2,442 research outputs found
An overview of Viscosity Solutions of Path-Dependent PDEs
This paper provides an overview of the recently developed notion of viscosity
solutions of path-dependent partial di erential equations. We start by a quick
review of the Crandall- Ishii notion of viscosity solutions, so as to motivate
the relevance of our de nition in the path-dependent case. We focus on the
wellposedness theory of such equations. In partic- ular, we provide a simple
presentation of the current existence and uniqueness arguments in the
semilinear case. We also review the stability property of this notion of
solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme
approximation method. Our results rely crucially on the theory of optimal
stopping under nonlinear expectation. In the dominated case, we provide a
self-contained presentation of all required results. The fully nonlinear case
is more involved and is addressed in [12]
Geometric approach to nonvariational singular elliptic equations
In this work we develop a systematic geometric approach to study fully
nonlinear elliptic equations with singular absorption terms as well as their
related free boundary problems. The magnitude of the singularity is measured by
a negative parameter , for , which reflects on
lack of smoothness for an existing solution along the singular interface
between its positive and zero phases. We establish existence as well sharp
regularity properties of solutions. We further prove that minimal solutions are
non-degenerate and obtain fine geometric-measure properties of the free
boundary . In particular we show sharp
Hausdorff estimates which imply local finiteness of the perimeter of the region
and a.e. weak differentiability property of
.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos
Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis
201
TORSO DEFORMATION IN FRONTAL SLED TESTS: COMPARISION BETWEEN THOR NT, THOR NT WITH THE CHALMERS SD-1 SHOULDER, AND PMHS
This study compares the thoracic deformation response of the 50th percentile male THOR NT
frontal crash dummy and the response of the THOR modified with the SD-1 shoulder (THOR SD-1)
relative to the thoracic response of eight 50th percentile male PMHS. The prototype Chalmers
University SD-1 shoulder was designed to be more human-like in terms of geometry and range of
motion in comparison to the standard THOR NT shoulder. The dummies and PMHS were restrained
by a three-point restraint in a driver-side configuration and were subjected to a simulated 40 km/h
frontal crash. The most prominent difference between the responses of the dummies and PMHS
involved motion of the lower right anterior ribcage measurement site that is the farthest lateral
distance from the diagonal shoulder belt. During the impact event, this site moved substantially
anteriorly and away from the spine for the PMHS. The PMHS lower right “bulge out” behavior is
believed to be caused by inertial loading of the ribcage, underlying organs, and soft tissue overlying
the torso. The THOR SD-1 shoulder altered the shoulder belt position relative to the thoracic
deflection measurement sites resulting in a different distribution of deformation for the upper
measurement sites although the average upper site deformation was similar to that recorded for the
standard THOR shoulder
Collisional Excitation Of N+ At 50 KeV
The excitation spectrum of N+ has been observed by examining the energy lost by a 50- keV N+ beam passing through a He target. The spectrum exhibits dramatic features with large cross sections. Determination of the approximate ratio of metastable to ground-state ions in the primary ion beam has permitted measurement of excitation cross sections from both ground-state and metastable N+ ions colliding with He target atoms. © 1972 The American Physical Society
The Tychonoff uniqueness theorem for the G-heat equation
In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat
equation
Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes
Recent theoretical work suggests that violation of the Equivalence Principle
might be revealed in a measurement of the fractional differential acceleration
between two test bodies -of different composition, falling in the
gravitational field of a source mass- if the measurement is made to the level
of or better. This being within the reach of ground based
experiments, gives them a new impetus. However, while slowly rotating torsion
balances in ground laboratories are close to reaching this level, only an
experiment performed in low orbit around the Earth is likely to provide a much
better accuracy.
We report on the progress made with the "Galileo Galilei on the Ground" (GGG)
experiment, which aims to compete with torsion balances using an instrument
design also capable of being converted into a much higher sensitivity space
test.
In the present and following paper (Part I and Part II), we demonstrate that
the dynamical response of the GGG differential accelerometer set into
supercritical rotation -in particular its normal modes (Part I) and rejection
of common mode effects (Part II)- can be predicted by means of a simple but
effective model that embodies all the relevant physics. Analytical solutions
are obtained under special limits, which provide the theoretical understanding.
A simulation environment is set up, obtaining quantitative agreement with the
available experimental data on the frequencies of the normal modes, and on the
whirling behavior. This is a needed and reliable tool for controlling and
separating perturbative effects from the expected signal, as well as for
planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan
16, 2006. 16 2-column pages, 9 figure
Inhibition of Nitric Oxide Inhibition of Nitric Oxide Synthase Does Not Alter Dynamic Cerebral Autoregulation in Humans
The aim of this study was to determine whether inhibition of nitric oxide synthase (NOS) alters dynamic cerebral autoregulation in humans. Beat-to-beat blood pressure (BP) and cerebral blood flow (CBF) velocity (transcranial Doppler) were measured in eight healthy subjects in the supine position and during 60° head-up tilt (HUT). NOS was inhibited by intravenous N G-monomethyl-L-arginine (L-NMMA) infusion. Dynamic cerebral autoregulation was quantified by transfer function analysis of beat-to-beat changes in BP and CBF velocity. Pressor effects of L-NMMA on cerebral hemodynamics were compared with those of phenylephrine infusion. In the supine position, L-NMMA increased mean BP from 83 ± 3 to 94 ± 3 mmHg (P \u3c 0.01). However, CBF velocity remained unchanged. Consequently, cerebrovascular resistance index (CVRI) increased by 15% (P \u3c 0.05). BP and CBF velocity variability and transfer function gain at the low frequencies of 0.07-0.20 Hz did not change with L-NMMA infusion. Similar changes in mean BP, CBF velocity, and CVRI were observed after phenylephrine infusion, suggesting that increase in CVRI after L-NMMA was mediated myogenically by increase in arterial pressure rather than a direct effect of cerebrovascular NOS inhibition. During baseline tilt without L-NMMA, steady-state BP increased and CBF velocity decreased. BP and CBF velocity variability at low frequencies increased in parallel by 277% and 217%, respectively (P \u3c 0.05). However, transfer function gain remained unchanged. During tilt with L-NMMA, changes in steady-state hemodynamics and BP and CBF velocity variability as well as transfer gain and phase were similar to those without L-NMMA. These data suggest that inhibition of tonic production of NO does not appear to alter dynamic cerebral autoregulation in humans
Nitric Oxide Synthase Inhibition Does Not Affect Regulation of Muscle Sympathetic Nerve Activity During Head-Up Tilt
To test the hypothesis that systemic inhibition of nitric oxide (NO) synthase does not alter the regulation of sympathetic outflow during head-up tilt in humans, in eight healthy subjects NO synthase was blocked by intravenous infusion of NG-monomethyl-L-arginine (L-NMMA). Blood pressure, heart rate, cardiac output, total peripheral resistance (TPR), and muscle sympathetic nerve activity (MSNA) were recorded in the supine position and during 60° head-up tilt. In the supine position, infusion of L-NMMA increased blood pressure, via increased TPR, and inhibited MSNA. However, the increase in MSNA evoked by head-up tilt during L-NMMA infusion (change in burst rate: 24 ± 4 bursts/min; change in total activity: 209 ± 36 U/min) was similar to that during head-up tilt without L-NMMA (change in burst rate: 23 ± 4 bursts/min; change in total activity: 251 ± 52 U/min, n = 6, all P \u3e 0.05). Moreover, changes in TPR and heart rate during head-up tilt were virtually identical between the two conditions. These results suggest that systemic inhibition of NO synthase with L-NMMA does not affect the regulation of sympathetic outflow and vascular resistance during head-up tilt in humans
Convergence of nonlocal threshold dynamics approximations to front propagation
In this note we prove that appropriately scaled threshold dynamics-type
algorithms corresponding to the fractional Laplacian of order converge to moving fronts. When the resulting interface
moves by weighted mean curvature, while for the normal velocity is
nonlocal of ``fractional-type.'' The results easily extend to general nonlocal
anisotropic threshold dynamics schemes.Comment: 19 page
Dynamics of a lattice Universe
We find a solution to Einstein field equations for a regular toroidal lattice
of size L with equal masses M at the centre of each cell; this solution is
exact at order M/L. Such a solution is convenient to study the dynamics of an
assembly of galaxy-like objects. We find that the solution is expanding (or
contracting) in exactly the same way as the solution of a
Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average
density as our model. This points towards the absence of backreaction in a
Universe filled with an infinite number of objects, and this validates the
fluid approximation, as far as dynamics is concerned, and at the level of
approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum
Gravit
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