Full Numerical Calculations Research Articles

L* neural networks from different magnetic field models and their applicability

The third adiabatic invariant L* plays an important role in modeling and understanding the radiation belt dynamics. The typical way to numerically calculate the L* value follows the method described by Roederer (1970), which is just a line integration method that is computationally slow and expensive. This work describes the application of an artificial neural network technique to a series of magnetospheric field models for calculating L* values in microseconds instead of seconds without losing significant accuracy, thereby delivering to the radiation belt community various L* neural networks. These neural networks will enable comprehensive solar‐cycle long studies of radiation belt processes and can also help the development of operational radiation belt models because of the speed in calculating L*. The main focus of this work is to test the applicability of each L* neural network, an aspect not addressed in the previous studies, under different interplanetary and magnetospheric conditions. Specifically, we describe the conditions when the neural network is providing a good approximation to the full numerical calculation of L* and when the traditional but more time‐consuming method should be used. These L* neural networks are available for download at http://lanlstar.net.

Heuristic drift-based model of the power scrape-off width in low-gas-puff H-mode tokamaks

A heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced. Grad B and curv B drifts into the scrape-off layer (SOL) are balanced against near-sonic parallel flows out of the SOL, to the divertor plates. The overall particle flow pattern posited is a modification for open field lines of Pfirsch–Schlüter flows to include order-unity sinks to the divertors. These assumptions result in an estimated SOL width of ∼2aρp/R. They also result in a first-principles calculation of the particle confinement time of H-mode plasmas, qualitatively consistent with experimental observations. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL width, derived above, with heat from the main plasma. The separatrix temperature is calculated based on a two-point model balancing power input to the SOL with Spitzer–Härm parallel thermal conduction losses to the divertor. This results in a heuristic closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and in scaling with recent experimental data. Further work should include full numerical calculations, including all magnetic and electric drifts, as well as more thorough comparison with experimental data.

On some integral equations arising in the pressure analysis of inclined wells in anisotropic formations

In this note we look at the effects of anisotropic permeability on the distribution of pressure around an uncased or cased wellbore. We suggest a useful approximation for the form of the density of point sources distributed around the wellbore in order to simulate its influence on the pressure field. We consider both steady state and transient pressure distributions and perform full numerical calculation of some examples to check the accuracy of the approximation.

Second-order and fluctuation-induced first-order phase transitions with functional renormalization group equations

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with $U(2)\times U(2)$ symmetry, in which there is a parameter $\lambda_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of $\lambda_2\to0$, the $U(2)\times U(2)$ theory is reduced to an $O(8)$ scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the $O(8)$ system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as $\lambda_2$ increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the $\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

Mechanism of cavitation bubble luminescence

We introduced briefly the main progress in the research of single bubble sonoluminescence, and summarized our theoretical calculation research of this topic. Solving the equations of fluid mechanics, we performed the full numerical calculation. We found that the mechanism of the cavitation bubble luminescence is high temperature, high pressure and high density gas light emission. Corresponding to the temperature approached inside the bubble, sometimes atomic or molecular line emission process dominates and sometimes the continuum contributes the most. With the research of single bubble shape instability, we found that it is the perturbation of spherical asymmetry of the driving acoustic pressure results in its upper threshold.

Feshbach resonances of harmonically trapped atoms

Employing a short-range two-channel description we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a new parameterization of the energy-dependent scattering length which differs from the one previously employed. We validate the model by comparison to full numerical calculations for Li-Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.

Numerical simulations of the laminar flow in pipes with wire coil inserts

Helical wire coils fitted inside a round pipe is a simple and well-known heat transfer enhancement technique in order to improve the overall performance of heat exchangers. Three-dimensional numerical simulations of the incompressible laminar flow that develops into smooth round pipes of diameter, d, with wire coil inserts of helical pitch, p, and diameter, e, have been accomplished with the finite volume method. In particular, we describe the behaviour of the Fanning friction factor, f, as a function of the Reynolds number, Re = ρUd/ μ, where, U = 4 Q/ πd 2, is the mean velocity based in the flow rate, Q, and ρ and μ the density and dynamic viscosity of the fluid, respectively. For a wire coil of 40 pitches in length with dimensionless pitch p/ d = 2.5 and dimensionless wire diameter e/ d = 0.074, both pitch-periodic and full domain numerical results have been validated with experiments. We have found an excellent agreement with both numerical models and experimental results for Re < 500, showing the friction factor a quasi-linear dependence on Re when is plotted in log–log axes. For 500 < Re < 600 both experimental and full domain numerical results of the values for the friction factor leave the quasi-linear trend observed for Re < 500. Our full domain numerical calculations reveal the onset of a linear instability into the range 500 < Re < 550 that becomes the flow unsteady and breaks the periodic axial pattern of the flow. The friction factor becomes constant in the range, 600 < Re < 850, and only the full numerical model shows a good agreement with the experimental results, but periodic numerical simulations fail. For 850 < Re, even the full domain laminar model fails due to the onset of turbulent outbreaks. Finally, the effect of the pitch on the friction factor has been addressed by performing a parametrical study with a pitch-periodic computational domain for wire coils within the dimensionless pitch range, 1.50 ⩽ p/ d ⩽ 4.50, and dimensionless wire diameter, e/ d = 0.074, showing that the increase of the nondimensional pitch, p/ d, decreases the friction factor.

Stochastic heating of a molecular nanomagnet

We study the excitation dynamics of a single molecular nanomagnet by static and pulsed magnetic fields. Based on a stability analysis of the classical magnetization dynamics we identify analytically the fields parameters for which the energy is stochastically pumped into the system in which case the magnetization undergoes diffusively and irreversibly a large angle deflection. An approximate analytical expression for the diffusion constant in terms of the fields parameters is given and assessed by full numerical calculations.

THE EFFECT OF A TIME-VARYING ACCRETION DISK SIZE ON QUASAR MICROLENSING LIGHT CURVES

Microlensing perturbations to the magnification of gravitationally lensed quasar images are dependent on the angular size of the quasar. If quasar variability at visible wavelengths is caused by a change in the area of the accretion disk, it will affect the microlensing magnification. We derive the expected signal, assuming that the luminosity scales with some power of the disk area, and estimate its amplitude using simulations. We discuss the prospects for detecting the effect in real-world data and for using it to estimate the logarithmic slope of the luminosity's dependence on disk area. Such an estimate would provide a direct test of the standard thin accretion disk model. We tried fitting six seasons of the light curves of the lensed quasar HE 0435-1223 including this effect as a modification to the Kochanek et al. (2006) approach to estimating time delays. We find a dramatic improvement in the goodness of fit and relatively plausible parameters, but a robust estimate will require a full numerical calculation in order to correctly model the strong correlations between the structure of the microlensing magnification patterns and the magnitude of the effect. We also comment briefly on the effect of this phenomenon for the stability of time delay estimates.

Tangential electroviscous drag on a sphere surrounded by a thin double layer near a wall for arbitrary particle–wall separations

When a charged particle moves along a charged wall in a polar fluid, it experiences an electroviscous lift force normal to the surface and an electroviscous drag, superimposed on the viscous drag, parallel to the surface. Here a theoretical analysis is presented to determine the electroviscous drag on a charged spherical particle surrounded by a thin electrical double layer near a charged plane wall, when the particle translates parallel to the wall without rotation, in a symmetric electrolyte solution at rest. The electroviscous (electro-hydrodynamic) forces, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, for electroviscous ion concentration (perturbed ion clouds), electroviscous potential (perturbed electric potential) and electroviscous or electro-hydrodynamic flow field (perturbed flow field). The problem was previously solved for small gap widths and low Peclet numbers in the inner region around the gap between the sphere and the wall, using lubrication theory. Here the restriction on the particle–wall distances is removed, and an analytical and numerical solution is obtained valid for the whole domain of interest. For large sphere–wall separations the solution approaches that for the electroviscous drag on an isolated sphere in an unbounded fluid. For small particle–wall distances it differs from that obtained by the use of lubrication theory, showing that lubrication theory is inadequate for electroviscous problems. The analytical results are in complete agreement with the full numerical calculations. For small particle–wall distances a model is given which provides both physical insight and an easy way to calculate the force with high precision.

Biphoton compression in a standard optical fiber: Exact numerical calculation

The generation of two-photon wave packets, produced by spontaneous parametric down-conversion in crystals with linearly chirped quasi-phase-matching grating, is analyzed. Although they are spectrally broad, two-photon wave packets produced in this way are not Fourier-transform limited. We discuss the temporal compression of the wave packets, exploiting the insertion of a standard optical fiber in the path of one of the two photons. The effect is analyzed by means of full numerical calculation, and the exact dispersion dependencies in both the crystal and the fiber are considered. The study paves the way for practical realization of this idea.

Fermi surface of a trapped dipolar Fermi gas

Under the framework of the semiclassical theory, we investigate the equilibrium-state properties of a spin polarized dipolar Fermi gas through full numerical calculation. We show that the Fermi surfaces in both real and momentum spaces are stretched along the attractive direction of dipolar interaction. We further verify that the deformed Fermi surfaces can be well approximated by ellipsoids. In addition, the deformation parameters slightly depend on the local real- and momentum-space densities. We also study the interaction strength dependence of the energy and real- and momentum-space densities. By comparing them with variational results, we find that the ellipsoidal ansatz usually generates accurate results for weak dipolar interaction, while under strong dipolar interaction limit, notable discrepancy can be observed. Finally, we map out the stability boundary of the system.

Semi-Analytical Approach for Analysis of BER in Conventional and Staggered Bit Patterned Media

We present a semi-analytical approach for the analysis of synchronization in bit patterned media (BPM) recording. The analysis is based on full numerical micromagnetic calculations of the reversal surfaces of separate BPM element. These reversal surfaces are used to define writing window zones for correct recording in BPM element arrays. The simulations show that staged media lead to improved performance and larger writing window zones (WWZs). The presented model and results are important for estimating BPM designs in terms of density, bit-error rates (BERs), and performance.

High-Frequency Behavior of the Dynamic Mobility and Dielectric Response of Concentrated Colloidal Dispersions

A matched asymptotic analysis of the system of equations governing the electrokinetic cell model of ref 4 (Ahualli, S.; Delgado, A.; Miklavcic, S.; White, L. R. Langmuir 2006, 22, 7041) is performed. Asymptotic expressions are obtained for the dynamic mobility and complex conductivity response of a dense suspension of charged spherical particles to an applied electric field. The asymptotic expressions are compared with full numerical calculations of the linear response functions as a function of surface (zeta) potential, electrolyte strength, and particle density. We find that the numerical procedure used is robust and highly accurate at a very high frequency under a wide range of double-layer conditions. The asymptotic form for the dielectric response of the system is accurate to megahertz frequencies. The asymptotic formulas for the other response functions have limited viability as predictive tools within the current range of experimentally accessible frequencies but are useful as checks on numerical calculations.

Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnolddiffusion

We study a chain of nonlinear interacting spins driven by a static and a time-dependentmagnetic field. The aim is to identify the conditions for the locally and temporallycontrolled spin switching. Analytical and full numerical calculations show the possibilityof stochastic control if the underlying semiclassical dynamics is chaotic. Thisis achievable by tuning the external field parameters according to the methoddescribed in this paper. We show analytically for a finite spin chain that Arnolddiffusion is the underlying mechanism for the present stochastic control. Quantummechanically we consider the regime where the classical dynamics is regular orchaotic. For the latter we utilize the random matrix theory. The efficiency and thestability of the non-equilibrium quantum spin states are quantified by the timedependence of the Bargmann angle related to the geometric phases of the states.

Vortices in Bose-Einstein condensates with dominant dipolar interactions

We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of $^{52}\text{C}\text{r}$ atoms with dipole-dipole and $s$-wave contact interactions confined in an axially symmetric harmonic trap. We obtain the vortex states by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. We investigate the properties of a single vortex and calculate the critical angular velocity for different values of the $s$-wave scattering length. We show that, whereas the standard variational approach breaks down in the limit of pure dipolar interactions, exact solutions of the Gross-Pitaevskii equation can be obtained for values of the $s$-wave scattering length down to zero. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis for different values of the angular velocity of the rotating trap.

Mode identification in rapidly rotating stars

Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method (MacGregor et al. 2007) have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula (Tassoul 1980), provided that the underlying rotation profile is not too differential (Lignieres & Georgeot 2008, Reese et al. 2009). Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars. Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars (Lignieres & Georgeot 2008).

A Method of Parameters Estimation of Water-Lubricated Hybrid Journal Bearings for Ultra-Precision Machine Tool Spindle

Water-lubricated hybrid journal bearings have been developed to support the ultra-precision machine tool spindles, due to the prominent properties of high load capacity and stiffness, high rotational accuracy, excellent thermal stability, low power consuming and environmental friendliness. Quasi-analytical procedures are deduced to present a relatively easy and rapid method for estimating of the parameters of the water-lubricated hybrid bearings without resorting to complex full numerical calculation. The procedures are based on the lumped resistance method, which have been extended to the situation dominated by the turbulence and inertia effects. The results show good agreement with the full numerical solution, especially when the bearing operating at moderate eccentricities. The procedures can be taken as a real time analytical tool for parametric study and preliminary engineering design of water-lubricated hybrid journal bearings.

Effect of an external electric field on the diffusion-influenced reversible reaction of a neutral particle and a charged particle in three dimensions

The diffusion-influenced reversible reaction of a neutral particle and a charged particle in an external field is analytically solved in three dimensions. A generalized nonisotropic boundary condition is used and a kinetic equation for the probability density function is set up. A tridiagonal matrix equation is derived for the coefficients of the series solution and we obtain the solution within the diagonal approximation in the Laplace domain. We also find that the long time asymptotic behavior of the first term solution shows a kinetic transition from a power law to an exponential behavior as the field strength is increased. The full numerical calculation reveals that the first term solution deviates slightly at short times but gives good result at long times. Thus it contributes dominantly to the kinetic transition behavior at long times. For the irreversible limit, we find a different kinetic transition behavior from a power law to an exponential increase through a constant in the transition region for the initially bound state.

Erratum: Gravitational recoil from binary black hole mergers: The close-limit approximation [Phys. Rev. D74, 124010 (2006)

[abridged] The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. We present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ~ 64 km/s for a symmetric mass ratio eta = M_1 M_2/(M_1+M_2)^2 ~ 0.19 and an initial proper separation of 4 M, where M is the total ADM mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. If we supplement this estimate with PN calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 84 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 220-265 km/s. We also provide non-linear fits to these estimated upper and lower bounds. These estimates are subject to uncertainties related to issues such as the choice of initial data and higher effects in perturbation theory. Nonetheless, our estimates are consistent with previous results in the literature and suggest a narrower range of possible recoil velocities.