Cutoff Surface Research Articles

Integrating out geometry: holographic Wilsonian RG and the membrane paradigm

We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.

Non-relativistic fluid dual to asymptotically AdS gravity at finite cutoff surface

Using the non-relativistic hydrodynamic expansion, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to the second order of the expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy ensity of dual fluid does not run with the cutoff surface. The incompressible Navier-Stokes equations are also obtained in both cases.

Holographic multiverse and the measure problem

We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation between the UV cutoff scale ξ on the boundary and the hypersurface Σ on which the wave function is defined in the bulk. We propose that in the limit ξ → 0 this hypersurface should be used as the cutoff surface in the multiverse measure. Furthermore, we argue that in the inflating regions of spacetime with a slowly varying Hubble rate H the hypersurfaces Σ are surfaces of constant comoving apparent horizon (CAH). Finally, we introduce a measure prescription (called CAH+) which appears to have no pathological features and coincides with the constant CAH cutoff in regions of slowly varying H.

On O–X mode conversion in a 3D inhomogeneous plasma

An analysis of Maxwell's equations valid in a region of an ordinary wave to extraordinary wave conversion in plasmas confined by sheared and curved magnetic fields is carried out to derive an approximate system of wave equations in a three-dimensional (3D) inhomogeneous simplified stellarator-like geometry. The case is considered in which the ordinary wave cut-off surface and extraordinary wave cut-off surface, whose curvature is neglected, intersect at a point corresponding to the maximum of an incoming wave transverse distribution. The set of reduced partial differential wave equations is solved analytically by an integral representation of solutions. The form of the integral representation is justified by identifying the contour of integration. An asymptotic representation of the solution in the WKB domain is obtained that gives conversion coefficients for beams of WKB waves with a finite transverse distribution of rf field.

Wilsonian approach to fluid/gravity duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

Surface patterning on periodicity of femtosecond laser-induced ripples

Properties of femtosecond laser-induced ripples on patterned metal surfaces are investigated through using a crossed two-step line-scribing method. It is found that the ripple periodicity tends to decrease with larger surface roughness but increase with higher laser fluence. For the increased roughness, the change in ripple periodicity becomes more sensitive to the incident laser fluence. A cut-off surface roughness that prevents from altering the ripple periodicity is also revealed to increase with the lower laser fluence. These phenomena are discussed in the view of surface plasmon polaritons in the laser-induced plasma and the modified dielectric constant of the roughened surfaces.

270 翼形遠心送風機の騒音発生メカニズム : 翼通過周波数騒音とケーシング内共鳴(空力音響現象のメカニズムと計測制御,OS-22 流体関連振動・音響メカニズムと計測制御,総合テーマ「伝統を,未来へ!」)

The present study intended mechanism clarification of blade passing frequency (BPF) noise generation in wing profile centrifugal blower. First, visualized flow in the vicinity of cut-off that source of BPF noise brought out relation between blade passing and flow. Next, fluctuating pressure on cut-off surface was measured by probe microphone. Distribution of fluctuating pressure pinpointed major source of BPF noise. Measurement of fluctuating pressure on cut-off by probe microphone and detection of blade position by laser brought out relation between blade passing and fluctuating pressure. Measuring transfer function in casing cleared that the noise was amplified by resonance.

Investigation of the poloidal spectral resolution of O-mode reflectometry with two-dimensional full-wave modeling

Both the plasma poloidal curvature and the curvature of the probing wave-front play an important role for the spectral resolution of microwave reflectometry. The propagation of electromagnetic waves in a cylindrical plasma with a refractive index monotonically decreasing towards its center leads to elongation of the wave-front (i.e. an increase of the radius of curvature near the axis of radiation). Such a phase-front alteration can result in a major modification of the reflectometry response regarding on high k θ fluctuations. At the same time, the curvature of the cutoff surface in cylindrical plasma is always less than the curvature of the cutoff density for an O-mode wave. For specific geometry of the TEXTOR tokamak we perform numerical two-dimensional full-wave reflectometry synthesizing. The response from poloidaly rotating coherent density perturbation was analyzed on the variety of the plasma cutoff curvature and density scale length, which affects the incident wave-front curvature. The simulations are shown that the increase of the incident wave front curvature extends the spectral resolution of conventional reflectometer with gain antennas. On the other hand, the effect from the cutoff curvature is found to be much weaker as compare to the wave-front effect.

On the spatial structure and dispersion of slow magnetosonic modes coupled with Alfvén modes in planetary magnetospheres due to field line curvature

The structure of the slow mode coupled with Alfvén mode in the axially symmetric magnetosphere is studied in the paper. Due to the coupling, the slow magnetosonic wave gets dispersion across magnetic shells and becomes not strictly guided. The slow mode is found to be captured between the resonant and cutoff surfaces, where the wave vector radial component goes to infinity and to zero, accordingly. The resonant surface is farther from the Earth than the cutoff surface. The slow mode resonance frequency is much lower than the Alfvén resonance frequency due to small value of the sound velocity near the equator. The maximum of the slow mode amplitude expressed in terms of the parallel magnetic field is concentrated near the equator, but expressed in hydromagnetic terms is concentrated near the ionospheres.

Analysis of the Sawing Process With Abrasive Circular Saw Blades

This study simulates the sawing process with an abrasive circular saw blade and analyzes the generation of cutoff surfaces in the sawing process with the consideration of the blade deflection caused by the asymmetric wear of the blade outer edge. The analysis is built on the previous work of Matsui (1956, J. Jpn. Soc. Precis. Eng., 22, pp. 477–481) who presented an analytical formula for cutting force acting on a conical cutting edge. In this paper, the Matsui formula is modified to take into account the “size effect” of grinding and used to calculate the grinding force acting on the blade surface. A differential equation is constructed, and the related numerical solutions are provided to describe the blade deflection behavior in the sawing process. The study then discusses the influences of the “size effect,” workpiece length, workpiece speed and feed rate, as well as cutting edge density on sawing accuracies. Also discussed are workpiece speed and cutting edge density on the maximum deviation of the cutoff surface.

Proposal for detection of non-Markovian decay via current noise

We propose to detect non-Markovian decay of an exciton qubit coupled to multi-mode bosonic reservoir via shot-noise measurements. Non-equilibrium current noise is calculated for a quantum dot embedded inside a \QTR{it}{p-i-n} junction. An additional term from non-Markovian effect is obtained in the derivation of noise spectrum. As examples, two practical photonic reservoirs, photon vacuum with the inclusion of cut-off frequency and surface plasmons, are given to show that the noise may become super-Poissonian due to this non-Markovian effect. Utilizing the property of super-radiance is further suggested to enhance the noise value.

Electron temperature measurements in plasmas with surface wave absorption and wave cutoff frequency

A method for the measurements of electron temperature in the plasma using cutoff frequency and surface wave absorption frequency is described. The cutoff frequency, which gives directly the plasma density, is obtained from the transmission spectrum measured between two antennas exposed to the plasma. The surface wave absorption frequency, which has the information of the sheath determined by the electron density and the electron temperature, is obtained from the reflection spectrum measured at radiating antenna. The electron temperature is derived from the dispersion equation of the surface wave with the electron density measured from cutoff frequency.

On O–X mode conversion in spherical tokamaks

In this paper mode conversion of the ordinary wave to the extraordinary wave in a cold magnetized plasma at electron cyclotron frequencies is examined. A reduced set of wave equations, accounting for both the 2D inhomogeneity of the magnetic field and an arbitrary poloidal component of the magnetic field and coupling of the ordinary wave to the extraordinary wave near the O-mode cutoff surface, is derived. An integral representation of solutions to this set of equations is found. The conversion and reflection coefficients are calculated and analysed.

Multicomponent Liquid−Liquid Equilibria Prediction for Aromatic Extraction Systems Using COSMO-RS

A novel method based on unimolecular quantum mechanical calculations has been used to predict the multicomponent liquid−liquid equilibria (LLE). The recently developed COnductor-like Screening MOdel (COSMO), along with the most common quantum chemical package of Gaussian03 has been used in this work. COSMO-RS combines the COSMO model calculations with exact statistical thermodynamics of pairwise interacting surface segments and has been used for the evaluation of molecular interactions in liquids. COSMO-RS has been used to predict the LLE for 158 multicomponent data sets, which consist of 80 ternary, 9 quaternary, and 4 quinary systems, several of which are examined at different temperatures. The effective contact surface area (aeff), the hydrogen-bonding coefficient (chb), and the cutoff surface charge density for hydrogen bonding (σhb) have been estimated simultaneously, using 10 ternary data sets that consist of 11 different functional groups (CH3, CH2, CH, CHCH2, C−CH3, OH, CH2O, C−(CH2), COO, C−Cl, CH2−CN) and 9 different solvents (sulfolane, dimethyl sulfoxide, N-methyl pyrrolidone, furfural, propylene carbonate, triethylene glycol, tetraethylene glycol, ethylene carbonate, dicyanobutane). Cavity radii (ri) values up to 1.17 times greater than the Bondi radius have been used. The prediction has been initially benchmarked on the octane−toluene−sulfolane system at three temperatures: 25, 35, 45 °C, for which the root-mean-square deviations (RMSDs) are <1% for mole fraction predictions. Thereafter, the LLE has been predicted for 158 multicomponent data sets. An important aspect of our work is that, for the first time, quaternary and quinary systems have been predicted using COSMO-RS. The overall RMSD is <5% for multicomponent systems, compared to ∼1% for NRTL and UNIQUAC models and 5% for UNIFAC models.

A study on cut-off low vertical structure and precipitation in the Mediterranean region

Cut-off lows are common features of Mediterranean meteorology in warm months and are often related to severe weather. The present work introduces a classification of cut-off episodes, based on the vertical extension of the depression and the presence of a linked surface vortex, also analyzing precipitation patterns. Ten years of warm-season ERA-40 reanalysis, available every six hours on a 2.5° × 2.5° grid, are processed to extract a database of cut-off lows and surface cyclones, along with the related total and convective precipitation at the ground. The high temporal resolution of the dataset permits a detailed characterization of short lasting events, so far poorly analyzed.

Prediction of Binary VLE for Imidazolium Based Ionic Liquid Systems Using COSMO-RS

A novel method based on unimolecular quantum mechanical calculation has been used to predict the binary vapor−liquid equilibria (VLE) of ionic liquids (ILs).The recently developed conductor-like screening model (COSMO), along with the most common quantum chemical package of GAUSSIAN 03, has been used in this work. These conductor-like screening model calculations combined with exact statistical thermodynamics provide the information necessary for the evaluation of molecular interactions in liquids. An effective parametrization has been done using 10 associated and 22 binary nonassociated systems; these 32 systems are all non-ILs. The effective contact surface area aeff and the hydrogen-bonding coefficient chb have been estimated using a sequential scheme. The root-mean-square error obtained for excess Gibb's free energy is ∼0.1 for aeff and chb. Values for α‘ (misfit constant), σhb (cutoff surface charge density for hydrogen bonding), and cavity radii (ri) as given in the literature have been used as defa...

Spatial and spectral resolution of the plasma Doppler reflectometry

An approach to numerical simulations of microwave scattering in Doppler reflectometry is developed that is based on calculations of the two-dimensional spatial weighting function in the Born approximation. The knowledge of the spatial weighting (or instrumental) function, which contains complete information on both forward and backward scattering processes, allows one to calculate the output signal of a quadrature diagnostic detector for any given distribution of the electron plasma density fluctuations. The weighting functions were computed for axisymmetric distributions of the background plasma density and for arbitrarily specified fields in the mouths of the emitting and receiving antennas. Simulations carried out for different model representations of the scattering fluctuations yielded quantitative estimates of both the spatial and wavenumber resolutions of Doppler reflectometry. The simulations showed that the resolution of the method proposed worsens with increasing curvature of the cut-off surface. Conditions are determined under which the resolution of the diagnostics in small-and medium-size tokamaks can be substantially improved by using converging microwave beams. The possibility of utilizing focused probing microwave beams in Doppler reflectometry on ITER-scale devices is discussed.

Formation of a cylindrical ion beam in the field of an axisymmetric system of ring currents at a low Hall current

A study is made of the structure of an accelerating layer with a closed Hall current and the geometry of an ion beam in an external magnetic field created by an arbitrary axisymmetric system of ring currents under conditions such that the Hall current can be ignored. It is shown that the ion trajectories are perpendicular to the magnetron cutoff surface for electrons and that the cathode plasma boundary coincides with a magnetic field line. A magnetic field configuration is found in which the cutoff surface is a plane surface perpendicular to the axis of the system. It is shown that, for a small ratio of the gyroradius of the electrons (in terms of the maximum energy acquired by them in the layer) to the characteristic size of the structure, such a configuration provides sufficient means to ensure the formation of slightly converging ion beams or those that are essentially parallel to the system axis.

The influence of a southward and northward turning of the interplanetary magnetic field on the geomagnetic cut-off of cosmic rays, on the mirror points positions of geomagnetically trapped particles, and on their rate of precipitations in the atmosphere

A number of geomagnetic observations indicate that the orientation of the interplanetary magnetic field (IMF) plays a definite role in triggering several magnetospheric processes. In this theoretical study based on the superposition of a dipole geomagnetic field model and an uniform IMF, it is shown that when the northward component of the IMF decreases ( d B z / d t < 0 ), the geomagnetic cut-off surface moves to larger equatorial distances, the altitude of the mirror points of charged particles trapped in the geomagnetic field increases, and the value of their equatorial pitch angle decreases. Furthermore, we show that the loss cone angle of trapped particles decreases when d B z / d t is negative. The southward component of the magnetic field generated by an enhancement of the ring current produces similar effects everywhere inside this ring current loop.

O-X mode conversion in an axisymmetric plasma at electron cyclotron frequencies

The cold plasma dielectric function is employed to represent the plasma response of an axisymmetric steady state to incident waves at frequencies on the order of the electron cyclotron frequency. A boundary layer analysis of Maxwell’s equation valid near the mode conversion region is carried out to obtain an approximate system of wave equations. The independent variables of the wave equations are the flux surface label and poloidal angle. The case is analyzed in which the O mode cut-off surface and X mode cut-off surface intersect. An integral representation of solutions is given. It is shown that for a wide class of incident waves all such waves are transmitted with total mode conversion and no mode reflection. This work cannot assure that solutions with mode reflection do not occur, although a broad search for solutions, possibly with mode reflection, was unsuccessful.