wall in Newtonian fluids is well developed, the deposition dynamics in commonly encountered non-Newtonian fluids remains much less studied. Here, we investigate the dynamics of a confined bubble moving in shear-thinning fluids with systematic experiments, varying the zero-shear-rate capillary number $Ca_0$ in the range of $O(10^{-3}\unicode{x2013}10^2)$ considering the zero-shear-rate viscosity. The thickness of the deposited liquid film, the bubble speed and the bubble front/rear menisci are measured, which are further rationalized with the recent theoretical studies based on appropriate rheological models. Compared with Newtonian fluids, the film thickness decreases for both the carboxymethyl cellulose and Carbopol solutions when the shear-thinning effect dominates. We show that the film thickness follows the scaling law from Aussillous & Quéré (Phys. Fluids, vol. 12, no. 10, 2000, pp. 2367–2371) with an effective capillary number $Ca_e$ , considering the characteristic shear rate in the film as proposed by Picchi et al. (J. Fluid Mech., vol. 918, no. A7, 2021, pp. 1–30). $Ca_e$ is calculated by the Carreau number and the power-law index from the Carreau–Yasuda rheological model. The shear-thinning effect also influences the bubble speed and delays the transition to the parabolic region in the bubble front and rear menisci. In particular, a high degree of undulations on the bubble surface results in an intricate rear viscosity distribution for the rear meniscus and the deviation between the experiments and theory may require a further investigation to resolve the axial velocity field. Our study may advance the fundamental understandings and engineering guidelines for coating processes involving thin-film flows and non-Newtonian fluids.

GEOMETRIC PROPERTIES OF MULTIVALENT FUNCTIONS ASSOCIATED WITH PARABOLIC REGIONS

The main purpose of this article is to derive the connections between the parabolic starlike and parabolic uniformly convex functions by applying an integral operator on multivalent functions. In addition, a parabolic region in the half-plane is introduced to study the family of parabolic multivalent convex functions of order a and type β.

Investigating the effect of position-dependent effective mass on the valence-band electronic states of GaAs/GaAsSb/GaAs parabolic quantum wells modulated by intense laser fields

This article has theoretically investigated the valence-band electronic properties of GaAs/GaAsSb/GaAs parabolic quantum well structures. To this end, an analytical expression has been developed to describe the position-dependent effective mass in the GaAsSb parabolic well region as a function of well geometry. Simultaneous effects of a non-resonant high-frequency intense laser field and an applied electric field have been studied using the Finite Element Method within the framework of the effective mass approximation. The laser-dressed confinement potential profile, bound states, and the corresponding wave functions have been examined as a function of geometric and structural parameters of GaAsSb well. The obtained numerical findings have shown that the well geometry was modulated to achieve a Gaussian-like profile from a parabolic shape and a double-well structure from a single-well one under intense laser irradiations. Simultaneous effects of intense laser and electric fields have indicated the formation of asymmetric geometric profiles from symmetric quantum well structures. The analysis of valence-band energy states has revealed pronounced blueshifts and redshifts in the electromagnetic energy spectrum, increasing the strength of the intense laser and applied electric fields. Studies have demonstrated that the valence-band electronic features were adjusted to alter the well half-width and the antimony concentration. These tunable valence-band-based properties can be profitable in designing and applying new devices operating in the optoelectronic field.

Application Of Strip Domain And Parabolic Region On Univalent Holomorphic Functions

In this paper, by using univalent functions connected with the strip domain,parabolic starlike and parabolic uniformly convex functions are introduced.Some relations between these classes are proved.

Approximation of Certain Non-vanishing Analytic Functions in a Parabolic Region

Approximation of Certain Non-vanishing Analytic Functions in a Parabolic Region

Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues

We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As an application, we obtain a parabolic region free of the transmission eigenvalues associated with the Maxwell equation.

Jet Collimation and Acceleration in the Giant Radio Galaxy NGC 315

Abstract We study the collimation and acceleration of jets in the nearby giant radio galaxy NGC 315, using multifrequency Very Long Baseline Array observations and archival High Sensitivity Array and Very Large Array data. We find that the jet geometry transitions from a semi-parabolic shape into a conical/hyperbolic shape at a distance of ≈105 gravitational radii. We constrain the frequency-dependent position of the core, from which we locate the jet base. The jet collimation profile in the parabolic region is in good agreement with the steady axisymmetric force-free electrodynamic solution for the outermost poloidal magnetic field line anchored to the black hole event horizon on the equatorial plane, similar to the nearby radio galaxies M87 and NGC 6251. The velocity field derived from the asymmetry in brightness between the jet and counterjet shows gradual acceleration up to the bulk Lorentz factor of Γ ∼ 3 in the region where the jet collimation occurs, confirming the presence of the jet acceleration and collimation zone. These results suggest that the jets are collimated by the pressure of the surrounding medium and accelerated by converting Poynting flux to kinetic energy flux. We discover limb brightening of the jet in a limited distance range where the angular resolution of our data is sufficient to resolve the jet transverse structure. This indicates that either the jet has a stratified velocity field of fast-inner and slow-outer layers or the particle acceleration process is more efficient in the outer layer owing to the interaction with the surroundings on parsec scales.

Shaping of melting and dissolving solids under natural convection

Abstract

Note on Instability Regions in the Circular Rayleigh Problem of Hydrodynamic Stability

Batchelor and Gill’s semicircular bound on the range of the complex wave velocity of an arbitrary unstable mode in the stability problem of inviscid incompressible homogeneous axial flows with respect to axisymmetric disturbances is further reduced. Significance In the circular Rayleigh problem of hydrodynamic stability, we have obtained a parabolic instability region. The significance of this result is that it depends on the discriminant $$\Psi (r)$$ which plays a vital role in deciding whether a basic axial flow is stable or not to axisymmetric disturbances. However, our parabolic instability region is an unbounded one unlike the semicircular instability region of Batchelor and Gill, which has the weakness that it does not depend on $$\Psi (r)$$ . So we have demonstrated that our parabola intersects the semicircle of Batchelor and Gill for two classes of basic flows, and consequently the semicircular instability region of Batchelor and Gill is further reduced. Moreover, we have stated the stability problem consisting of a second-order ODE and associated boundary conditions in three different but related variables. The significance of this is that further analytical results can be obtained for this problem, and some of these are presented in our subsequent paper.

An improved instability region for the extended Rayleigh problem of hydrodynamic stability

For the extended Rayleigh problem of hydrodynamics stability dealing with homogeneous shear flows with variable cross section, we have obtained a parabolic instability region. This improved parabolic instability region intersects with the semicircular instability region under certain condition. The validity of the result is illustrated with an example of basic flows. Furthermore, we have obtained a bound for the complex part of the phase velocity.

Lattice points in elliptic paraboloids

We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems.

On the Criterion for Long Wave Stability of Shear Flows

The present paper deals with the stability problem of incompressible, inviscid and density stratified fluid in a channel with arbitrary cross section. For this problem we derive a criterion for long wave stability namely, if the wave number is less than or equal to a critical wave number $$k_{c}$$ then the disturbances is stable. The result is illustrated with plane Poiseuille flow and Couette flow basic flows. Furthermore, we have obtained an upper bound for the growth rate of an unstable mode, which is sharper than the known ones. Moreover, a parabolic instability region which does not depend on any condition and which intersect the known semielliptical instability region is derived under some conditions.

Calculating bound states resonances and scattering amplitudes for arbitrary 1D potentials with piecewise parabolas

Even for one-dimensional (1D) potentials, the calculation of highly excited bound states and resonances (in particular broad and overlapping ones) often requires heavy numerical tools. The method presented here is based on representing an arbitrary 1D potential as a set of piecewise parabolas, where the solutions of the Schrödinger equation within each parabolic region are analytic. Outgoing, incoming, or zero-valued boundary conditions are imposed to solve for bound and resonance states, while asymmetric boundary conditions are enforced to calculate scattering amplitudes. The developed method is also applicable for complex potentials, as for example found in non-Hermitian symmetric systems (such as optical waveguides, where the spectrum varies from real to complex as a function of gain and loss). We demonstrate for several model Hamiltonians that calculations of energies, decay rates, scattering amplitudes, and wave functions are obtained in high accuracy and with minimal computational effort in comparison to other widely used methods. We believe our approach will be useful in many areas of physics and chemistry, and for example can be used to calculate various types of resonances, to solve scattering problems in cold molecular collisions, and to create analytical basis functions for multidimensional potentials.

Characteristics and model of the initial spray caused by an aircraft elastic tire rolling on the water-contaminated runway

The initial spray caused by a rolling aircraft elastic pneumatic tire is studied by Smoothed Particle Hydrodynamics method. The tire spray is divided into four types: bow wave, rooster tail, impact-generated side plume and wave-generated side plume. The distributions of the particles involved in the different types of spray in the initial unperturbed water film are studied, with the relationship between the momentum transfer, the relative position of water particles and the aircraft tire being proposed. The impact-generated side plume is caused by the direct impact of tire, while the wave-generated side plume is caused by the breakup of the wave developed by the tire. The particles involved in the wave-generated side plume all come from a parabolic region inside the strip of initial injected particles at a given time. The width of the parabolic region reduces with the increasing water depth. The strips and the kinematic characteristics of particles at any time are both similar. A model is developed to predict the direction and magnitude of the momentum transfer velocity in water film based on the similarity of the strips and the kinematic characteristics of the particles, which works well for the cases with small tire load and thick water film.

A Unified Instability Region for the Extended Taylor–Goldstein Problem of Hydrodynamic Stability

AbstractWe consider inviscid, incompressible shear flows with variable density and variable cross section. For this problem, we derived a new estimate for the growth rate of an unstable mode and a parabolic instability region which intersects semiellipse instability region under some condition.

Certain Results on Φ−Like and Starlike Functions in a Parabolic Region

Certain Results on Φ−Like and Starlike Functions in a Parabolic Region

Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body

The asymptotic behavior of the vorticity for the steady incompressible Navier–Stokes equations in a two-dimensional exterior domain is described in the case where the velocity at infinity u∞ is nonzero. It is well known that the asymptotic behavior of the velocity field is given by the fundamental solution of the Oseen system which is the linearization of the Navier–Stokes equation around u∞. Concerning the vorticity, the previous asymptotic expansions were relevant only inside a parabolic region called the wake region. Here we present an asymptotic expansion for the vorticity relevant everywhere. Surprisingly, the found asymptotic behavior is not given by the Oseen linearization and has a power of decay that depends on the data. This strange behavior is specific to the two-dimensional problem and is not present in three dimensions.