Conformal Coordinates Research Articles

Motion4D-library extended

Motion4D-library extended

Holographic description of Kerr–Bolt–AdS–dS spacetimes

We show that there exists a holographic 2D CFT description of a Kerr–Bolt–AdS–dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr–Bolt–AdS–dS spacetimes and find in the “near region”, the wave equation in extremal limit could be written in terms of the SL ( 2 , R ) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr–Bolt–AdS–dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL ( 2 , R ) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Greenʼs functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

Hidden conformal symmetry of extremal black holes

We study the hidden conformal symmetry of extremal black holes. We introduce a new set of conformal coordinates to write the $SL(2,R)$ generators. We find that the Laplacian of the scalar field in many extremal black holes, including Kerr(-Newman), Reissner-Nordstrom, warped ${\mathrm{AdS}}_{3}$, and null warped black holes, could be written in terms of the $SL(2,R)$ quadratic Casimir. This suggests that there exist dual conformal field theory (CFT) descriptions of these black holes. From the conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is nonvanishing, and the excitations of the other sector are suppressed. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction.

Hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-dilaton-axion black holes

The hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-Dilaton-Axion (EMDA) black holes is addressed in this paper. For the non-extreme one, employing the wave equation of massless scalars, the conformal symmetry with left temperature $ {T_L} = \frac{M}{{2\pi a}} $ and right temperature $ {T_R} = \frac{{\sqrt {{{M^2} - {a^2}}} }}{{2\pi a}} $ in the near region is found. The conformal symmetry is spontaneously broken due to the periodicity of the azimuthal angle. The microscopic entropy is derived by the Cardy formula and is fully in consistence with the Bekenstein-Hawking area-entropy law. The absorption cross section in the near region is calculated and exactly equals that in a 2D CFT. For the extreme case, by redefining the conformal coordinates, the duality between the solution space and CFT is studied. The microscopic entropy is found to exactly agree with the area-entropy law.

Coupled Numerical Modelling of Wind and Waves and the Theory of the Wave Boundary Layer

The description of a coupled wind and wave model in conformal coordinates is given. The wave model is based on potential equations for the flow with a free surface, extended with the algorithm of breaking dissipation. The wave boundary-layer (WBL) model is based on the Reynolds equations with the K − e closure scheme with the solutions for air and water matched through the interface. The structure of the WBL and vertical profiles of the wave-produced momentum flux (WPMF) in a long-term simulation of the coupled dynamics are investigated and parameterized. The shape of the β function connecting elevation and surface pressure is studied up to high nondimensional wave frequencies. The errors of a linear presentation of the surface pressure are estimated. The β function and the universal shape of the WPMF profile obtained in coupled simulations allow a formulation of the one-dimensional theory of the WBL, and the carrying out of a detailed study of the WBL structure including the dependence of the drag coefficient on the wind speed. It is shown that a wide scatter of the experimental data on the drag coefficient can be explained, taking into account the age of waves. It is suggested that a reduction of the drag coefficient at high wind speeds can be qualitatively explained by the high-frequency wave suppression.

On the stability of a soft-wall model

We investigate the stability and fluctuations of a soft-wall model that has an asymptotically anti-de Sitter metric and a scalar field that has an asymptotically power-law dependence in the conformal coordinate. By imposing UV boundary conditions, the soft-wall mass scale can be fixed to be near the TeV scale and causes the radion to no longer be massless. A hierarchy between the weak scale and the Planck scale can be generated for various particle spectrum behavior, although natural values only occur for a gravitational sector containing scalar fields that act like unparticles. In addition, if bulk standard model fields have nonstandard couplings to the gravitational sector, then a discrete particle spectrum can be realized in the nongravitational sector. This allows for the possibility of an unparticle solution to the hierarchy problem.

Role of conformation transitions in adenylate kinase

A recent paper by Pisliakov et al. (1) asserts that it is a response to several papers, which, according to the authors (1), imply that “motions along conformational coordinates play an important role in the chemical step” (1). Because ref. 1 and most of the cited papers in ref. 1 [references 3,6,7, and 14 in Pisliakov et al. (1)] are concerned with adenylate kinase (AdK), my comments refer to this enzyme. AdK has an open state, to which the substrates bind and from which the products are released, as well as a closed state, in which catalysis takes place. None of these cited references are concerned with the chemical reaction or suggest that there is coupling between the closing/opening conformational transitions and the chemistry; catalysis in these papers refers to the overall rate and not to the chemical step. They show that the opening transition after the chemical reaction is the rate-determining step [reference 14 in (1); i.e., in AdK, like triosephosphate isomerase, the chemistry has reached perfection] (2). The two other papers, of which I am a coauthor, study the closing transition encoded in the structure [references 6 and 7 in (1)] and the role of fast motions as lubricants (3) for hinge regions.

Detection of Subtle Dynamical Changes Induced by Unresolved “Conformational Coordinates” in Single-Molecule Trajectories via Goodness-of-Fit Tests

Single-molecule experiments are allowing researchers to track the evolution of a few order parameters characterizing complex biomolecules. At fine temporal resolution, artifacts of unresolved degrees of freedom, for example, those induced by collective molecular motion, often influence the dynamics. Reliably detecting subtle changes in dynamics at the nanoscale can be difficult due to the inherent stochasticity, but such changes can have relevance to understanding complex enzyme kinetics. Surrogate models can be used to summarize the information content in single-molecule time series (containing fluctuations occurring over multiple time scales). The focus in this article is on detecting slow time scale changes through the use of the surrogates. The conditional density, associated with the surrogates, allows one to formulate quantitative hypothesis tests which can detect the influence of unresolved coordinates in cases where the dynamics are modulated subtly. The relevance of quantitative (and appropriate) testing methods to analyze single-molecule time series is discussed and demonstrated. A brief discussion on some merits of using frequentist (versus Bayesian) time series methods to analyze single-molecule data is also presented. Idealized simulations mimicking features relevant to some enzyme systems where an "unresolved conformational coordinate" slowly evolves (1) with inertia and (2) diffusively are studied in the nonstationary (nonergodic) setting; however, the findings are also relevant to experimentally measured time series and stationary signals.

Electron-Conformational Model of SR-Based Ca2+ Clock Mode

Most of the calcium that activates cardiac contraction comes from the sarcoplasmic reticulum (SR) from where it is released through the Ryanodine Receptors (RyRs). It is well known that the SR overload results in the release of Ca from the SR in the form of waves driving some cardiac arrhythmias. Recently it has been experimentally documented that the isolated SR is capable to spontaneously and rhythmically release Ca2+ (SR-based Ca2+ clock). This self-sustained intracellular Ca2+ oscillator contributes substantially to the late phase of the diastolic depolarization of cardiac pacemaker cells under normal physiological conditions. Interaction of “a surface membrane oscillator” and “an internal oscillator” with “cycles of Ca2+ uptake and release by the SR” can drive normal cardiac automaticity. To describe the SR-based Ca2+ clock mode we propose a simple, physically-reasonable electron-conformational (EC) model for the RyR and present a theory to describe the RyR lattice dynamics. Each RyR is modelled with a single open and closed electronic state. In addition to the fast electronic degree of freedom, RyR channels are characterized by a slow classical conformational coordinate, which specifies the RyR channel conductance. The RyR gating implies a conformational Langevin dynamics, Ca2+-induced electronic transitions, quantum tunneling and thermal transitions. The cooperativity in the RyR lattice is assumed to be determined by the inter-channel conformational coupling. Model simulations of the of 11x11 RyR cluster revealed different regimes depending on the cis- and trans-Ca concentrations and parameters of EC-model. The SR overload is shown to result in RyR lattice auto-oscillations with spontaneous RyR channel openings and closures. We have studied this Ca2+ clock mode, in particular, its stability, under different model suggestions as regards the RyR conformational potential (diabatic and adiabatic regimes), EC-model parameters.Supported by the RFBR 07-04-96126

Conformational Analysis in a Multidimensional Energy Landscape: Study of an Arginylglutamate Repeat

The identification of the distinct conformation classes of a molecule is a common and often crucial step in establishing structure-function relationships. Many different methods have been suggested for that purpose which differ in their choice of a (dis)similarity measure and clustering algorithm. The present study discusses and analyzes these issues, proposing a method based on principal component analysis (PCA), which is applied to conformations obtained from molecular dynamics (MD) simulations of an arginylglutamate repeat. Simulations are done at different pH values, using both standard MD and constant-pH MD methods, with the peptide displaying a very high conformational variety. The conformational analysis starts with a comprehensive comparison of different sets of conformational coordinates and of their ability to preserve structural similarity between conformations. The selected set of conformational coordinates is then used to investigate the preservation of structural similarity after PCA transformation, concluding the need of using a multidimensional conformation space. This conformation space is then used to derive a multidimensional probability density and the corresponding energy landscape. The application of a simple cutoff algorithm to the resulting multidimensional landscape is then shown to produce a consistent set of distinct and homogeneous conformation classes. Overall, this methodology provides an efficient way to identify the major conformation classes of a molecule in a way that directly reflects the density of states in the multidimensional conformation space, contrasting with the more heuristic nature of standard clustering methods.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

Plasma equilibrium in 3D magnetic confinement systems and soliton theory

Single-valued conformal flux (magnetic) coordinates can always be introduced on arbitrary toroidal magnetic surfaces. It is shown how such coordinates can be obtained by transforming Boozer magnetic coordinates on the surfaces. The metrics is substantially simplified and the coordinate grid is orthogonalized at the expense of a more complicated representation of the magnetic field in conformal flux coordinates. This in turn makes it possible to introduce complex angular flux coordinates on any toroidal magnetic surface and to develop efficient methods for a complex analysis of the geometry of equilibrium magnetic surfaces. The complex analysis reveals how the plasma equilibrium problem is related to soliton theory. Magnetic surfaces of constant mean curvature are considered to exemplify this relationship.

Using a Scale-Selective Filter for Dynamical Downscaling with the Conformal Cubic Atmospheric Model

Abstract This article examines dynamical downscaling with a scale-selective filter in the Conformal Cubic Atmospheric Model (CCAM). In this study, 1D and 2D scale-selective filters have been implemented using a convolution-based scheme, since a convolution can be readily evaluated in terms of CCAM’s native conformal cubic coordinates. The downscaling accuracy of 1D and 2D scale-selective filters is evaluated after downscaling NCEP Global Forecast System analyses for 2006 from 200-km resolution to 60-km resolution over Australia. The 1D scale-selective filter scheme was found to downscale the analyses with similar accuracy to a 2D filter but required significantly fewer computations. The 1D and 2D scale-selective filters were also found to downscale the analyses more accurately than a far-field nudging scheme (i.e., analogous to a boundary-value nudging approach). It is concluded that when the model is required to reproduce the host model behavior above a specified length scale then the use of an appropriately designed 1D scale-selective filter can be a computationally efficient approach to dynamical downscaling for models having a cube-based geometry.

Remarks on symplectic twistor spaces

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With these we define a moduli space of $\omega$-compatible complex structures. We recall the theory of flag manifolds in order to study the Siegel domain and other domains alike, which is the fibre of the referred twistor space. Finally the structure equations for the twistor of a Riemann surface with the canonical symplectic-metric connection are deduced, based on a given conformal coordinate on the surface. We then relate with the moduli space defined previously.

Dynamical soft-wall AdS/QCD

We present a solution of the five-dimensional gravity-dilaton-tachyon equations of motion with a pure AdS{sub 5} metric and a quadratic dilaton and linear tachyon in conformal coordinates. This leads to an infrared soft-wall model where the dilaton profile gives rise to linear Regge trajectories for the four-dimensional mass spectrum of the dual gauge theory. Even though our approach is phenomenological the scalar fields resemble the dilaton and the closed string tachyon of a noncritical string theory. Interestingly, the linear tachyon has the correct profile to imply that chiral symmetry is not restored for highly excited states. Our solution thus provides a dynamical bottom-up model of linear confinement in holographic QCD.

Ionization Spectroscopy of Conformational Isomers of Propanal: The Origin of the Conformational Preference

Two different conformational isomers of propanal, cis and gauche, are investigated by the vacuum-UV mass-analyzed threshold ionization (VUV-MATI) spectroscopy to give accurate adiabatic ionization potentials of 9.9997 +/- 0.0006 eV and 9.9516 +/- 0.0006 eV, respectively. cis-Propanal, which is the more stable conformer in the neutral state, becomes less stable in the cation compared to gauche-propanal. Vibrational structures revealed in the MATI spectra indicate that cis and gauche isomers undergo their unique structural changes upon ionization. The ionization of gauche-propanal induces a geometrical change along the conformational coordinate, suggesting that the steric effect in the ground state is diminished upon ionization. Natural bonding orbital (NBO) calculations provide the extent of hyperconjugation in each conformational isomer of propanal.

Time-dependent gravitating solitons in five-dimensional warped space-times

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for a fixed value of the conformal time coordinate. Time-dependent solutions containing both topological and nontopological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multisoliton solutions may describe time-dependent kink-antikink systems.

Transformation of Lambert Conic Conformal Coordinates from a Global Datum to a Local Datum

This paper treats the problem of how to transform from global datum, for example, from the International Terrestrial Reference System (ITRS), to a local datum, for example, regional or national, for the practical case of the Lambert projection of the sphere or the ellipsoid-of-revolution to the cone. We design the two projection constants n(ϕ1, ϕ2) and m(ϕ1) for the Universal Lambert Conic projection of the ellipsoid-of-revolution. The task to transform from a global datum with respect to the ellipsoid-of-revolution EA,B 2 to local datum with respect to the alternative ellipsoid-of-revolution Ea,b 2, without local ellipsoidal height, is solved by an extended numerical example. Ideas in this paper could be of interest to those working with maps and coordinates transformation from global geodetic datum to local geodetic datum and vice versa, under the Universal Lambert Conic projection, and applicable to precise positioning and navigation, boundary demarcation and determination in the marine environment.

Coordinate confusion in conformal cosmology

Abstract A straightforward interpretation of standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmologies is that objects move apart because of the expansion of space, and that sufficiently distant galaxies must be receding at velocities exceeding the speed of light. Recently, however, it has been suggested that a simple transformation into conformal coordinates can remove superluminal recession velocities, and hence the concept of the expansion of space should be abandoned. This work demonstrates that such conformal transformations do not eliminate superluminal recession velocities for open or flat matter-only FLRW cosmologies, and all possess superluminal expansion. Hence the attack on the concept of the expansion of space based on this is poorly founded. This work concludes by emphasizing that the expansion of space is perfectly valid in the general relativistic framework; however, asking the question of whether space really expands is a futile exercise.

A multi-domain spectral method for initial data of arbitrary binaries in general relativity

We present a multi-domain spectral method to compute initial data of binary systems in general relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible to describe a black hole component by the puncture ansatz as well as through an excision technique. First examples are given for binary black hole excision data that fulfil the requirements of the quasi-stationary framework, which combines the conformal thin sandwich formulation of the constraint equations with the isolated horizon conditions for black holes in quasi-equilibrium. These numerical solutions were obtained to extremely high accuracy with moderate computational effort. Moreover, the method proves to be applicable even when tending towards limiting cases such as large mass ratios of the binary components.