Toroidal Dimensions Research Articles

SITAR: A Code for ICRH Antenna–Plasma Coupling

We have developed an ICRF (ion cyclotron range of frequency) heating antenna code, SITAR (Simulation of ICRH anTennA Resistance), for stripline antenna to find out its impedance in the presence of plasma. The antenna is of finite poloidal and toroidal dimensions and screened from the plasma by the Faraday shield that shorts out the toroidal components of the radio frequency field. Antenna lead current as well as toroidal and poloidal current of antenna have been taken into account. A slab geometry model for coupling of antenna with tokamak plasma and a linear model of the perpendicular refractive index for the propagation of ICRF wave in the evanescent region have been considered. The plasma in the coupling region is described by a cold plasma dielectric tensor with nonuniform density and toroidal magnetic field along the radial direction.

On warped string vacuum profiles and cosmologies. Part II. Non-supersymmetric strings

We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type Mp+1× R × T10−p−2 depending on a single coordinate. In the absence of fluxes and for p < 8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Their asymptotics are always tadpole-dependent and isotropic at one end lying at a finite distance, while at the other end, which can lie at a finite or infinite distance, they can be tadpole-dependent isotropic or tadpole-free anisotropic. We then elaborate on the general setup for including symmetric fluxes, and present the three families of exact solutions that emerge when the orientifold potential and a seven-form flux are both present. These solutions include a pair of boundaries, which are always separated by a finite distance. In the neighborhood of one, they all approach a common supersymmetric limit, while the asymptotics at the other boundary can be tadpole-free isotropic, tadpole-free anisotropic or again supersymmetric. We also discuss corresponding cosmologies, with emphasis on their climbing or descending behavior at the initial singularity. In some cases the toroidal dimensions can contract during the cosmological expansion.

Nonlinear dynamic analysis of nonlocal composite laminated toroidal shell segments subjected to mechanical shock

The present study deals with the nonlinear forced vibration of composite shallow nano toroidal shell segments. The improved Donnell shell theory is used with the nonlinear geometric strains, i.e., von Karman, Stein, and McElman’s assumptions. A coupled nonlinear partial differential equations using nonlocal theory, including the influence of nano-scales, is derived. The boundary conditions are simply supported and clamped–clamped, and the nano toroid shell is subjected to impulse radial dynamic excitation. The linear solution is verified by comparing natural frequencies with the available results using Galerkin’s method. The approximated linear mode shapes of the free vibration, which satisfy the boundary conditions, are used as the assumed multi-mode displacement functions required to solve the nonlinear vibration. Using Hamilton’s principle, the nonlinear equations of motion in generalized coordinates are solved using the displacement field by applying Galerkin’s and Runge–Kutta’s methods. Using the presented model, the effects of layer stacking, toroidal shell segments curvature (convex and concave toroidal shells), length scale parameter, and material properties are studied in detail, and some conclusions are surveyed. It is observed that the nonlocal parameter demonstrates a considerable effect on the dynamics behavior characteristics response of the toroidal shell segments. Furthermore, different fiber orientation effects, displacement fields, time response, and geometry parameters, i.e., thickness, and length are studied. Results indicate that natural frequencies significantly depend on the toroid dimensions, boundary conditions, layer stacking, curvature change, and considered wave numbers.

Gravitational Interaction in the Chimney Lattice Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

Gravitational potentials and forces in the Lattice Universe: a slab

We study the effect of the slab topology $T\times R\times R$ of the Universe on the form of gravitational potentials and forces created by point-like masses. We obtain two alternative forms of solutions: one is based on the Fourier series expansion of the delta function using the periodical property along the toroidal dimension, and another one is derived by direct summation of solutions of the Helmholtz equation for the source particle and all its images. The latter one takes the form of the sum of Yukawa-type potentials. We demonstrate that for the present Universe the latter solution is preferable for numerical calculations since it requires less terms of the series to achieve the necessary precision.

Variations of cops and robbers game on grids

Cops and robber is a two player turn-based game played on a graph where cops try to capture the robber. The cop number of a graph is the minimum number of cops required to capture the robber. We consider two variants of this game, namely cops and attacking robber and lazy cops and robber. In cops and attacking robber version, the robber can attack a cop and remove that cop from the game, whereas in lazy cops and robber version only one cop is allowed to move on a cop’s turn. We investigate the cop number of various grids (planar, cylindrical, toroidal and high dimension) and hypercubes for these variants.

Analysis of Rectangular Cross-Section Toroidal Helix Geometry for Winding Length Optimization

Recent advances in additive direct-write circuit technology have enabled the fabrication of inductive winding geometries previously considered impossible by conventional methods. In this letter, a winding fabricated around a rectangular cross-section toroidal core is considered. As an extension of research embedding toroidal cores within printed circuit board, this letter considers the minimization of the winding length when the vertical path, along the toroidal z-direction, is not restricted to be perfectly vertical, which is only possible with direct-write techniques. It will be shown that the exact analysis results in a transcendental equation for the optimized vertical midpoints of the winding turns. However, a few reasonable approximations allow an analytical expression for this optimized midpoint to be found. Comparisons of this approximate analytical solution to the exact solution found by numerical methods will be presented for typical toroid dimensions. The accuracy of this approximate solution with changing turn density will also be presented. For typical toroid dimensions, it was found that the choice of midpoint can change the total winding length by as much as 10%. The analytical approximate solution for the midpoint was found to deviate by 2.75% of angular gap from the exact solution, which resulted in an error in the minimum winding length of only 0.07%, a result which will be discussed in this letter.

Design and analysis of mock-up of CFETR water cooled ceramic blanket for neutronics experiment

The water cooled ceramic breeder (WCCB) blanket is one of the blanket candidates for China Fusion Engineering Test Reactor (CFETR). The neutronics experiment of the WCCB blanket is to validate the neutron transport codes and nuclear data libraries. A scaled down mock-up of the WCCB blanket should be designed considering constraints of economic costs and experimental conditions before the neutronics experiment. In this work, the mock-up was designed keeping neutronics and geometric characteristics of the original equatorial outboard blanket module of CFETR. The radial arrangement of the mock-up was designed firstly, including tungsten armor, first wall, breeding zone 1, beryllium layer 1, cooling plate 1, breeding zone 2, beryllium layer 2, cooling plate 2. Then the toroidal and poloidal dimensions of mock-up were optimized. Five mock-ups with the same radial arrangement and different toroidal and poloidal dimensions were selected as initial mock-ups. The nuclear response of these five mock-ups, including neutron intensity, neutron spectra and tritium production rate were analyzed. After the optimization, the size of the experimental mock-up was determined as 20.00 cm (Toroidal) × 20.00 cm (Poloidal) × 17.27 cm (Radial). The analyzed results showed that the neutronics performance of the mock-up were similar with the real blanket module and it can be employed to carry out neutronics experiments.

Stable Cosmological Kaluza\u2013Klein Spacetimes

We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinian field equations coupled to a wave map type and a Maxwell type equation by the Kaluza–Klein reduction. The Milne universe solves those field equations when the additional parts arising from the toroidal dimensions are chosen constant. We prove future stability of the Milne universe within this class of spacetimes, which establishes stability of a large class of cosmological Kaluza–Klein vacua. A crucial part of the proof is the implementation of a new gauge for Maxwell-type equations in the cosmological context, which we refer to as slice-adapted gauge.

Explaining low ell anomalies in the CMB power spectrum with resonant superstring excitations during inflation

We explore the possibility that both the suppression of the ell = 2 multipole moment of the power spectrum of cosmic microwave background temperature fluctuations and the possible dip for ell = 10–30 can be explained as well as a possible new dip for ell approx 60 as the result of the resonant creation of sequential excitations of a fermionic (or bosonic) closed superstring that couples to the inflaton field. We consider a D,=,26 closed bosonic string with one toroidal compact dimension as an illustration of how string excitations might imprint themselves on the CMB. We analyze the existence of successive momentum states, winding states or oscillations on the string as the source of the three possible dips in the power spectrum. Although the evidence of these dips are of marginal statistical significance, this might constitute the first observational evidence of successive superstring excitations in Nature.

Interplay between edge magnetic topology, pressure profile and blobs in the edge of RFX-mod

The observation of the periodic pressure profile time oscillations in the edge region (0.93 < r/a < 1) of a RFX-mod device allows one to investigate the role of pressure as a turbulence regulation mechanism. The proportionality between the radial correlation length of edge fluctuations and the radial characteristic pressure length Lp suggests a sort of regulation of the turbulent spatial scale, where Lp sets the radial dimension of the blobs. Moreover, the spatial scale regulation is confirmed by observing a linear scaling between the energy injection scale and the toroidal dimension of the edge coherent structures. On the other hand, the link between ∇Pe and turbulence level does not hold locally: the edge fluctuation level is higher in the toroidal region of lower edge pressure gradient. Hence if coherent structures are generated locally in the region of strongest ∇Pe, they flow and accumulate where ∇Pe is lower.

Solution-Phase Structures of Gallium-Containing Pyrogallol[4]arene Scaffolds

The variations in architecture of gallium-seamed (PgC4Ga) and gallium-zinc-seamed (PgC4GaZn) C-butylpyrogallol[4]arene nanoassemblies in solution (SANS/NMR) versus the solid state (XRD) have been investigated. Rearrangement from the solid-state spheroidal to the solution-phase toroidal shape differentiates the gallium-containing pyrogallol[4]arene nanoassemblies from all other PgCnM nanocapsules studied thus far. Different structural arrangements of the metals and arenes of PgC4Ga versus PgC4GaZn have been deduced from the different toroidal dimensions, C–H proton environments and guest encapsulation of the two toroids. PGAA of mixed-metal hexamers reveals a decrease in gallium-to-metal ratio as the second metal varies from cobalt to zinc. Overall, the combined study demonstrates the versatility of gallium in directing the self-assembly of pyrogallol[4]arenes into novel nanoarchitectures.

Shape of Compact Toroidal Dimensions Tθd and Casimir Effect on MD × Tθd Spacetime

We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is MD × Tθ2, where MD is the D-dimensional Minkowski spacetime and Tθ2 the twisted torus described by R1, R2, and θ. For the case R1 = R2 we found that the massive bulk scalar field Casimir energy is singular for D=even and this singularity is R-dependent and remains even when the force is calculated. Also the massless Casimir energy and force is regular only for D = 4 (!). This is very interesting phenomenologically. We examine the energy and force as a function of θ. Also we address the stabilization problem of the compact space. We also briefly discuss some phenomenological implications.

Clustered frequency analysis of shear Alfvén modes in stellarators

The shear Alfvén spectrum in three-dimensional configurations, such as stellarators and rippled tokamaks, is more densely populated due to the larger number of mode couplings caused by the variation in the magnetic field in the toroidal dimension. This implies more significant computational requirements that can rapidly become prohibitive as more resolution is requested. Alfvén eigenfrequencies and mode structures are a primary point of contact between theory and experiment. A new algorithm based on the Jacobi–Davidson method is developed here and applied for a reduced magnetohydrodynamics model to several stellarator configurations. This technique focuses on finding a subset of eigenmodes clustered about a specified input frequency. This approach can be especially useful in modeling experimental observations, where the mode frequency can generally be measured with good accuracy and several different simultaneous frequency lines may be of interest. For cases considered in this paper, it can be a factor of 102–103 times faster than more conventional methods.

Toroidal DNA Condensates: Unraveling the Fine Structure and the Role of Nucleation in Determining Size

Toroidal DNA condensates have attracted the attention of biophysicists, biochemists, and polymer physicists for more than thirty years. In the biological community, the quest to understand DNA toroid formation has been motivated by its relevance to gene packing in certain viruses and by the potential use of DNA toroids in artificial gene delivery (e.g., gene therapy). In the physical sciences, DNA toroids are appreciated as a superb model system for studying particle formation by the collapse of a semiflexible, polyelectrolyte polymer. This review focuses on experimental studies from the past few years that have significantly increased our understanding of DNA toroid structure and the mechanism of their formation. Highlights include structural studies that show the DNA strands within toroids to be packed in an ideal hexagonal lattice, and also in regions with a nonhexagonal lattice that are required by the topological constraints associated with winding DNA into a toroid. Recent studies of DNA toroid formation have also revealed that toroid size limits result from a complex interplay between kinetic and thermodynamic factors that govern both toroid nucleation and growth. The work discussed in this review indicates that it will ultimately be possible to obtain substantial control over DNA toroid dimensions.

Contribution of Hydrophobicity to Thermodynamics of Ligand-DNA Binding and DNA Collapse

The importance of understanding the dynamics of DNA condensation is inherent in the biological significance of DNA packaging in cell nuclei, as well as for gene therapy applications. Specifically, the role of ligand hydrophobicity in DNA condensation has received little attention. Considering that only multivalent cations can induce true DNA condensation, previous studies exploring monovalent lipids have been unable to address this question. In this study we have elucidated the contribution of the hydrophobic effect to multivalent cation- and cationic lipid-DNA binding and DNA collapse by studying the thermodynamics of cobalt hexammine-, spermine-, and lipospermine-plasmid DNA binding at different temperatures. Comparable molar heat capacity changes (ΔCp) associated with cobalt hexammine- and spermine-DNA binding (−23.39 cal/mol K and −17.98 cal/mol K, respectively) suggest that upon binding to DNA, there are insignificant changes in the hydration state of the methylene groups in spermine. In contrast, the acyl chain contribution to the ΔCp of lipospermine-DNA binding (ΔCp ϕ=ΔCp lipospermine−ΔCp spermine) is significant (−220.94 cal/mol K). Although lipopermine induces DNA ordering into “tubular” suprastructures, such structures do not assume toroidal dimensions as observed for spermine-DNA complexes. We postulate that a steric barrier posed by the acyl chains in lipospermine precludes packaging of DNA into dimensions comparable to those found in nature.

Velocity fields of edge/Scrape-Off-Layer turbulence in Alcator C-Mod

Using high speed movies of edge/Scrape-Off-Layer emission, velocity fields of the turbulent fluctuations have been measured in a small region of the poloidal/radial plane at the plasma’s outboard midplane. Gas-puff-imaging is used to localize the emission in the toroidal dimension. The measured Dα line emission responds to the underlying spatio-temporal dynamics of density and temperature. Time-delay cross-correlation analysis is applied to the 64×64 pixel movie images and yields time-averaged velocity fields for the emission perturbations. The spatial resolution of the velocity determinations is a few mm over the viewed region. It is found that the velocities inside the separatrix are almost purely poloidal. In the SOL the radial velocity component is outward, and significant radial acceleration is observed. The poloidal and radial components of the SOL velocities vary with the discharge conditions. The magnitudes of all the velocity components measured this way range from 0 to ∼1000m/s.

Human DNA ligase I completely encircles and partially unwinds nicked DNA

The end-joining reaction catalysed by DNA ligases is required by all organisms and serves as the ultimate step of DNA replication, repair and recombination processes. One of three well characterized mammalian DNA ligases, DNA ligase I, joins Okazaki fragments during DNA replication. Here we report the crystal structure of human DNA ligase I (residues 233 to 919) in complex with a nicked, 5' adenylated DNA intermediate. The structure shows that the enzyme redirects the path of the double helix to expose the nick termini for the strand-joining reaction. It also reveals a unique feature of mammalian ligases: a DNA-binding domain that allows ligase I to encircle its DNA substrate, stabilizes the DNA in a distorted structure, and positions the catalytic core on the nick. Similarities in the toroidal shape and dimensions of DNA ligase I and the proliferating cell nuclear antigen sliding clamp are suggestive of an extensive protein-protein interface that may coordinate the joining of Okazaki fragments.

Toroidal Contact Model: Computational Results

The classical computational model assumes touching of the contact members by a perfectly conducting small sphere that constricts the current flow, giving rise to a repulsive electrodynamical force. Accepting more contact spots (usually each spot is considered with its own sphere) and a superposing of effects is done without allowing for the reciprocal influences of these spots. However, it can image a greater touching zone than that with a spot alone, such as a circular toroidal one, having the same cross-section radius as the classical model small sphere has. Starting from the relationships deduced in the author's earlier articles, the computed variations of current density from constriction zones of the toroidal model against the distances from the symmetry axis, and from the contact surface, are presented here as representative diagrams. The dependency diagrams of the electrodynamical forces for such a configuration, on the relative values of the contact members and of the toroid dimensions are presented too, point out the appearance of attractive forces between contacts.Rounding the two introductory works for the toroidal contact model, this article could help find practical building solutions of contacts that avoid the opening tendency at great currents, and work out new computations for contact heating.

Evidence that both kinetic and thermodynamic factors govern DNA toroid dimensions: effects of magnesium(II) on DNA condensation by hexammine cobalt(III).

Millimolar concentrations of divalent cations are shown to affect the size of toroids formed when DNA is condensed by multivalent cations. The origins of this effect were explored by varying the order in which MgCl(2) was added to a series of DNA condensation reactions with hexammine cobalt chloride. The interplay between Mg(II), temperature, and absolute cation concentration on DNA condensation was also investigated. These studies reveal that DNA condensation is extremely sensitive to whether Mg(II) is associated with DNA prior to condensation or Mg(II) is added concurrently with hexammine cobalt(III) at the time of condensation. It was also found that, in the presence of Mg(II), temperature and dilution can have opposite effects on the degree of DNA condensation. A systematic comparison of DNA condensates observed in this study clearly illustrates that, under our low-salt conditions, toroid size is determined by the kinetics of toroid nucleation and growth. However, when Mg(II) is present during condensation, toroid size can also be limited by a thermodynamic parameter (e.g., undercharging). The path dependence of DNA condensation presented here illustrates that regardless of which particular factors limit toroid growth, toroids formed under the various conditions of this study are largely nonequilibrium structures.