Finite Radius Research Articles

Application of infinite line source and cylindrical‐perfect‐conductors theories to heat pulse measurements with large sensors

AbstractThe infinite line source (ILS) theory for soil thermal property determination with heat pulse (HP) sensors is simple and widely‐used, but ignores the finite probe radius (r) and heat capacity (Cp). The cylindrical‐perfect‐conductors (CPC) theory, which accounts for r and Cp by using the identical‐cylindrical‐perfect‐conductors (ICPC) or the dissimilar‐cylindrical‐perfect‐conductors (DCPC) approaches, can be applied to estimate soil thermal property values with improved accuracy. In this study, the ILS and CPC theories were evaluated, and the finite r and Cp effects were quantified using numerical simulations and laboratory measurements with a large HP sensor of dissimilar probes. The errors due to finite probe properties were saturation dependent: Dry soils had a 14% reduction in the maximum temperature rise of the HP signal, while only slight temperature differences occurred in wet sandy soils. The finite probe effects were minor on ICPC‐ and DCPC‐thermal property values with relative errors generally less than 5%, but the absolute values of relative errors for dry soils were greater than 6%. Errors caused by ignoring the finite probe effects changed linearly with the ratio of soil heat capacity (C) versus C of the heating and sensing probes. The dissimilar probe r had negligible effect on HP signals and thermal property estimates with the specific sensor used in this study. The effects of finite probe size and properties should be considered in HP sensor design. The CPC theory is recommended for estimating soil thermal properties with large HP sensors.

Importance of gyrokinetic exact Fokker-Planck collisions in fusion plasma turbulence.

Gyrokinetic simulations of turbulence are fundamental to understanding and predicting particle and energy loss in magnetic fusion devices. Previous works have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius effects. This work moves beyond models to demonstrate important corrections using a gyrokinetic Fokker-Planck collision operator with the exact field-particle terms, in realistic simulations of turbulence in magnetically confined fusion plasmas. The exact operator shows significant corrections for temperature-gradient-driven trapped electron mode turbulence and zonal flow damping, and for microtearing modes in a Joint European Torus pedestal under ITER-like wall conditions. Analysis of the corrections using parameter scans motivates an accurate model which closely reproduces the exact results while reducing computational demands.

Spatial distribution of atomic electronic density for elements 1–54 as coming from a Hartree–Fock treatment within the minimum atomic parameters paradigm

AbstractThe minimum atomic parameters/Moscow–Aachen–Paris (MAP) basis sets—reintroduced in the previous paper—are analyzed with respect to spatial features as orbital shape, possible fits to alternative orbital sets (numerical or quasi‐numerical orbitals, nodeless Slater orbitals), respect of Kato's condition and radial distribution of energy components. For comparing orbital spaces the Frobenius angle between the orbital subspaces they span is introduced as numerical tool. It is shown that the electronic density of the MAP states is depleted around the nucleus with respect to the other orbital sets. Despite this, the similarity between the respective subspaces in all cases (except a unique case of the Pd atom) as measured by the cosine of the Frobenius angle amounts above 0.96 for all atoms. Deviations from the perfect value of Kato's condition amounts systematically to 0.3 and 0.5 for all elements considered. Integrating one‐electron energy contributions from r = ∞ to a finite radius, MAP and Bunge orbitals show about the same values, but for the inner region governed by the polynomial oscillations.

Key impact of phase dynamics and diamagnetic drive on Reynolds stress in magnetic fusion plasmas

Reynolds stress is a key facet of turbulence self-organization. In the magnetized plasmas of controlled fusion devices, the zonal flows that are driven by the averaged Reynolds stress modify the confinement performance. We address this problem with full-f gyrokinetic simulations of ion temperature gradient-driven turbulence. From the detailed analysis of the three-dimensional electric potential and transverse pressure fields, we show that the diamagnetic contribution to the Reynolds stress—stemming from finite Larmor radius effects—exceeds the electrostatic contribution by a factor of about two. Both contributions are in phase, indicating that pressure does not behave as a passive scalar. In addition, the Reynolds stress induced by the electric drift velocity is found to be mainly governed by the gradient of the phase of the electric potential modes rather than by their magnitude. By decoupling Reynolds stress drive and turbulence intensity, this property indicates that a careful analysis of phase dynamics is crucial in the interpretation of experiments and simulations.

A substrate for brane shells from Toverline{T}

A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace Toverline{T} . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

Gyrokinetic theory of low-frequency electromagnetic waves in finite-β anisotropic plasmas

We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than the ion cyclotron frequency in finite-β anisotropic uniform plasmas. Here, β is the ratio between plasma and magnetic pressures. Kinetic effects due to both the finite Larmor radii and wave-particle resonances are fully kept in the analysis. Corresponding linear dispersion relation and wave polarizations, valid for general β value and perpendicular wavelength, are then specifically derived for a bi-Maxwellian plasma. Analytic expressions for the criteria of kinetic firehose and mirror instabilities are also given. The mode frequency, stability, and wave polarization of a broad spectrum of normal modes are then investigated numerically in a systematic study over a set of parameters. Our study clearly demonstrates that, due to the finite ion Larmor radius effect, the ion-sound wave, mirror mode, and shear Alfvén wave are intrinsically coupled.

Fermionic Condensate on Finite Radius Cones

The fermionic condensate is investigated for a field localized on a finite radius 2- dimensional cone in the presence of a magnetic flux threading the cone apex. On the edge of the cone a boundary condition is imposed that differs from the MIT bag boundary condition, most frequently used for the confinement of fermions. The fermionic condensate is decomposed into the boundary-free and edge-induced contributions. Both these parts are periodic functions of the magnetic flux with the period equal to the flux quantum.

Spatio-temporal modulation of self-assembled central aggregates of buoyant colloids in sessile droplets using vapor mediated interactions

A functional sessile droplet containing buoyant colloids (ubiquitous in applications like chemical sensors, drug delivery systems, and nanoreactors) forms self-assembled aggregates. The particles initially dispersed over the entire drop-flocculates at the center. We attribute the formation of such aggregates to the finite radius of curvature of the drop and the buoyant nature of particles. Initially, larger particles rise to the top of the droplet (due to higher buoyancy force), and later the smaller particles join the league, leading to the graded size distribution of the central aggregate. This can be used to segregate polydisperse hollow spheres based on size. The proposed scaling analysis unveils insights into the distinctive particle transport during evaporation. However, the formation of prominent aggregates can be detrimental in applications like spray painting, sprinkling of pesticides, washing, coating, lubrication, etc. One way to avoid the central aggregate is to spread the droplets completely (contact angle ~ 00), thus theoretically creating an infinite radius of curvature leading to uniform deposition of buoyant particles. Practically, this requires a highly hydrophilic surface, and even a small inhomogeneity on the surface would pin the droplet giving it a finite radius of curvature. Here, we demonstrate using non-intrusive vapor mediated Marangoni convection (Velocity scale ~ O(103) higher than the evaporation-driven convection) can be vital to an efficient and on-demand manipulation of the suspended micro-objects. The interplay of surface tension and buoyancy force results in the transformation of flow inside the droplet leads to spatiotemporal disbanding of agglomeration at the center of the droplet.

Dispersion relations for waves in visco-gravitating anisotropic magnetoplasmas

The effect of Braginskii's full viscosity tensor on an infinite non-conducting, gravitating anisotropic plasma in which the medium is trapped in a strong magnetic field is discussed in the context of Braginskii's magnetohydrodynamic model with Chew–Goldberger–Low double adiabatic approximation and finite Larmor radius (FLR) correction. Through linearization of the perturbed equations, the general dispersion relation is derived for the separate compression, shear, and drift viscosity components as well as the FLR corrections. We investigate the stability for parallel and transverse perturbations with respect to the direction of the magnetic field, and both gravitational and fire-hose instabilities are found. The role of each viscous term is to suppress instability, but each component works in different ways. The FLR acts in a way that is very similar to the drift viscosity. The instability threshold is found to be independent of viscosity for compression and shear viscosity, but both the drift viscosity and FLR corrections can change the critical wavenumber for the instability. The compression viscosity is most effective at reducing the growth rate of the gravitational instability, whereas the shear viscosity works to suppress the fire-hose instability. The result of the present study may be useful for the study of large scale compression, shear, and drift plasma flow in and around clusters of galaxies and galactic disks and for the solar and stellar wind.

Magnetic field penetration through a circular aperture in a perfectly conducting plate excited by a coaxial loop

The transmission of an electromagnetic field produced by a current loop of finite radius through a coaxial circular aperture in a perfectly conducting plate is evaluated through a rapidly convergent formulation in an exact form. By applying the equivalence principle, the problem is first formulated in the Hankel transform domain, obtaining a set of dual integral equations in which the equivalent surface magnetic current density defined on the aperture is not known. The set of dual integral equations is regularised in a second-kind Fredholm integral equation by applying the Abel integral-transform technique. The solution is achieved by expanding the unknown in a set of orthogonal basis functions that correctly reproduce the behaviour of the equivalent magnetic current at the edge of the aperture. Finally, under particular assumptions, a low-frequency solution is extracted in a closed form. Numerical results are reported to validate the accuracy and efficiency of the proposed formulations.

Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis

A $$(2+2)$$ -dimensional kinetic equation, directly inspired by the run-and-tumble modeling of chemotaxis dynamics is studied so as to derive a both “2D well-balanced” and “asymptotic-preserving” numerical approximation. To this end, exact stationary regimes are expressed by means of Laplace transforms of Fourier–Bessel solutions of associated elliptic equations. This yields a scattering S-matrix which permits to formulate a time-marching scheme in the form of a convex combination in kinetic scaling. Then, in the diffusive scaling, an IMEX-type discretization follows, for which the “2D well-balanced property” still holds, while the consistency with the asymptotic drift-diffusion equation is checked. Numerical benchmarks, involving “nonlocal gradients” (or finite sampling radius), carried out in both scalings, assess theoretical findings. Nonlocal gradients appear to inhibit blowup phenomena.

Random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids

We present a random matrix approach to study the general vibrational properties of stable amorphous solids with translational invariance using the correlated Wishart ensemble. Within this approach, both analytical and numerical methods can be applied. Applying the random matrix theory to the correlated Wishart ensemble, we found the analytical form of the vibrational density of states and the dynamical structure factor. The ratio between the number of bonds and the number of degrees of freedom controls the Ioffe-Regel frequency, which determines the crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, whose frequency is close to the Ioffe-Regel crossover. In the isostatic case, we obtain the low-frequency cusplike singularity of the vibrational density of states, which was observed numerically. We also present a simple numerical random matrix model with finite interaction radius, whose properties rapidly converge to the analytical results with increasing the interaction radius. For a finite interaction radius, the numerical model demonstrates the presence of quasilocalized vibrations with a power-law low-frequency density of states.

Discontinuous solutions of the unsteady boundary-layer equations for a rotating disk of finite radius

Abstract

Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons

We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.

Comprehensive solutions for underwater tunnels in rock masses with different GSI values considering blast-induced damage zone and seepage forces

Rock excavation using drill and blast method is commonly used in tunneling world-wide. Drill and blast method has inherent disadvantage of deteriorating surrounding rock mass due to development of a blast-induced damage zone with reduced strength and stiffness parameters and increased permeability. Traditional tunnel analysis adopts same parameters for the entire rock mass, leading to the underestimation of tunnel stability. The blast damage zone with finite thickness is significant in tunnel stability. Tunneling below the groundwater table affects the hydraulic equilibrium. This will, in turn, cause seepage into the tunnel through the pores and discontinuities in the rock masses. The developed seepage force should be considered as an additional body force acting on both damaged and undamaged rock masses. This study presents a new analytical closed-form solution for the determination of stresses, strains, and displacements around a circular deep underwater tunnel with the consideration of the seepage forces and the damaged zone. The solutions are presented for tunnels excavated in pervious elastic–brittle–plastic rock masses with Mohr–Coulomb failure criterion. The damaged zone is assumed to have cylindrical shape with finite radius. The plastic zones may be formed in both damaged and undamaged rock masses, independently. In order to solve the proposed problem, three different paths for plasticity evolution including six different states that can possibly be encountered in the problem are considered. The results indicate that the seepage and the damaged zone have significant effects on the tunnel convergence and the distribution of stresses in the rock mass.

Classification theorem and properties of singular solutions to the Tolman–Oppenheimer–Volkoff equation

The Tolman–Oppenheimer–Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center. Hence, the thermodynamic consistency of the EoS precludes pathological solutions in which the integration terminates at finite radius (because of horizons, or divergences / zeroes of energy density). At the center, the mass function either vanishes (regular solutions) or it is negative (singular solutions). For singular solutions, the metric at the center is locally isomorphic to negative-mass Schwarzschild spacetime. This means that matter is stabilized because the singularity is strongly repulsive. We show that singular solutions are causally well behaved: they are bounded-acceleration complete, and they are conformal to a globally hyperbolic spacetime with boundary. Finally, we show how to modify unphysical equations of state in order to obtain non-pathological solutions, and we undertake a preliminary investigation of dynamical stability for singular solutions.

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r0. A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r0. As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. Good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

Influence of FLR correction on Jeans instability in rotating radiative QMHD fluid model

ABSTRACT The descriptive exploration of Jeans instability under the QMHD fluid model for magnetized radiative plasma, preserving the consequences of rotation and finite ion Larmor radius. The problem of equations is formulated by using the quantum magnetohydrodynamic fluid model. The general dispersion relations were achieved using a standard mode analysis by formulating a linearized equation set and the dispersion relations are explained in the transverse and parallel propagations of the magnetic field. Those latter particular situations are discussed in the light of the axis of rotation in the longitudinal and transverse magnetic field. From the numerical calculation, we observe that Jean's criteria are changed due to the existence of FLR corrections, the feature of radiation, quantum correction, and magnetic field. From the graphical presentation, we find that the effect of FLR correction with rotation, quantum correction, and the magnetic field is a more stabilizing impact on comparing the system than the simple gaseous plasma medium. The result demonstrates that the system's growth rate is affected by FLR, rotation, magnetic field, and quantum correction.

Helicity-dependent all-optical switching based on the self-trapped triplet excitons

Triplet excitons in organic materials are nonradiative and tightly bound as self-trapped ones due to the strong electron-lattice coupling. They exhibit a finite radius and long lifetime and so can be regarded as the isolated quantum dots. In this work, we theoretically demonstrate that the spin polarization of self-trapped triplet excitons can be coherently controlled by the short circularly polarized laser pulses, acting as a helicity-dependent all-optical switching effect. Such a switching can be achieved within dozens of femtoseconds and conducted in a reproducible manner. The pulse parameter dependence on the switching ratio is further investigated. Our calculation provides a theoretical foundation for exploring the ultrafast all-optical recording and information processing technique based on the organic materials.

Deep-MOND polytropes

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $\zeta(y)$ is (for $\gamma\not=1$) $[\int_0^y \zeta \bar y^2 d\bar y]^{1/2}=-yd(\zeta^{\gamma-1})/dy$. Or, $\theta^n(y)=y^{-2}[(y\theta')^2]'$, where $\theta=\zeta^{\gamma-1}$, and $n\equiv (\gamma-1)^{-1}$. I discuss properties of the solutions, contrasting them with those of their Newtonian analogues -- the Lane-Emden polytropes. Due to the stronger MOND gravity, all DML polytropes have a finite mass, and for $n<\infty$ ($\gamma>1$) all have a finite radius. (Lane-Emden spheres have a finite mass only for $n\le 5$.) I use the DML polytropes to study DML scaling relations. For example, they satisfy a universal relation (for all $\mathcal{K}$ and $\gamma$) between the total mass, $M$, and the mass-average velocity dispersion $\sigma$: $MGa_0=(9/4)\sigma^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\bar\sigma$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\bar\sigma,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $\gamma>1$), and all satisfy the above universal $M-\sigma$ relation. This more extended class of models exhibits the central-surface-densities relation: a tight relation between the baryonic and the dynamical central surface densities predicted by MOND.