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The asymptotics from the two-fluid incompressible Navier-Stokes-Maxwell system with Ohm's law to solenoidal Ohm's law was pointed out in Arsenio-Saint-Raymond's work [3] . We justify rigorously this limit in the context of global-in-time classical solutions. The key is to derive the global-in-time uniform in e energy estimate of the rescaled system with Ohm's law by employing the decay properties of both the electric field E e and the wave equation with linear damping of the divergence free magnetic field B e , then take the limit as e → 0 to obtain the solutions of the system with solenoidal Ohm's law.

In recent years, due to the digitization of the electrical devices electric load demand has been increased. Power security and stabilization are the other two challenges which necessitate the need of electrical energy storage. Along with the technological constraints, economical and environmental issues are the other challenges in the development of energy storage technologies. Fast response and high energy density features are the two key points due to which Superconducting Magnetic Energy Storage (SMES) Devices can work efficiently while stabilizing the power grid. Two types of geometrical combinations have been utilized in the expansion of SMES devices till today; solenoidal and toroidal. It has been found that the solenoidal arrangement is easier to fabricate and provides efficient approach to handle stresses produced by Lorentz forces. This work represents the development of 2.5MJ SMES solenoidal Magnet using 2G (SuperPower, YBCO having Tc=90K @ 0T) HTS tape. The effect of the operating current (passing through a single superconducting tape) has been evaluated. A reference magnetic flux of 3.5T has been considered in designing of HTS SMES. It has been found that the parallel fields for solenoidal magnet are large as compared to perpendicular fields which results into large magnitudes of Lorentz forces acting on HTS tape which may leading to structural instabilities and can cause failure. It has been concluded that higher currents can be used in order to lower down the total length of the superconductor as it can reduce the overall cost of the device

In the present paper, a Vortex Particle Method is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on Chorins operator splitting approach for the Navier–Stokes equations written in vorticity–velocity formulation, and consists of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz–Hodge Decomposition, while the no-slip condition is enforced by an indirect boundary integral equation. The above decomposition and splitting are discussed in comparison to the analogous decomposition for the pressure-velocity formulation of the governing equations. The Vortex Particle Method is implemented with a completely meshless algorithm, as neither advection nor diffusion requires topological connection of the point lattice. The results of the meshless approach are compared with those obtained by a mesh-based Finite Volume Method, where the pseudo-compressible iteration is exploited to enforce the solenoidal constraint on the velocity field. Several benchmark tests were performed for verification and validation purposes. In particular, we analyzed the two-dimensional flow past a circle, past an ellipse with incidence and past a triangle for different Reynolds numbers.

Symmetric drainage flow of a compressible fluid from a thin fracture modeled as a long narrow 2D channel is studied on the basis of linearized compressible Navier-Stokes equations with the no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion; whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that, at large times, this no-slip flow exhibits a time-dependent slip-like mass flow rate linearly proportional to the channel gap instead of the cubic power of the gap for the Poiseuille-type of flow. The drainage rate is also proportional to the kinematic viscosity, opposite to Poiseuille-type of flow, which produces a drainage rate proportional to the inverse of the kinematic viscosity. The same drainage rate formula also applies to drainage flow from a semi-sealed thin fracture.

In this paper, we propose and analyze the stability and thedissipative structureof a new dynamic term-by-term stabilizedfinite element formulationfor the Navier–Stokes problem that can be viewed as a variationalmultiscale(VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradientterms, respectively, of themomentum equationthat cannot be captured by thefinite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability inanisotropicspace–timediscretizations, which is proved usingnumerical analysisfor alinearized problemand demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and severalnumerical examplesthat serve to justify our claims.

In this paper, we study the lowest-order mixed finite element method for the axisymmetric Darcy problem using Raviart–Thomas elements. In contrast to the Cartesian setting, the method is non-conforming in the sense that the discretely divergence-free functions are not solenoidal. We derive several estimates that measure the inconsistency of the method and derive error estimates of the discrete pressure and velocity solutions. We show that if the domain is convex, then the errors converge with optimal order modulo logarithmic terms. Numerical experiments are presented, and they indicate that the estimates are sharp.

The aim of this paper is to give an existence and uniqueness of solutions for the Cauchy problem of the Navier–Stokes type equations associated to the sublaplacian provided by the left invariant vector fields on the Heisenberg group. To avoid the difficulty of the non-commutative which is intrinsic in 2-step stratified Lie groups, we construct the solenoidal space by using the right invariant vector fields on the Heisenberg group.

A Beltrami field is an eigenvector of the curl operator. Beltrami fields describe steady flows in fluid dynamics and force free magnetic fields in plasma turbulence. By application of the Lie-Darboux theorem of differential geoemtry, we prove a local representation theorem for Beltrami fields. We find that, locally, a Beltrami field has a standard form amenable to an Arnold-Beltrami-Childress flow with two of the parameters set to zero. Furthermore, a Beltrami flow admits two local invariants, a coordinate representing the physical plane of the flow, and an angular momentum-like quantity in the direction across the plane. As a consequence of the theorem, we derive a method to construct Beltrami fields with given proportionality factor. This method, based on the solution of the eikonal equation, guarantees the existence of Beltrami fields for any orthogonal coordinate system such that at least two scale factors are equal. We construct several solenoidal and non-solenoidal Beltrami fields with both homogeneous and inhomogeneous proportionality factors., 5 figures

Due to fast response and high energy density characteristics, Superconducting Magnetic Energy Storage (SMES) can work efficiently while stabilizing the power grid. The challenges like voltage fluctuations, load shifting and seasonal load demands can be accomplished through HTS magnet as this device has a great potential to supply power for a time span varies from few seconds to hours. Solenoidal configuration has been widely employed (over toroidal) in the development of SMES prototypes as it is simpler to manufacture and allows an easier handling of the mechanical stresses imposed on the structure due to Lorentz forces. A micro-SMES of capacity 10 MJ can be employed to mitigate the challenges like load leveling, dynamic stability, transient stability, voltage stability, frequency regulation, transmission capability enhancement, power quality improvement, automatic generation control, uninterruptible power supplies, etc. In this work, solenoidal configuration has been engaged in the development of 10 MJ SMES Magnet using 2 G (SuperPower, YBCO having Tc = 90 K @0T) High Temperature Superconducting (HTS) tape. The superconducting tape has been cooled at 14 K using conduction cooling. The effect of maximum operating current (3250A, 2600A, 1950A and 1300A) on the inductance, maximum storable energy and length of superconductor has also been evaluated for a constant deliverable energy of 10 MJ. A numerical analysis is done on 10 MJ HTS SMES where perpendicular field of 3T has been considered. The effect of aspect ratio (solenoidal height to bore diameter ratio) on the normal component of the magnetic field has also been assessed. Lorentz forces (N/m3) have been evaluated in the superconducting domain. It has been concluded that it would be beneficial to operate at higher currents (i.e. more current through single tape) as it can reduce the total length of the superconductor. The perpendicular component of magnetic flux for the analysis is found to 2.96T which is less than 3T.

In this paper, we deal with the solenoidal conservative Lie algebra associated to the classical normal form of Hopf-zero singular system. We concentrate on the study of some representations and Z 2 -equivariant normal form for such singular differential equations. First, we list some of the representations that this Lie algebra admits. The vector fields from this Lie algebra could be expressed by the set of ordinary differential equations where the first two of them are in the canonical form of a one-degree of freedom Hamiltonian system and the third one depends upon the first two variables. This representation is governed by the associated Poisson algebra to one sub-family of this Lie algebra. Euler’s form, vector potential, and Clebsch representation are other representations of this Lie algebra that we list here. We also study the non-potential property of vector fields with Hopf-zero singularity from this Lie algebra. Finally, we examine the unique normal form with non-zero cubic terms of this family in the presence of the symmetry group Z 2 . The theoretical results of normal form theory are illustrated with the modified Chua’s oscillator.

It seems that the potential and linear force-free magnetic fields are inadequate to represent the observed magnetic events occurring in different regions of the solar corona. To reconstruct the nonlinear force-free fields from the solar surface magnetograms, various analytical and numerical methods have already been examined by different authors. Here, using the Lagrange multiplier technique, a constrained optimization approach for reconstructing force-free magnetic fields is proposed. In the optimization procedure the solenoidal property is considered as a constraint on the initial non-force-free field. In the Wheatland et al. (2000) method as an unconstrained optimization, both solenoidal and force-free conditions are fulfilled approximately. In contrast, the constrained optimization method, up to numerical precision, leads us to a nearly force-free magnetic field with exactly zero divergence. The solutions are obtained and tested by the Low and Lou (1990) semi-analytic solution.

A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold $M$ and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field $X$ with a global cross-section there exist some 4-dimensional symplectic manifold $\tilde{M}\supset M$ and a smooth Hamilton function $H: \tilde{M}\to \mathbb R$ such that for some $c\in \mathbb R$ one gets $M = \{H=c\}$ and the Hamiltonian vector field $X_H$ restricted on this level coincides with $X$. For divergence free vector fields with singular points such the extension is impossible but the existence of local cross-section allows one to reduce the dynamics to the study of symplectic diffeomorphisms in some sub-domains of $M$. We also consider the case of a divergence free vector field $X$ with a smooth integral having only finite number of critical levels. It is shown that such a noncritical level is always a 2-torus and restriction of $X$ on it possesses a smooth invariant 2-form. The linearization of the flow on such a torus (i.e. the reduction to the constant vector field) is not always possible in contrast to the case of an integrable Hamiltonian system but in the analytic case ($M$ and $X$ are real analytic), due to the Kolmogorov theorem, such the linearization is possible for tori with Diophantine rotation numbers., 17 pages, no figures

Motivated by [21] , we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier–Stokes equations with large horizontal velocity. In particular, we proved that when the initial density is close enough to a positive constant, then given divergence free initial velocity field of the type ( v 0 h , 0 ) ( x h ) + ( w 0 h , w 0 3 ) ( x h , x 3 ) , we shall prove the global wellposedness of (1.1) . The main difficulty here lies in the fact that we will have to obtain the L 1 ( R + ; Lip ( R 3 ) ) estimate for convection velocity in the transport equation of (1.1) . Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic Littlewood–Paley theory here.

The history of Bergman spaces goes back to the book [4] in the early fifties by S. Bergman, where the first systematic treatment of the subject was given, and since then there have been a lot of papers devoted to this area. Some standard works here are [5] , [8] , [15] , [28] and the references therein, which contain a broad summary and historical notes of the subject, that frees us from referring to missing details. In their recent works Gonzalez-Cervantes, Luna-Elizarraras and Shapiro [11] , [12] , laid the foundations for the generalization of the theory of Bergman spaces induced by Laplacian (sometimes called solenoidal and irrotational, or harmonic) vector fields by taking advantage on the intimate connections between harmonic vector fields theory and quaternionic analysis for the Moisil-Theodorescu operator (MT-operator for short). A deeper discussion of the last mentioned relation can be found in [1] . On the setting of general bounded domains in R 3 , we extend the aforementioned study in a very natural way to the case of an introduced v-MT-operator for v ∈ R 3 , proving several properties of induced Bergman spaces and some relative results about Stokes and Borel-Pompieu formulas for v-MT-hyperholomorphic functions, i.e., functions which belong to kernel of the v-MT-operator. In addition, we show that this v-MT operator satisfies a conformal co-variant property. Application of all the above allows to study of Bergman type spaces induced by v-Laplacian vector fields theory, which represents the main goal of this paper.

The ability of large-eddy simulations (LES) to resolve the most energetic coherent structures of a spatially-evolving supersonic turbulent boundary layer over a flat plate at M ∞ = 2 and R e θ ≈ 6000 is analyzed using three different local subgrid scale models. Additionally, an Implicit LES (ILES), which relies on the intrinsic numerical dissipation to act as a subgrid model, is investigated to assess the consistency and the accuracy of the method. Direct comparison with data from high resolution DNS calculations (Pirozzoli and Bernardini, 2011) provides validation of the different modeling approaches. Turbulent statistics up to the fourth-order are reported, which help emphasizing some salient features related to near-wall asymptotic behavior, mesh resolution and models prediction. Detailed analysis of the near-wall asymptotic behavior of all relevant quantities shows that the models are able to correctly reproduce the near-wall tendencies. The thermodynamic fluctuations, T r m s and ρ r m s , show a lack of independence from SGS modeling and grid refinement in contrast to the velocity fluctuations. The pressure fluctuations, which are associated with the acoustic mode, are not significantly affected by the modeling and the mesh resolution. Furthermore, the comparison of different contributions to the viscous dissipation reveals that the solenoidal dissipation plays the most dominant role regardless of the model. Finally, it is found that the ILES is more likely to produce consistent near-wall behavior even with a numerical scheme that has a small amount of numerical dissipation to emulate the effects of unresolved scales.

We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method include great flexibility of polygonal meshes and automatic divergence-free constraint on the magnetic flux field. In this work, we rigorously prove the well-posedness of the method and the solenoidal nature of the discrete magnetic flux field. We also derive stability energy estimates. The design of the method includes three choices for the construction of the nodal mass matrix and criteria to more alternatives. This approach is novel in the VEM literature and allows us to preserve a commuting diagram property. We present a set of numerical experiments that independently validate theoretical results. The numerical experiments include the convergence rate study, energy estimates and verification of the divergence-free condition on the magnetic flux field. All these numerical experiments have been performed on triangular, perturbed quadrilateral and Voronoi meshes. Finally, we demonstrate the development of the VEM method on a numerical model for Hartmann flows as well as in the case of magnetic reconnection.

We study existence of minimizers of the least gradient problem inf v ∈ B V g ⁡ ∫ Ω φ ( x , D v ) , where B V g = { v ∈ B V ( Ω ) : ∫ ∂ Ω g v = 1 } , φ ( x , p ) : Ω × R n → R is a convex, continuous, and homogeneous function of degree 1 with respect to the p variable, and g satisfies the compatibility condition ∫ ∂ Ω g d S = 0 . We prove that for every 0 ≢ g ∈ L ∞ ( ∂ Ω ) there are infinitely many minimizers in B V ( Ω ) . Moreover there exists a divergence free vector field T ∈ ( L ∞ ( Ω ) ) n that determines the structure of level sets of all minimizers, i.e. T determines D u | D u | , | D u | -a.e. in Ω, for every minimizer u . We also prove some existence results for general 1-Laplacian type equations with Neumann boundary condition. A numerical algorithm is presented that simultaneously finds T and a minimizer of the above least gradient problem. Applications of the results in conductivity imaging are discussed.

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.

We describe, analyse and reduce micro-current effects in one\ud class of lattice Boltzmann equation simulation method describing im-miscible fluids within the continuum approximation, due to Lishchuk et al. (Phys. Rev. E 67 036701 (2003)). This model's micro-current flow �field and associated density adjustment, when considered in the\ud linear, low-Reynolds number regime, may be decomposed into independent, superposable contributions arising from various error terms in its immersed boundary force. Error force contributions which are rotational (solenoidal) are mainly responsible for the micro-current (corresponding density adjustment). Rotationally anisotropic error\ud terms arise from numerical derivatives and from the sampling of the interface-supporting force. They may be removed, either by eliminating the causal error force or by negating it. It is found to be straightforward to design more effective stencils with significantly improved performance.\ud Practically, the micro-current activity arising in Lishchuk's method is reduced by approximately three quarters by using an appropriate stencil and approximately by an order of magnitude when the effects of sampling are removed.

A new facility for the measurement of AC loss in superconductors at high dB/dt has been developed. The test device has a spinning rotor consisting of permanent magnets arranged in a Halbach array; the sample, positioned outside of this, is exposed to a time varying AC field with a peak radial field of 0.566 T. At a rotor speed of 3600 RPM the frequency of the AC field is 240 Hz, the radial dB/dt is 543 T/s and the tangential dB/dt is 249 T/s. Loss is measured using nitrogen boiloff from a double wall calorimeter feeding a gas flow meter. The system is calibrated using power from a known resistor. YBCO tape losses were measured in the new device and compared to the results from a solenoidal magnet AC loss system measurement of the same samples (in this latter case measurements were limited to a field of amplitude 0.1 T and a dB/dt of 100 T/s). Solenoidal magnet system AC loss measurements taken on a YBCO sample agreed with the Brandt loss expression associated with a 0–0.1 T Ic of 128 A. Subsequently, losses for two more YBCO tapes nominally identical to the first were individually measured in this spinning magnet calorimeter (SMC) machine with a Bmax of 0.566 T and dB/dt of up to 272 T/s. The losses, compared to a simplified version of the Brandt expression, were consistent with the average Ic expected for the tape in the 0–0.5 T range at 77 K. The eddy current contribution was consistent with a 77 K residual resistance ratio, RR, of 4.0. The SMC results for these samples agreed to within 5%. Good agreement was also obtained between the results of the SMC AC loss measurement and the solenoidal magnet AC loss measurement on the same samples.

In this note, we prove the flowbox theorem for divergence-free Lipschitz vector fields., Dans cette note, nous prouvons le théorème du flot tubulaire pour les champs vectoriels Lipschitz à divergence nulle.

Hard and electromagnetic (EM) probes are excellent tools for studying the quark-gluon plasma (QGP). These probes include jet production and modification, productions of heavy flavor hadrons and quarkonia, and productions of photon and dileptons. They provide essential information to characterize the properties of the QGP such as the parton energy loss mechanism and the temperature, lifetime, and viscosity of the QGP. The Solenoidal Tracker at RHIC (STAR) experiment utilizes t excellent detectors to measure these probes, and provides numerous results via hard and EM probes. This overview reports some of the selected results from e + e − and direct virtual photon productions, heavy flavor hadrons and quarkonia, and jets.

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

This paper studies the stability of a stationary solution of the Navier–Stokes system with a constant velocity at infinity in an exterior domain. More precisely, this paper considers the stability of the Navier–Stokes system governing the stationary solution which belongs to the weak L 3 -space L 3 , ∞ . Under the condition that the initial datum belongs to a solenoidal L 3 , ∞ -space, we prove that if both the L 3 , ∞ -norm of the initial datum and the L 3 , ∞ -norm of the stationary solution are sufficiently small then the system admits a unique global-in-time strong L 3 , ∞ -solution satisfying both L 3 , ∞ -asymptotic stability and L ∞ -asymptotic stability. Moreover, we investigate L 3 , r -asymptotic stability of the global-in-time solution. Using L p – L q type estimates for the Oseen semigroup and applying an equivalent norm on the Lorentz space are key ideas to establish both the existence of a unique global-in-time strong (or mild) solution of our system and the stability of our solution.

In the framework of the program to fabricate a high-field superconducting magnet of the order of 19 T @4.2 K with a 150 mm free bore, a 15 T hybrid solenoidal superconducting magnet with a 78 mm bore was developed and preliminary tested. The purpose of the program is to upgrade the material test facilities in the Institute of Plasma Physics Chinese Academy of Science (ASIPP) and further extend their measurement functionality. This paper presents the design of the 15 T hybrid magnet and its preliminary test results. The magnet comprises two high-performance Nb3Sn coils, one ITER Nb3Sn coil and one NbTi coil respectively for the high-, medium- and low field section. The axial length of the homogeneity within a 99 % magnetic field region is designed to more than 40 mm, and the ratio between the peak and central magnetic field is expected to be less than 1.025. The Nb3Sn coils were reacted separately, after which all coils including the NbTi coil were impregnated with CTD-101 K individually. Then, the impregnated sub-coils were assembled into a concentric-coaxial configuration and electrically connected in series. The hybrid magnet was inserted to a liquid helium bath for the excitation test, it finally reaches 97.8 % of the design current with a 14.84 T central magnetic field.

We present the systematic study of dielectron production in U + U collisions at s N N = 193 GeV by Solenoidal Tracker At RHIC (STAR) experiment. Invariant mass, transverse momentum, and centrality differential measurements of dielectron yields are compared to Monte-Carlo hadronic contributions excluding ρ -meson. In each comparison, there is an excess in the Low Mass Region (LMR) that can be described by a model calculation including a broadened ρ spectral function. With detector acceptance correction applied, the dielectron excess invariant mass spectra in U + U collisions at s N N = 193 GeV and in Au + Au collisions at s N N = 27 , 39 , and 62.4 GeV are reported. System-size and energy dependences of low mass excess yield are discussed together with model comparisons.

Most numerical analysis performed in the past for MHD flows in liquid-metal blankets were based on the assumption of low magnetic Reynolds number and involved numerical codes that utilized electric potential as the main electromagnetic variable. One limitation of this approach is that such codes cannot be applied to truly unsteady processes, for example, MHD flows of liquid-metal breeder/coolant during unsteady events in plasma, such as major plasma disruptions, edge-localized modes and vertical displacements, when changes in plasmas occur at millisecond timescales. Our newly developed code MOONS (Magnetohydrodynamic Object-Oriented Numerical Solver) uses the magnetic field as the main electromagnetic variable to relax the limitations of the low magnetic Reynolds number approximation for more realistic fusion reactor environments. The new code, written in Fortran, implements a 3D finite-difference method and is capable of simulating multi-material domains. The constrained transport method was implemented to evolve the magnetic field in time and assure that the magnetic field remains solenoidal within machine accuracy at every time step. Various verification tests have been performed including purely hydrodynamic flows and MHD flows at low and finite magnetic Reynolds numbers. Test results have demonstrated very good accuracy against known analytic solutions and other numerical data.

A newly developed three-dimensional spiral injection scheme for beam insertion into a solenoidal storage ring is reported. A new planned muon g−2/EDM experiment at J-PARC aims to measure g − 2 to a factor of 5 better statistical precision and a factor of 100 better sensitivity for the electric dipole moment (EDM) measurement compared to previous experiments. The J-PARC experiment will use a 3-T MRI solenoid magnet as the muon storage ring with a 0.66 m diameter to achieve a 1-ppm level of local uniformity. The previous g − 2 injection scheme is not applicable for beam injection into a small ring. The new scheme provides a smooth injection utilizing a radial solenoidal fringe field, without causing an error field in the storage volume. The expected storage efficiency is 80% and over, which is to be compared to 3.5% for the previous g − 2 experiment. In addition, the ability to control the storage plane is important for the EDM measurement. In this paper, we introduce the conceptual design and required beam parameters in terms of Twiss functions and the expected injection efficiency.

The non-uniqueness of the atomistic stress tensor is a well-known issue when defining continuum fields for atomistic systems. In this paper, we study the non-uniqueness of the atomistic stress tensor stemming from the non-uniqueness of the potential energy representation. In particular, we show using rigidity theory that the distribution associated with the potential part of the atomistic stress tensor can be decomposed into an irrotational part that is independent of the potential energy representation, and a traction-free solenoidal part. Therefore, we have identified for the atomistic stress tensor a discrete analog of the continuum generalized Beltrami representation (a version of the vector Helmholtz decomposition for symmetric tensors). We demonstrate the validity of these analogies using a numerical test. A program for performing the decomposition of the atomistic stress tensor called MDStressLab is available online at http://mdstresslab.org .

Magma-fracturing during melt migration is associated with the propagation of a pore-generating damage front ahead of high-pressure fluid injection, which facilitates the transport of melt in the asthenosphere and initiates dike propagation in the lithosphere. We examine the propagation of porous flow in a damageable matrix by applying the two-phase theory for compaction and damage proposed by Bercovici et al. (2001a) and Bercovici and Ricard (2003) in 2-D. Damage (void generation and microcracking) is treated by considering the generation of interfacial surface energy by deformational work. We examine the stability of 1-D solitary waves to 2-D perturbations, and study the formation of finite-amplitude, two-dimensional solitary waves with and without solenoidal (rotational) flow of the matrix. We show that the wavelength and growth rate of the most unstable perturbations are dependent on both background porosity and the presence of solenoidal flow field. The effect of damage on finite amplitude 2-D solitary waves is then examined with numerical experiments. Stably propagating circular waves become flattened (elongated perpendicular to gravity) for small porosity, or elongated (parallel to gravity) for large porosity with increased damage. We show that the weakening of the matrix due to damage leads to these changes in wave geometry, which indicates a transition from magmatic porous flow to dike-like or sill-like magma-fracturing as magma passes through a semi-brittle/semi-ductile zone in the lithosphere.

We present a divergence free vector field in the Sobolev space H 1 such that the flow associated to the field does not belong to any Sobolev space. The vector field is deterministic but constructed as the realization of a random field combining simple elements. This construction illustrates the optimality of recent quantitative regularity estimates as it gives a straightforward example of a well-posed flow which has nevertheless only very weak regularity.

Benefiting from the progress of manufacturing technology of fiber-reinforced composite structures, the angle of a fiber is allowed to change continuously, and stiffness can be different at different positions of a structure. Therefore, the design optimization has large freedom to improve the performance of a structure. A fundamental issue in the design optimization is how to describe the spatially varying fiber angles. In the present study, the fiber angle arrangement is described by using a parametric divergence-free vector field (pDVF) that is constructed through an expansion by using a set of basis vector fields. A basis vector field is obtained by multiplying the gradient vectors of a compact supported radial basis function with an anti-symmetric matrix. Then the expansion coefficients are regarded as design variables in the optimization. The proposed method is able to describe continuous curvilinear fibers, and it ensures that the fibers in one ply do not cross each other.

Despite compelling astrophysical evidence for the existence of dark matter in the universe, we have yet to positively identify it in any terrestrial experiment. If such matter is indeed particle in nature, it may have a new interaction as well, carried by a dark counterpart to the photon. The DarkLight experiment proposes to search for such a beyond-the-standard-model dark photon through complete reconstruction of the final states of electron–proton collisions. In order to accomplish this, the experiment requires a moderate-density target and a very high intensity, low energy electron beam. I describe DarkLight's approach and focus on the implications this has for the design of the experiment, which centers on the use of an internal gas target in Jefferson Lab's Low Energy Recirculating Facility. I also discuss upcoming beam tests, where we will place our target and solenoidal magnet in the beam for the first time.

An 8 T superconducting solenoid was commissioned at the Australian National University to make precision measurements of fusion cross-sections. During operation at high field, forces between the solenoid and the iron yoke that houses it must always be maintained within safe limits and precision location of the solenoid coil with tight tolerances is necessary to achieve this. Thermal contraction of components can impact the locating structure of the solenoid coil, leading to unsafe forces. For effective operation, the solenoid’s magnetic field axis must be aligned with the optical axis of the beam. After overcoming fundamental flaws in the original design, the solenoid was properly mechanically suspended and aligned with an offset of x= 0.3 ± 0.5 mm, y= 0.8 ± 0.3 mm, as measured using an α source. The improvements to this structure allowed successful completion of the first fusion measurements with the 8T solenoidal separator, and demonstrated that it is now ready for a program of fusion measurements.

A solenoidal magnetic field has been used to enhance the ion flux of a laser ion source. However, the dependence of the increase in ion current on the charge-state has not been clarified. In this study, to control the purity of the charge-state in the laser ion source, we investigated the effect of a solenoidal magnetic field on the charge-state distribution of ions in laser ion sources with a solenoid. The results indicate that the flux of ions with a heavier and/or lower charge-state can be increased using higher magnetic flux densities, and that each charged ion has an optimal solenoidal magnetic flux density that maximizes its flux. These results imply that it is possible to increase the purity of the desired charge-state ions by selecting a suitable solenoidal magnetic flux density.

Selective Laser Melting (SLM) was used to produce 3D-printed net shape NdFeB (Neodymium Iron Boron) permanent magnets that exhibit relatively large internal permanent magnetization structures, without exposure to any external magnetizing field. The macroscopic magnetization, M → ( r → ) , does not create a significant magnetic stray field outside the as-produced sample, and is pole avoiding and solenoidal. The permanent magnetization can be detected via the stray field that appears after cutting the sample into pieces. From the field measurements it can be concluded that the magnetization is mainly in the 3D-printing planes which are parallel to M → ( r → ) . Maximum magnetic flux densities of almost 80 mT are recorded 1 mm above the cut surfaces in the air. Dependencies of the effect on SLM process parameters, as well as on the sample size and shape are discussed. Although a deep understanding is still missing, a possible mechanism that may partly explain the formation of these self-organized macroscopic magnetization structures is proposed. The discovered effect may offer new routes for producing magnetized rare earth-transition metal (RE-TM) permanent magnets without using a magnetizer, and it shows that the SLM 3D-printing process can lead to new material behavior.

The traditional transfer matrix used in particle accelerators has been modified to easily take into account a non-zero angular canonical momentum, without the hard edge approximation of the field. To this end, we reformulate the transfer matrix based on an existing method, but by using both the explicit real transformation matrix in the Larmor frame of the 4D transverse phase space, and the real 4D transfer matrix of a solenoidal field in this frame and in the laboratory frame. This reformulation allows to clearly identify differences with the traditional matrix when performing analytic inter-comparisons. The implementation is also easier to perform. A comparison with computer simulation further illustrates its usefulness.

A new detector array, Solenogam, has been developed at the Australian National University Heavy Ion Accelerator Facility. Coupled initially to the SOLITAIRE 6.5 T, gas-filled, solenoidal separator, and later to an 8 T solenoid, the system enables the study of long-lived nuclear states through γ -ray and conversion-electron spectroscopy in a low-background environment. The detector system is described and results from the commissioning experiments are presented.

This is a complement of the former works by Costin and Maz’ya (2008) [2] and Hamamoto and Takahashi (2019) [6] , on sharp Hardy–Leray inequality for solenoidal (i.e., divergence-free) fields in R 3 with some axisymmetry conditions. Here we derive the same best constant, with no assumption of axial symmetry.

In a medium energy beam transport line transverse rms emittance growth associated with spherical aberration is analysed. An analytical expression is derived for beam optics in a solenoid field considering terms up to the third order in the radial displacement. Two important phenomena: effect of spherical aberrations in axial-symmetric focusing lens and influence of nonlinear space charge forces on beam emittance growth are discussed for different beam distributions. In the second part nonlinear effect associated with chromatic aberration that describes the growth of emittance and distortion of phase space area is discussed.

In this paper, we introduce the notion of measure expansivity for volume preserving diffeomorphisms and divergence free vector fields. We prove that the following three theorems. (1) The C 1 -interior of measure expansive volume preserving diffeomorphism is Anosov. (2) A C 1 -generic volume preserving diffeomorphism is Anosov. (3) The C 1 -interior of measure expansive divergence free vector field is Anosov.

Given solenoidal vector u 0 ∈ H ˙ − 2 δ ∩ H 1 ( R 2 ) , ρ 0 − 1 ∈ L 2 ( R 2 ) , and ρ 0 ∈ L ∞ ∩ W ˙ 1 , r ( R 2 ) with a positive lower bound for δ ∈ ( 0 , 1 2 ) and 2 r 2 1 − 2 δ , we prove that 2-D incompressible inhomogeneous Navier–Stokes system (1.1) has a unique global solution provided that the viscous coefficient μ ( ρ 0 ) is close enough to 1 in the L ∞ norm compared to the size of δ and the norms of the initial data. With smoother initial data, we can prove the propagation of regularities for such solutions. Furthermore, for 1 p 4 , if ( ρ 0 − 1 , u 0 ) belongs to the critical Besov spaces B ˙ p , 1 2 p ( R 2 ) × ( B ˙ p , 1 − 1 + 2 p ∩ L 2 ( R 2 ) ) and the B ˙ p , 1 2 p ( R 2 ) norm of ρ 0 − 1 is sufficiently small compared to the exponential of ‖ u 0 ‖ L 2 2 + ‖ u 0 ‖ B ˙ p , 1 − 1 + 2 p , we prove the global well-posedness of (1.1) in the scaling invariant spaces. Finally for initial data in the almost critical Besov spaces, we prove the global well-posedness of (1.1) under the assumption that the L ∞ norm of ρ 0 − 1 is sufficiently small.

Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.

A continuum X is called solenoidal if it is circle-like and nonplanar. X is 1 n -homogeneous if the action of its homeomorphism group Homeo ( X ) on X has exactly n orbits; i.e. there are exactly n types of points in X . Recently Jimenez-Hernandez, Minc and Pellicer-Covarrubias [6] constructed a family of 1 n -homogeneous solenoidal continua, for every n > 2 . Modifying the spaces obtained by them, as well as an earlier construction of the author for n = 2 , for every n > 2 we construct two different uncountable families of arcless 1 n -homogeneous solenoidal continua Σ n and Σ n ′ . We also show that there is an uncountable family of countably nonhomogeneous solenoidal continua Σ ∞ ; i.e. each Y ∈ Σ ∞ has (infinitely) countably many types of points. For every Y ∈ ⋃ n ∈ N Σ n ∪ Σ ∞ any orbit of Homeo ( Y ) is uncountable. With respect to the degree of homogeneity, in the realm of solenoidal continua containing pseudoarcs, our examples complete the gap between homogeneous solenoids of pseudoarcs and uncountably nonhomogeneous pseudosolenoids. A number of questions related to the study is raised.

Solving the Navier–Stokes equations when the density field contains a large and sharp discontinuity—such as a water/air free surface—is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that does not compromise on the mass-conservation properties. The equations are discretised using a symmetric interior-penalty discontinuous Galerkin finite element method that is divergence-free to machine precision. A slope limiter made specifically for exactly divergence-free (solenoidal) fields is presented and used to illustrate the difficulties in obtaining convectively stable fields that are also exactly solenoidal. The lessons learned from this are applied in constructing a simpler method based on the use of an existing scalar slope limiter applied to each velocity component. We show by numerical examples how both presented slope limiting methods are vastly superior to the naive non-limited method. The methods can solve difficult two-phase problems with high density-ratios and high Reynolds numbers—typical for marine and offshore water/air simulations—in a way that conserves mass and stops unbounded energy growth caused by the Gibbs phenomenon.

We provide analytic solutions of the net magnetic field generated by spherical and solenoidal coils enclosed in highly-permeable, coaxial magnetic shields. We consider both spherical and cylindrical shields in the case of the spherical coil and only cylindrical shields for the solenoidal coil. Comparisons of field homogeneity are made and we find that the solenoidal coil produces the more homogeneous field for a given number of windings. The models are useful as theoretical and conceptual guides for coil design, as well as for benchmarking finite-element analysis. We also demonstrate how the models can be generalized to explore field inhomogeneities related to winding misplacement., 29 pages, 11 figures

We present herewith detailed theoretical modeling coupled with experimental analysis of a micromachined inductive suspension (MIS). The reported MIS is based on two coaxial 3D solenoidal microcoils realized using our wirebonding technology. The two coils are excited using an AC signal with 180° phase-shift and a conductive proof mass (PM) is stably levitated on top of the coils. Using a micromechanical displacement sensor, we experimentally derive the lateral, vertical and angular stiffness constants of our MIS. Based on the analytical model presented here, we discuss the stability of the levitated proof mass as a function of the geometrical parameters of the design. We further test our model by applying it to another previously reported MIS structure realized using planar technology, providing stability diagrams as well as design guidelines for further developments of the micromachined inductive suspension as, for instance, miniature rotating gyroscopes.

The most sensitive desktop-sized ionizer utilising electron bombardment is currently the solenoidal ion source. We present an alternate design for such an ion source whereby the solenoidal windings of the electromagnet are replaced by a shaped cylindrical permanent magnet in order to reduce the complexity and running costs of the instrument. Through finite element modelling of the magnetic field in COMSOL and experimental measurements on a small-scale prototype magnet stack, we demonstrate the required shape of the permanent magnet in order to generate the needed field, and the necessity of soft iron collars to smooth fluctuations along the central axis.

The four-dimensional transport of the transverse phase space of the extracted beam was calculated for the CAPRICE electron cyclotron resonance (ECR) ion source at GSI. It is especially of interest for an ECR ion source, where asymmetric beams of the transverse phase spaces are extracted in the presence of a strong solenoidal field, and this axial magnetic field adds an angular momentum to extracted beam, resulting in a strong horizontal and vertical (x–y) coupled beam. The paper presents multi-particle tracking simulations using the well-established particle-in-cell code BEAMPATH. The results illustrate that the beam brilliance can be improved by combination of multi-stage collimation with skew quadrupole decoupling.

A parallel and fully implicit method is developed for numerical simulations of the thermal convection of an incompressible fluid in a rotating spherical shell. The method is based on a pseudo-compressibility approach with dual time stepping in order to tackle with the numerical difficulty of the solenoidal condition in the incompressible Navier-Stokes equations. The numerical solution of the nonlinear governing equations is based on the method of lines, whereby the partial differential equations are transformed into ordinary differential equations by a suitable spatial discretization. A second-order cell-centered finite volume discretization based on a collocated cubed-sphere grid is used here. In order to relax the time step limit and accurately integrate the semi-discrete nonlinear ordinary differential equations in time, we employ a second-order explicit-first-step, single-diagonal-coefficient, diagonally implicit Runge–Kutta (ESDIRK) method with adaptive time stepping. The nonlinear algebraic system arising at each pseudo-time step is solved by a Newton–Krylov–Schwarz algorithm to achieve good load balance on modern supercomputers. The numerical results are in good agreement with the benchmark solutions and more accurate than those obtained with a fractional step approach in our previous research. Large-scale tests on the Tianhe-2 supercomputer indicate that the fully implicit solver can achieve good parallel scalabilities in both strong and weak senses.