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Hiroshi Koibuchi - One of the best experts on this subject based on the ideXlab platform.
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Surface tension in an Intrinsic Curvature model with fixed one-dimensional boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2008Co-Authors: Hiroshi KoibuchiAbstract:A triangulated fixed connectivity surface model is investigated by using the Monte Carlo simulation technique. In order to have the macroscopic surface tension \tau, the vertices on the one-dimensional boundaries are fixed as the edges (=circles) of the tubular surface in the simulations. The size of the tubular surface is chosen such that the projected area becomes the regular square of area A. An Intrinsic Curvature energy with a microscopic bending rigidity b is included in the Hamiltonian. We found that the model undergoes a first-order transition of surface fluctuations at finite b, where the surface tension \tau discontinuously changes. The gap of \tau remains constant at the transition point in a certain range of values A/N^\prime at sufficiently large N^\prime, which is the total number of vertices excluding the fixed vertices on the boundaries. The value of \tau remains almost zero in the wrinkled phase at the transition point while \tau remains negative finite in the smooth phase in that range of A/N^\prime.
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Phase transitions of an Intrinsic Curvature model on dynamically triangulated spherical surfaces with point boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: S. Obata, M. Egashira, T. Endo, Hiroshi KoibuchiAbstract:An Intrinsic Curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite Curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.
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phase transitions of an Intrinsic Curvature model on dynamically triangulated spherical surfaces with point boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: S. Obata, M. Egashira, T. Endo, Hiroshi KoibuchiAbstract:An Intrinsic Curvature model is investigated using canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size up to N = 4842 with two fixed vertices separated by the distance 2L. We found a first-order transition at finite Curvature coefficient α, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results for the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point boundaries in the crumpled phase. In contrast, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of σ is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behaviour of σ is consistent with the observed scaling relation σ~(2L/N)ν, where in the smooth phase, and ν = 0.93 ± 0.14 in the crumpled phase. We should note that the possibility of a continuous transition is not completely eliminated.
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Phase structure of Intrinsic Curvature models on dynamically triangulated disk with fixed boundary length
The European Physical Journal B, 2006Co-Authors: Hiroshi KoibuchiAbstract:A first-order phase transition is found in two types of Intrinsic Curvature models defined on dynamically triangulated surfaces of disk topology. The Intrinsic Curvature energy is included in the Hamiltonian. The smooth phase is separated from a non-smooth phase by the transition. The crumpled phase, which is different from the non-smooth phase, also appears at sufficiently small Curvature coefficient $\alpha$. The phase structure of the model on the disk is identical to that of the spherical surface model, which was investigated by us and reported previously. Thus, we found that the phase structure of the fluid surface model with Intrinsic Curvature is independent of whether the surface is closed or open.
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Phase transitions of a tethered membrane model with Intrinsic Curvature on spherical surfaces with point boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: Hiroshi KoibuchiAbstract:We found that the order for the crumpling transition of an Intrinsic Curvature model changes depending on the distance between two boundary vertices fixed on the surface of spherical topology. The model is a Curvature one governed by an Intrinsic Curvature energy, which is defined on triangulated surfaces. It was already reported that the model undergoes a first-order crumpling transition without the boundary conditions on the surface. However, the dependence of the transition on such boundary conditions is yet to be studied. In this paper, we have studied this problem using Monte Carlo simulations on surfaces up to a size N = 8412. The first-order transition changes to a second-order transition if the distance increases.
Stefan Wagner - One of the best experts on this subject based on the ideXlab platform.
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Intrinsic Curvature in the X-ray spectra of BL Lacertae objects
The Astrophysical Journal, 2005Co-Authors: Eric S. Perlman, Greg Madejski, Markos Georganopoulos, K. Andersson, T. Daugherty, Julian H. Krolik, Travis A. Rector, John T. Stocke, A. Koratkar, Stefan WagnerAbstract:We report results from XMM-Newton observations of 13 X-ray bright BL Lacertae objects, selected from the Einstein Slew Survey sample (SSS). The survey was designed to look for evidence of departures of the X-ray spectra from a simple power-law shape (i.e., Curvature and/or line features) and to find objects worthy of deeper study. Our data are generally well fit by power-law models, with three cases having hard (? < 2; dN/dE E-?) spectra that indicate synchrotron peaks at E 5 keV. Previous data had suggested a presence of absorption features in the X-ray spectra of some BL Lac objects. In contrast, none of these spectra show convincing examples of line features in either absorption or emission, suggesting that such features are rare among BL Lac objects, or, more likely, are artifacts caused by instrumental effects. We find significant evidence for Intrinsic Curvature [steepening by d?/d(log E) = 0.4 ? 0.15] in 14 of the 17 X-ray spectra. This cannot be explained satisfactorily via excess absorption, since the Curvature is essentially constant from 0.5-6 keV, an observation that is inconsistent with the modest amounts of absorption that would be required. We use the XMM-Newton Optical Monitor data with concurrent radio monitoring to derive broadband spectral energy distributions and peak frequency estimates. From these, we examine models of synchrotron emission and model the spectral Curvature we see as the result of episodic particle acceleration.
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Intrinsic Curvature in the X-ray Spectra of BL Lacertae Objects
The Astrophysical Journal, 2005Co-Authors: Eric S. Perlman, Greg Madejski, Markos Georganopoulos, K. Andersson, Julian H. Krolik, Travis A. Rector, John T. Stocke, A. Koratkar, Timothy Dougherty, Stefan WagnerAbstract:We report results from {\it XMM-Newton} observations of thirteen X-ray bright BL Lacertae objects, selected from the {\it Einstein} Slew Survey sample. The survey was designed to look for evidence of departures of the X-ray spectra from a simple power law shape (i.e., Curvature and/or line features), and to find objects worthy of deeper study. Our data are generally well fit by power-law models, with three cases having hard ($\Gamma
Sookkyung Lim - One of the best experts on this subject based on the ideXlab platform.
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Modeling the dynamics of an elastic rod with Intrinsic Curvature and twist using a regularized Stokes formulation
Journal of Computational Physics, 2013Co-Authors: Sarah D. Olson, Sookkyung Lim, Ricardo CortezAbstract:We develop a Lagrangian numerical algorithm for an elastic rod immersed in a viscous, incompressible fluid at zero Reynolds number. The elasticity of the rod is described by a version of the Kirchhoff rod model, where Intrinsic Curvature and twist are prescribed, and the fluid is governed by the Stokes equations in R^3. The elastic rod is represented by a space curve corresponding to the centerline of the rod and an orthonormal triad, which encodes the bend and twist of the rod. In this method, the differences between the rod configuration and its Intrinsic shape generate force and torque along the centerline. The coupling to the fluid is accomplished by the use of the method of regularized Stokeslets for the force and regularized rotlets for the torque. This technique smooths out the singularity in the fundamental solutions of the Stokes equations for the computation of the velocity of the rod centerline. In addition, the computation of the angular velocity of the rod requires the use of regularized (potential) dipoles. As a benchmark problem, we consider open and closed rods with Intrinsic Curvature and twist in a viscous fluid. Equilibrium configurations and dynamic instabilities are compared with known results in elastic rod theory. For cases when the exact solution is unknown, the numerical results are compared to those produced by the generalized immersed boundary (gIB) method, where the fluid is governed by the Navier-Stokes equations with small Reynolds number on a finite (periodic) domain. It is shown that the regularization method combined with Kirchhoff rod theory contributes substantially to the reduction of computation time and efficient memory usage in comparison to the gIB method. We also illustrate how the regularized method can be used to model microorganism motility where the organism is propelled by a flagellum propagating sinusoidal waves. The swimming speeds of this flagellum using the regularized Stokes formulation are matched well with classical asymptotic results of Taylor's infinite cylinder in terms of frequency and amplitude of the undulation.
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Dynamics of an open elastic rod with Intrinsic Curvature and twist in a viscous fluid
Physics of Fluids, 2010Co-Authors: Sookkyung LimAbstract:A twisted elastic rod with Intrinsic Curvature is considered. We investigate the dynamics of the rod in a viscous incompressible fluid. This fluid is governed by the Navier–Stokes equations and the fluid-rod interaction problem is solved by the generalized immersed boundary method combined with the Kirchhoff rod theory. We classify the equilibrium configurations of an open elastic rod as they depend on the rod’s Intrinsic characteristics and fluid properties. We assume that the Intrinsic Curvature and twist are distributed uniformly along the rod. In the case of zero Intrinsic Curvature (i.e., the stress-free state of the rod is straight), we find a critical value of twist, below which the straight state of the rod is stable. When the twist is above this critical value, however, the rod buckles locally and produces a loop or a plectoneme or a combination of both. When the constant Intrinsic Curvature is nonzero, we also find a critical value of twist that distinguishes a buckled rod from a stable helix. We also find that fluid viscosity plays an important role in determining equilibrium configuration in this paper.
S. Obata - One of the best experts on this subject based on the ideXlab platform.
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Phase transitions of an Intrinsic Curvature model on dynamically triangulated spherical surfaces with point boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: S. Obata, M. Egashira, T. Endo, Hiroshi KoibuchiAbstract:An Intrinsic Curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite Curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.
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phase transitions of an Intrinsic Curvature model on dynamically triangulated spherical surfaces with point boundaries
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: S. Obata, M. Egashira, T. Endo, Hiroshi KoibuchiAbstract:An Intrinsic Curvature model is investigated using canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size up to N = 4842 with two fixed vertices separated by the distance 2L. We found a first-order transition at finite Curvature coefficient α, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results for the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point boundaries in the crumpled phase. In contrast, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of σ is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behaviour of σ is consistent with the observed scaling relation σ~(2L/N)ν, where in the smooth phase, and ν = 0.93 ± 0.14 in the crumpled phase. We should note that the possibility of a continuous transition is not completely eliminated.
Eric S. Perlman - One of the best experts on this subject based on the ideXlab platform.
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Intrinsic Curvature in the x ray spectra of bl lacertae objects
arXiv: Astrophysics, 2005Co-Authors: Eric S. Perlman, Greg Madejski, Markos Georganopoulos, K. Andersson, Julian H. Krolik, Travis A. Rector, John T. Stocke, A. Koratkar, Timothy Dougherty, S J WagnerAbstract:We report results from {\it XMM-Newton} observations of thirteen X-ray bright BL Lacertae objects, selected from the {\it Einstein} Slew Survey sample. The survey was designed to look for evidence of departures of the X-ray spectra from a simple power law shape (i.e., Curvature and/or line features), and to find objects worthy of deeper study. Our data are generally well fit by power-law models, with three cases having hard ($\Gamma<2; dN/dE \propto E^{-\Gamma}$) spectra that indicate synchrotron peaks at $E \gsim 5$ keV. Previous data had suggested a presence of absorption features in the X-ray spectra of some BL Lacs. In contrast, none of these spectra show convincing examples of line features, either in absorption or emission, suggesting that such features are rare amongst BL Lacs, or, more likely, artifacts caused by instrumental effects. We find significant evidence for Intrinsic Curvature (steepening by $d\Gamma / d({\rm log} E) = 0.4 \pm 0.15$) in fourteen of the seventeen X-ray spectra. This cannot be explained satisfactorily via excess absorption, since the Curvature is essentially constant from $0.5-6$ keV, an observation which is inconsistent with the modest amounts of absorption that would be required. We use the {\it XMM-Newton} Optical Monitor data with concurrent radio monitoring to derive broadband spectral energy distributions and peak frequency estimates. From these we examine models of synchrotron emission and model the spectral Curvature we see as the result of episodic particle acceleration.
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Intrinsic Curvature in the X-ray spectra of BL Lacertae objects
The Astrophysical Journal, 2005Co-Authors: Eric S. Perlman, Greg Madejski, Markos Georganopoulos, K. Andersson, T. Daugherty, Julian H. Krolik, Travis A. Rector, John T. Stocke, A. Koratkar, Stefan WagnerAbstract:We report results from XMM-Newton observations of 13 X-ray bright BL Lacertae objects, selected from the Einstein Slew Survey sample (SSS). The survey was designed to look for evidence of departures of the X-ray spectra from a simple power-law shape (i.e., Curvature and/or line features) and to find objects worthy of deeper study. Our data are generally well fit by power-law models, with three cases having hard (? < 2; dN/dE E-?) spectra that indicate synchrotron peaks at E 5 keV. Previous data had suggested a presence of absorption features in the X-ray spectra of some BL Lac objects. In contrast, none of these spectra show convincing examples of line features in either absorption or emission, suggesting that such features are rare among BL Lac objects, or, more likely, are artifacts caused by instrumental effects. We find significant evidence for Intrinsic Curvature [steepening by d?/d(log E) = 0.4 ? 0.15] in 14 of the 17 X-ray spectra. This cannot be explained satisfactorily via excess absorption, since the Curvature is essentially constant from 0.5-6 keV, an observation that is inconsistent with the modest amounts of absorption that would be required. We use the XMM-Newton Optical Monitor data with concurrent radio monitoring to derive broadband spectral energy distributions and peak frequency estimates. From these, we examine models of synchrotron emission and model the spectral Curvature we see as the result of episodic particle acceleration.
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Intrinsic Curvature in the X-ray Spectra of BL Lacertae Objects
The Astrophysical Journal, 2005Co-Authors: Eric S. Perlman, Greg Madejski, Markos Georganopoulos, K. Andersson, Julian H. Krolik, Travis A. Rector, John T. Stocke, A. Koratkar, Timothy Dougherty, Stefan WagnerAbstract:We report results from {\it XMM-Newton} observations of thirteen X-ray bright BL Lacertae objects, selected from the {\it Einstein} Slew Survey sample. The survey was designed to look for evidence of departures of the X-ray spectra from a simple power law shape (i.e., Curvature and/or line features), and to find objects worthy of deeper study. Our data are generally well fit by power-law models, with three cases having hard ($\Gamma
