Toroidal Topology Research Articles

Residue interaction network analysis of Dronpa and a DNA clamp

Topology is an essential aspect of protein structure. The network paradigm is increasingly used to describe the topology and dynamics of proteins. In this paper, the effect of topology on residue interaction network was investigated for two different proteins: Dronpa and a DNA clamp, which have cylindrical and toroidal topologies, respectively. Network metrics including characteristic path lengths, clustering coefficients, and diameters were calculated to investigate their global topology parameters such as small-world properties and packing density. Measures of centrality including betweenness, closeness, and residue centrality were computed to predict residues critical to function. Additionally, the detailed topology of the hydrophobic pocket in Dronpa, and communication pathways across the interface in the DNA clamp, were investigated using the network. The results are presented and discussed with regard to existing residue interaction network properties of globular proteins and elastic network models on Dronpa and the DNA clamp. The topological principle underlying residue interaction networks provided insight into the architectural organization of proteins.

CASIMIR FORCE OF FERMIONS COUPLED TO MONOPOLES IN SIX-DIMENSIONAL SPACETIME

We calculate the Casimir force for a fermionic quantum field in a piston geometry with three parallel plates. The fermion satisfies bag boundary conditions on the plates and the spacetime is assumed to have compact extra dimensions. The calculation is performed in the cases where the extra space has toroidal and spherical topology. We are mainly interested in the case in which the fermion is coupled non-trivially to an extra-dimensional defect, with a torus extra-dimensional topological background. We found that in certain limits, the Casimir force corresponding to the defect-fermion system and to the sphere, has opposite sign, in reference to those corresponding to the toroidal extra-dimensional spaces.

Magnetic effects on spontaneous symmetry breaking/restoration in a toroidal topology

We study temperature and finite-size effects on the spontaneous symmetry breaking/restoration for a scalar field model under the influence of an external magnetic field, at finite chemical potential. We use the 2PI formalism and consider the large-$N$ limit. We find that there is a minimal size of the system to sustain the broken phase, which diminishes as the applied field increases but is independent of the chemical potential. We analyze the critical curves and show that the magnetic field enhances the broken-phase regions, while increasing the chemical potential leads to a diminishement of the critical temperature.

On attractor mechanism of [formula omitted] black holes

We construct a general family of exact non-extremal 4-dimensional black holes in AdS gravity with U(1) gauge fields non-minimally coupled to a dilaton and a non-trivial dilaton potential. These black holes can have spherical, toroidal, and hyperbolic horizon topologies. We use the entropy function formalism to obtain the near horizon data in the extremal limit. Due to the non-trivial self-interaction of the scalar field, the zero temperature black holes can have a finite horizon area even if only the electric field is turned on.

On the total mass of closed universes

The total mass, the Witten type gauge conditions and the spectral properties of the Sen-Witten and the 3-surface twistor operators in closed universes are investigated. It has been proven that a recently suggested expression ${\tt M}$ for the total mass density of closed universes is vanishing if and only if the spacetime is flat with toroidal spatial topology; it coincides with the first eigenvalue of the Sen-Witten operator; and it is vanishing if and only if Witten's gauge condition admits a non-trivial solution. Here we generalize slightly the result above on the zero-mass configurations: ${\tt M}=0$ if and only if the spacetime is holonomically trivial with toroidal spatial topology. Also, we show that the multiplicity of the eigenvalues of the (square of the) Sen-Witten operator is at least two, and a potentially viable gauge condition is suggested. The monotonicity properties of ${\tt M}$ through the examples of closed Bianchi I and IX cosmological spacetimes are also discussed. A potential spectral characterization of these cosmological spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the Sen-Witten and the 3-surface twistor operators, is also indicated.

Tailoring the network to the problem: topology configuration in hybrid electronic packet switched/optical circuit switched interconnects

SUMMARYWe consider a hybrid electronic packet switched and optical circuit switched interconnection network for future high performance computing and datacenter systems. Given the logical task‐to‐task communication graph of an application, our objective is to cluster the logical parallel tasks to compute resources and configure the (reconfigurable) optical part of the hybrid interconnect to efficiently serve application communication requirements. We formulate the clustering and topology configuration problem in such a network, prove that it is NP‐complete, and provide an optimal algorithm to solve it based on an integer linear programming formulation. The integer linear programming algorithm is used to optimally solve small‐scale instances of the problem for the purpose of obtaining performance bounds. Aiming at large‐scale, we also present a heuristic based on simulated annealing that trades‐off performance for responsiveness. We measure the performance of a hybrid interconnect employing the proposed algorithm using real workloads, as well as extrapolated traffic, and compare it against application mapping on conventional fixed, electronic‐only interconnects based on toroidal topologies. Copyright © 2013 John Wiley & Sons, Ltd.

Exact hairy black brane solutions in 5D anti–de Sitter space and holographic renormalization group flows

We construct a general class of exact, regular black hole solutions with toroidal horizon topology in 5-dimensional AdS gravity with a self-interacting scalar field. Due to the non-trivial backreaction of the scalar field, the no-hair theorems can be evaded so that an event horizon can be formed. The scalar field is regular everywhere outside the curvature singularity and it vanishes at the boundary where the potential is finite. We study the properties of these black holes in the context of AdS/CFT duality and comment on the dual operators, which saturate the unitarity bound. We present exact expressions for the beta-function and construct a c-function that characterizes the RG flow.

Topology and Origin of Effective Spin Meron Pairs in Ferromagnetic Multilayer Elements

We report on pairs of converging-diverging spin vortices in Co/Rh/NiFe trilayer disks. The lateral magnetization distribution of these effective spin merons is directly imaged by means of element-selective x-ray microscopy. By this method, both the divergence and circulation states of the individual layers are identified to be antisymmetric. Reversal measurements on corresponding continuous films reveal that biquadratic interlayer exchange coupling is the cause for the effective meron pair formation. Moreover, their three-dimensional magnetization structure is determined by micromagnetic simulations. Interestingly, the magnetic induction aligns along a flux-closing torus. This toroidal topology enforces a symmetry break, which links the core polarities to the divergence configuration.

Non-Existence of Toroidal Cohomogeneity-1 Near-Horizon Geometries

We prove that $D\geq 5$ dimensional stationary, non-static near horizon geometries with (D-3) rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D=4 dimensions the same result is obtained under the assumption of a non-negative cosmological constant.

FARADAY ROTATION DISTRIBUTIONS FROM STELLAR MAGNETISM IN WIND-BLOWN BUBBLES

Faraday rotation is a valuable tool for detecting magnetic fields. Here the technique is considered in relation to wind-blow bubbles. In the context of spherical winds with azimuthal or split monopole stellar magnetic field geometries, we derive maps of the distribution of position angle (PA) rotation of linearly polarized radiation across projected bubbles. We show that the morphology of maps for split monopole fields are distinct from those produced by the toroidal field topology; however, the toroidal case is the one most likely to be detectable because of its slower decline in field strength with distance from the star. We also consider the important case of a bubble with a spherical sub-volume that is field-free to approximate crudely a "swept-up" wind interaction between a fast wind (or possibly a supernova ejecta shell) overtaking a slower magnetized wind from a prior state of stellar evolution. With an azimuthal field, the resultant PA map displays two arc-like features of opposite rotation measure, similar to observations of the supernova remnant G296.5+10.0. We illustrate how PA maps can be used to disentangle Faraday rotation contributions made by the interstellar medium versus the bubble. Although our models involve simplifying assumptions, their consideration leads to a number of general robust conclusions for use in the analysis of radio mapping datasets.

Spontaneous symmetry restoration in a field theory at finite chemical potential in a toroidal topology

We consider the massive vector $N$-component $(\lambda\varphi^{4})_{D}$ theory defined on a Euclidean space with a toroidal topology. Using recently developed methods to perform a compactification of a $d$-dimensional subspace at finite chemical potential, we treat jointly the effects of temperature and spatial boundaries, setting forth grounds for an analysis of spontaneous symmetry restoration driven by temperature and spatial boundaries as a function of the chemical potential. We restrict ourselves to d=2, which corresponds to the heated system confined between two parallel planes (separation $L$) in dimensions D=3 and D=4. We present results, in the large-$N$ limit, which exhibit how finite size and chemical potential affect spontaneous symmetry restoration.

A concrete anti-de Sitter black hole with dynamical horizon having toroidal cross-sections and its characteristics

We propose a special solution of Einstein equations in the general Vaidya form representing a dynamical black hole having horizon cross-sections with toroidal topology. The concrete model enables us to study for the first time dynamical horizons with toroidal topology, its area law, and the question of matter flux inside the horizon, without using a cut-and-paste technology to construct the solution.

Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a c=1 “barrier”, analogous to the c=1 barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For d⩽1 we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For d>1 the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension dH=3. In the d>1 sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Hořava–Lifshitz models.

Strike point splitting in the heat and particle flux profiles compared with the edge magnetic topology in a n = 2 resonant magnetic perturbation field at JET

At JET the error field correction coils can be used to generate an n = 1 or n = 2 magnetic perturbation field (Liang et al 2007 Plasma Phys. Control. Fusion 49 B581). Various experiments at JET have already been carried out to investigate the mitigation of ELMs by resonant magnetic perturbations (RMPs) (Liang et al 2010 Nucl. Fusion 50 025013, Liang et al 2011 Nucl. Fusion 51 073001). However, the typical formation of a secondary strike point (strike point splitting) by RMPs observed in other machines (Jakubowski et al 2010 Contrib. Plasma Phys. 50 701–7, Jakubowski et al 2004 Nucl. Fusion 44 S1–11, Nardon et al 2011 J. Nucl. Mater. 415 S914–7, Eich et al 2003 Phys. Rev. Lett. 91 195003, Evans et al 2007 J. Nucl. Mater. 363–365 570–4, Evans et al 2005 J. Phys.: Conf. Ser. 7 174–90, Watkins et al 2009 J. Nucl. Mater. 390–391 839–42) has never been observed at JET before. In this work we will present discharges where for the first time a strike point splitting by RMPs at JET has been observed. We will show that in these particular cases the strike point splitting matches the vacuum edge magnetic field topology. This is done by comparing heat and particle flux profiles on the outer divertor plate with the magnetic footprint pattern obtained by field line tracing. Further the evolution of the strike point splitting during the ramp up phase of the perturbation field and during a q95-scan is investigated, and it will be shown that the spontaneous appearance of the strike point splitting is only related to some geometrical effects of the toroidal asymmetric magnetic topology.

Phase transition in the massive Gross-Neveu model in toroidal topologies

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($\ensuremath{\lambda}$), we find an asymptotic-freedom type of behavior, with $g\ensuremath{\rightarrow}0$ as $L\ensuremath{\rightarrow}0$ and/or $T\ensuremath{\rightarrow}\ensuremath{\infty}$. At $T=0$, and for $\ensuremath{\lambda}\ensuremath{\ge}{\ensuremath{\lambda}}_{c}^{(D)}$ (the strong-coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, ${L}_{c}^{(D)}$, and the deconfining temperature, ${T}_{d}^{(D)}$, are determined as functions of $\ensuremath{\lambda}$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\ensuremath{\approx}350\text{ }\text{ }\mathrm{MeV}$), the results obtained are of the same order of magnitude as the diameter ($\ensuremath{\approx}1.7\text{ }\text{ }\mathrm{fm}$) and the estimated deconfining temperature ($\ensuremath{\approx}200\text{ }\text{ }\mathrm{MeV}$) of hadrons.

Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics.

Liquid crystal beads constrained on thin cellulosic fibers: electric field induced microrotors and N–I transition

We directly visualize the response of nematic liquid crystal drops of toroidal topology threaded in cellulosic fibers, suspended in air, to an AC electric field and at different temperatures over the N–I transition. This new liquid crystal system can exhibit non-trivial point defects, which can be energetically unstable against expanding into ring defects depending on the fiber constraining geometries. The director anchoring tangentially near the fiber surface and homeotropically at the air interface makes a hybrid shell distribution that in turn causes a ring disclination line around the main axis of the fiber at the center of the droplet. Upon application of an electric field, E, the disclination ring first expands and moves along the fiber main axis, followed by the appearance of a stable “spherical particle” object orbiting around the fiber at the center of the liquid crystal drop. The rotation speed of this particle was found to vary linearly with the applied voltage. This constrained liquid crystal geometry seems to meet the essential requirements in which soliton-like deformations can develop and exhibit stable orbiting in three dimensions upon application of an external electric field. On changing the temperature the system remains stable and allows the study of the defect evolution near the nematic–isotropic transition, showing qualitatively different behaviour on cooling and heating processes. The necklaces of such liquid crystal drops constitute excellent systems for the study of topological defects and their evolution and open new perspectives for application in microelectronics and photonics.

Neel Effect current sensor featuring double core toroidal topology

A Neel Effect® current sensor featuring a double toroidal core is proposed. The measurement relies on the application of a harmonic excitation to the magnetic core and on the sensing of the magnetic flux density variations in the presence of a current to measure. The principle of a device designed so as to perform both those operations by means of the same winding is presented and validated experimentally. The measurement of DC currents is carried out over the [−200–200 A] range under different excitation conditions.

Study of multi-black-hole and ring-singularity apparent horizons

We study critical black hole separations for the formation of a common apparent horizon in systems of $N$ - black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for $N=2,3,4,5$, and relate them to the unequal mass binary black hole case. We then study the apparent horizon of the time symmetric initial geometry of a ring singularity of different radii. The apparent horizon is used as indicative of the location of the event horizon in an effort to predict a critical ring radius that would generate an event horizon of toroidal topology. We found that a good estimate for this ring critical radius is $20/(3\pi) M$. We briefly discuss the connection of this two cases through a discrete black hole 'necklace' configuration.

Can an astrophysical black hole have a topologically non-trivial event horizon?

In 4-dimensional General Relativity, there are several theorems restricting the topology of the event horizon of a black hole. In the stationary case, black holes must have a spherical horizon, while a toroidal spatial topology is allowed only for a short time. In this Letter, we consider spinning black holes inspired by Loop Quantum Gravity and by alternative theories of gravity. We show that the spatial topology of the event horizon of these objects changes when the spin parameter exceeds a critical value and we argue that the phenomenon may be quite common for non-Kerr black holes. Such a possibility may be relevant in astrophysics, as in some models the accretion process can induce the topology transition of the horizon.