2,668 research outputs found
Compact Toeplitz operators with continuous symbols on weighted Bergman spaces
Let L (n,dud0/21r) be a complete weighted Bergman space on the open unit disc n where du is a positive finite Borel measure on [O, 1). We show the following : When cp is a continuous function on the closed unit disc D, T</J is compact if and only if cp = 0 on an
Constraint Propagation of -adjusted Formulation - Another Recipe for Robust ADM Evolution System
With a purpose of constructing a robust evolution system against numerical
instability for integrating the Einstein equations, we propose a new
formulation by adjusting the ADM evolution equations with constraints. We apply
an adjusting method proposed by Fiske (2004) which uses the norm of the
constraints, C2. One of the advantages of this method is that the effective
signature of adjusted terms (Lagrange multipliers) for constraint-damping
evolution is pre-determined. We demonstrate this fact by showing the
eigenvalues of constraint propagation equations. We also perform numerical
tests of this adjusted evolution system using polarized Gowdy-wave propagation,
which show robust evolutions against the violation of the constraints than that
of the standard ADM formulation.Comment: 11 pages, 5 figures. To be published in Phys. Rev.
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Vibronic mixing enables ultrafast energy flow in light-harvesting complex II.
Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps
Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
We show how to treat the constraints and reality conditions in the
-ADM (Ashtekar) formulation of general relativity, for the case of a
vacuum spacetime with a cosmological constant. We clarify the difference
between the reality conditions on the metric and on the triad. Assuming the
triad reality condition, we find a new variable, allowing us to solve the gauge
constraint equations and the reality conditions simultaneously.Comment: LaTeX file, 12 pages, no figures; to appear in Classical and Quantum
Gravit
Constraint propagation in the family of ADM systems
The current important issue in numerical relativity is to determine which
formulation of the Einstein equations provides us with stable and accurate
simulations. Based on our previous work on "asymptotically constrained"
systems, we here present constraint propagation equations and their eigenvalues
for the Arnowitt-Deser-Misner (ADM) evolution equations with additional
constraint terms (adjusted terms) on the right hand side. We conjecture that
the system is robust against violation of constraints if the amplification
factors (eigenvalues of Fourier-component of the constraint propagation
equations) are negative or pure-imaginary. We show such a system can be
obtained by choosing multipliers of adjusted terms. Our discussion covers
Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also
mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure
Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
In order to find a way to have a better formulation for numerical evolution
of the Einstein equations, we study the propagation equations of the
constraints based on the Arnowitt-Deser-Misner formulation. By adjusting
constraint terms in the evolution equations, we try to construct an
"asymptotically constrained system" which is expected to be robust against
violation of the constraints, and to enable a long-term stable and accurate
numerical simulation. We first provide useful expressions for analyzing
constraint propagation in a general spacetime, then apply it to Schwarzschild
spacetime. We search when and where the negative real or non-zero imaginary
eigenvalues of the homogenized constraint propagation matrix appear, and how
they depend on the choice of coordinate system and adjustments. Our analysis
includes the proposal of Detweiler (1987), which is still the best one
according to our conjecture but has a growing mode of error near the horizon.
Some examples are snapshots of a maximally sliced Schwarzschild black hole. The
predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle,
reduced figures, rephrased introduction, and a native checked. :-
Symmetric hyperbolic system in the Ashtekar formulation
We present a first-order symmetric hyperbolic system in the Ashtekar
formulation of general relativity for vacuum spacetime. We add terms from
constraint equations to the evolution equations with appropriate combinations,
which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev.
Lett. 79, 4732 (1997)]. However our system is different from theirs in the
points that we primarily use Hermiticity of a characteristic matrix of the
system to characterize our system "symmetric", discuss the consistency of this
system with reality condition, and show the characteristic speeds of the
system.Comment: 4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs
update
The Rho kinases I and II regulate different aspects of myosin II activity
The homologous mammalian rho kinases (ROCK I and II) are assumed to be functionally redundant, based largely on kinase construct overexpression. As downstream effectors of Rho GTPases, their major substrates are myosin light chain and myosin phosphatase. Both kinases are implicated in microfilament bundle assembly and smooth muscle contractility. Here, analysis of fibroblast adhesion to fibronectin revealed that although ROCK II was more abundant, its activity was always lower than ROCK I. Specific reduction of ROCK I by siRNA resulted in loss of stress fibers and focal adhesions, despite persistent ROCK II and guanine triphosphate–bound RhoA. In contrast, the microfilament cytoskeleton was enhanced by ROCK II down-regulation. Phagocytic uptake of fibronectin-coated beads was strongly down-regulated in ROCK II–depleted cells but not those lacking ROCK I. These effects originated in part from distinct lipid-binding preferences of ROCK pleckstrin homology domains. ROCK II bound phosphatidylinositol 3,4,5P3 and was sensitive to its levels, properties not shared by ROCK I. Therefore, endogenous ROCKs are distinctly regulated and in turn are involved with different myosin compartments
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