Exact Field Research Articles

Study of the Antiferromagnetic Blume-Capel Model on kagomé Lattice

We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagomé lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.

Prehospital intubation for isolated severe blunt traumatic brain injury: worse outcomes and higher mortality.

Prehospital endotracheal intubation (ETI) for traumatic brain injury (TBI) is a controversial issue. The aim of this study was to investigate the effect of prehospital ETI in patients with TBI. Cohort-matched study using the US National Trauma Data Bank (NTDB) 2008-2012. Patients with isolated severe blunt TBI (AIS head ≥3, AIS chest/abdomen <3) and a field GCS ≤8 were extracted from NTDB. A 1:1 matching of patients with and without prehospital ETI was performed. Matching criteria were sex, age, exact field GCS, exact AIS head, field hypotension, field cardiac arrest, and the brain injury type (according PREDOT-code). The matched cohorts were compared with univariable and multivariable regression analysis. A total of 27,714 patients were included. Matching resulted in 8139 cases with and 8139 cases without prehospital ETI. Prehospital ETI was associated with significantly longer scene (median 9 vs. 8min, p<0.001) and transport times (median 26 vs. 19min, p<0.001), lower Emergency Department (ED) GCS scores (in patients without sedation; mean 3.7 vs. 3.9, p=0.026), more ventilator days (mean 7.3 vs. 6.9, p=0.006), longer ICU (median 6.0 vs. 5.0days, p<0.001) and total hospital length of stay (median 10.0 vs. 9.0days, p<0.001), and higher in-hospital mortality (31.4 vs. 27.5%, p<0.001). In regression analysis prehospital ETI was independently associated with lower ED GCS scores (RC -4.213, CI -4.562/-3.864, p<0.001) and higher in-hospital mortality (OR 1.399, CI 1.205/1.624, p<0.001). In this large cohort-matched analysis, prehospital ETI in patients with isolated severe blunt TBI was independently associated with lower ED GCS scores and higher mortality.

Active transport improves the precision of linear long distance molecular signalling

Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices.

On achieving pure electromagnetic left-handedness through magnetodielectric field compression

The relationship between electromagnetic phase and power flow in metamaterials composed of periodic magnetodielectric inclusions is investigated. The distribution of Poynting vectors in $k$ space across multiple Brillouin zones suggests that backward phase is a result of field compression within the inclusions, and that left-handedness can be achieved without negative electric or magnetic susceptibility (i.e., without out-of-phase dipole moments). This hypothesis is verified by showing that a one-dimensional periodic array of magnetodielectric slabs can be designed to mimic the properties of an ideal (homogeneous) left-handed medium. Furthermore, using exact fields and without any field averaging, it is shown that the structure can be designed such that practically all power is carried in the fundamental left-handed spectral component. In the limit where the fundamental contains all the power, this periodic structure has the same spectral power signature as that of a homogeneous left-handed medium. It is shown that this congruence does not manifest when the inclusions are purely dielectric, nor does it manifest for magnetodielectric inclusions in two or three dimensions.

Phase Diagram of the Antiferromagnetic Blume-Capel Model on Triangular Lattice

We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume- Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.

Charged particle tracking through electrostatic wire meshes using the finite element method

Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.

Three-dimensional steady thermodynamic analysis for a double-layer plate with a local heat source and harmonic load

Based on the three-dimensional heat conduction theory, von Karman equation and laminated plate theory, the three-dimensional steady thermodynamic behavior for a double-layer (coating/FGM) plate subjected to a local heat source and harmonic load is investigated in this paper. The exact three-dimensional steady temperature field has been obtained previously by using Poisson method and layer wise method, and then governing equations of the double-layer plate are solved by applying the finite difference method and Newmark method in space domain and time domain, respectively. Numerical results denote that functionally graded index, selected coating layer’s heat conduction coefficient, thickness ratio between total layers and coating layer, width of heat source strip, geometrical condition and boundary condition of the structure have great influence on the deflection and stresses for the double-layer plate.

Engineering Hybrid Guided Modes in Subwavelength Uniaxial Metamaterial Waveguides

We report anomalous dispersion properties of hybrid guided modes (HGMs) and their group velocity in a subwavelength uniaxial metamaterial waveguide with metal cladding. We derive exact dispersion relations and modal fields of HGMs by solving eigenvalue equation based on basic electromagnetic field theory in detail. Numerical results show that two fundamental HGMs and two types of high-order HGMs can be excited, and their exciting conditions are clarified. In addition, such HGMs can be engineered to belong to normal dispersion or anomalous dispersion. Importantly, the HGMs may be controlled to be forward or backward, and their group velocities may be very small in a certain frequency band. These properties make such metamaterial waveguides have many potential applications in integrated optics, information storage and biosensing.

Regularized image system for Stokes flow outside a solid sphere

The image system for a three-dimensional flow generated by regularized forces outside a solid sphere is formulated and implemented as an extension of the method of regularized Stokeslets. The method is based on replacing a point force given by a delta distribution with a smooth localized function and deriving the exact velocity field produced by the forcing. In order to satisfy zero-flow boundary conditions at a solid sphere, the image system for singular Stokeslets is generalized to give exact cancellation of the regularized flow at the surface of the sphere. The regularized image system contains the same elements as the singular counterpart but with coefficients that depend on a regularization parameter. As this parameter vanishes, the expressions reduce to the image system of the singular Stokeslet. The expression relating force and velocity can be inverted to compute the forces that generate a given velocity boundary condition elsewhere in the flow. We present several examples within the context of biological flows at the microscale in order to validate and highlight the usefulness of the image system in computations.

Spherical aberration from trajectories in real and hard-edge solenoid fields

For analytical, real and hard-edge solenoidal axial magnetic fields, the low-energy electron trajectories are obtained using the third-order paraxial ray equation. Using the particle trajectories, it is shown that the spherical aberration in the hard-edge model is high and it increases monotonously with hard edginess, although the focal length converges, in agreement with a recent field and spherical aberration model. The model paved the way for a hard-edge approximation that gives correct focal length and spherical aberration, which is verified here by the trajectory method. In essence, we show that exact hard-edge fields give infinite spherical aberrations.

Q-colourings of the triangular lattice: exact exponents and conformal field theory

We revisit the problem of Q-colourings of the triangular lattice using a mapping onto an integrable spin-one model, which can be solved exactly using Bethe ansatz techniques. In particular we focus on the low-energy excitations above the eigenlevel g2, which was shown by Baxter to dominate the transfer matrix spectrum in the Fortuin–Kasteleyn (chromatic polynomial) representation for , where . We argue that g2 and its scaling levels define a conformally invariant theory, the so-called regime IV, which provides the actual description of the (analytically continued) colouring problem within a much wider range, namely . The corresponding conformal field theory is identified and the exact critical exponents are derived. We discuss their implications for the phase diagram of the antiferromagnetic triangular-lattice Potts model at non-zero temperature. Finally, we relate our results to recent observations in the field of spin-one anyonic chains.

Exact EM field excited by a short horizontal wire antenna lying on a conducting soil

To date, only under restrictive assumptions can we derive closed-form expressions for the fields generated by an electrically small horizontal wire antenna situated on a planar conducting soil. Such assumptions limit the validity of the derived formulas to specified frequency ranges, or to the case of highly-conducting material media. The purpose of this work is to relax all the constraints underlying the derivation of the previously published solutions to this half-space problem, and develop an analytical technique that allows to reduce the integral representations for the field components generated by the dipole source to a well-known elementary contour integral, whose evaluation is straightforward. Numerical results are presented to show the advantages of the obtained explicit formulas, which are valid regardless of the operating frequency, over the previous solutions.

Helicity is the only integral invariant of volume-preserving transformations

We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.

Y-shaped jets driven by an ultrasonic beam reflecting on a wall

This paper presents an original experimental and numerical investigation of acoustic streaming driven by an acoustic beam reflecting on a wall. The water experiment features a 2MHz acoustic beam totally reflecting on one of the tank glass walls. The velocity field in the plane containing the incident and reflected beam axes is investigated using Particle Image Velocimetry (PIV). It exhibits an original y-shaped structure: the impinging jet driven by the incident beam is continued by a wall jet, and a second jet is driven by the reflected beam, making an angle with the impinging jet. The flow is also numerically modeled as that of an incompressible fluid undergoing a volumetric acoustic force. This is a classical approach, but the complexity of the acoustic field in the reflection zone, however, makes it difficult to derive an exact force field in this area. Several approximations are thus tested; we show that the observed velocity field only weakly depends on the approximation used in this small region. The numerical model results are in good agreement with the experimental results. The spreading of the jets around their impingement points and the creeping of the wall jets along the walls are observed to allow the interaction of the flow with a large wall surface, which can even extend to the corners of the tank; this could be an interesting feature for applications requiring efficient heat and mass transfer at the wall. More fundamentally, the velocity field is shown to have both similarities and differences with the velocity field in a classical centered acoustic streaming jet. In particular its magnitude exhibits a fairly good agreement with a formerly derived scaling law based on the balance of the acoustic forcing with the inertia due to the flow acceleration along the beam axis.

Disorder-driven itinerant quantum criticality of three-dimensional massless Dirac fermions

Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder driven semimetal to metal quantum phase transition of three dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent ($z$) and correlation length exponent ($\nu$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field theoretical analysis.

Supersymmetric solutions to Euclidean Romans supergravity

We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions.

Manifolds with vectorial torsion

The present note deals with the properties of metric connections ∇ with vectorial torsion V on semi-Riemannian manifolds (Mn,g). We show that the ∇-curvature is symmetric if and only if V♭ is closed, and that V⊥ then defines an (n−1)-dimensional integrable distribution on Mn. If the vector field V is exact, we show that the V-curvature coincides up to global rescaling with the Riemannian curvature of a conformally equivalent metric. We prove that it is possible to construct connections with vectorial torsion on warped products of arbitrary dimension matching a given Riemannian or Lorentzian curvature—for example, a V-Ricci-flat connection with vectorial torsion in dimension 4, explaining some constructions occurring in general relativity. Finally, we investigate the Dirac operator D of a connection with vectorial torsion. We prove that for exact vector fields, the V-Dirac spectrum coincides with the spectrum of the Riemannian Dirac operator. We investigate in detail the existence of V-parallel spinor fields; several examples are constructed. It is known that the existence of a V-parallel spinor field implies dV♭=0 for n=3 or n≥5; for n=4, this is only true on compact manifolds. We prove an identity relating the V-Ricci curvature to the curvature in the spinor bundle. This result allows us to prove that if there exists a nontrivial V-parallel spinor, then RicV=0 for n≠4 and RicV(X)=X▪dV♭ for n=4. We conclude that the manifold is conformally equivalent either to a manifold with Riemannian parallel spinor or to a manifold whose universal cover is the product of R and an Einstein space of positive scalar curvature. We also prove that if dV♭=0, there are no non-trivial ∇-Killing spinor fields.

Electromagnetic Wave Theory for Calculation of Exact Magnetic Field in Case of BWO

Overall efficiency of high power microwave generating device depends upon input current in the form of electron beam and currents required for electromagnets. In order to increase the efficiency of device, if electromagnets are replaced by permanent magnets, overall efficiency of device shall increase. So, calculation of exact magnetic field is required. In this paper, the exact relation of magnetic field required in high power microwave generation using Backward Wave Oscillator (BWO) is found. BWO interacts with slow waves and is the most promising device to produce high power microwaves. The interaction involves the beams from high current density and the waveguide mode. An exact relation that specifically relates the various parameters of the waveguide like slow wave structures (SWS) dimensions, input beam voltage and operational frequency with axial magnetic field is derived. The derived equation gives calculation of exact values of magnetic field for focusing of beams. Theoretical and simulated work show good agreement with the previously available experimental data. So, with the derived electromagnetic wave relation exact value of magnetic field is calculated for desired frequency and power regime.

Differential Equations of Electrodiffusion: Constant Field Solutions, Uniqueness, and New Formulas of Goldman--Hodgkin--Katz Type

The equations governing one-dimensional, steady-state electrodiffusion are considered when there are arbitrarily many mobile ionic species present, in any number of valence classes, possibly also with a uniform distribution of fixed charges. Exact constant field solutions and new formulas of Goldman-Hodgkin-Katz type are found. All of these formulas are exact, unlike the usual approximate ones. Corresponding boundary conditions on the ionic concentrations are identified. The question of uniqueness of constant field solutions with such boundary conditions is considered, and is re-posed in terms of an autonomous ordinary differential equation of order $n+1$ for the electric field, where $n$ is the number of valence classes. When there are no fixed charges, the equation can be integrated once to give the non-autonomous equation of order $n$ considered previously in the literature including, in the case $n=2$, the form of Painlev\'e's second equation considered first in the context of electrodiffusion by one of us. When $n=1$, the new equation is a form of Li\'enard's equation. Uniqueness of the constant field solution is established in this case.

Correction to “Closed orbits of a charge in a weakly exact magnetic field”

Correction to “Closed orbits of a charge in a weakly exact magnetic field”