17,315 research outputs found
Hybrid Simulation Safety: Limbos and Zero Crossings
Physical systems can be naturally modeled by combining continuous and
discrete models. Such hybrid models may simplify the modeling task of complex
system, as well as increase simulation performance. Moreover, modern simulation
engines can often efficiently generate simulation traces, but how do we know
that the simulation results are correct? If we detect an error, is the error in
the model or in the simulation itself? This paper discusses the problem of
simulation safety, with the focus on hybrid modeling and simulation. In
particular, two key aspects are studied: safe zero-crossing detection and
deterministic hybrid event handling. The problems and solutions are discussed
and partially implemented in Modelica and Ptolemy II
Next-to-MHV Yang-Mills kinematic algebra
Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie
algebraic structure that suggest the existence of a hidden infinite-dimensional
kinematic algebra. Explicitly realizing such a kinematic algebra is a
longstanding open problem that only has had partial success for simple helicity
sectors. In past work, we introduced a framework using tensor currents and
fusion rules to generate BCJ numerators of a special subsector of NMHV
amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly
realize a kinematic algebra for all NMHV amplitudes. Master numerators are
obtained directly from the algebraic rules and through commutators and
kinematic Jacobi identities other numerators can be generated. Inspecting the
output of the algebra, we conjecture a closed-form expression for the master
BCJ numerator up to any multiplicity. We also introduce a new method, based on
group algebra of the permutation group, to solve for the generalized gauge
freedom of BCJ numerators. It uses the recently introduced binary BCJ relations
to provide a complete set of NMHV kinematic numerators that consist of pure
gauge.Comment: 45pages + appx./ref
On the kinematic algebra for BCJ numerators beyond the MHV sector
The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ? ((epsilon i .epsilon j )(2)) terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents control the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory
KPZ equation in one dimension and line ensembles
For suitably discretized versions of the Kardar-Parisi-Zhang equation in one
space dimension exact scaling functions are available, amongst them the
stationary two-point function. We explain one central piece from the technology
through which such results are obtained, namely the method of line ensembles
with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200
Internally Electrodynamic Particle Model: Its Experimental Basis and Its Predictions
The internally electrodynamic (IED) particle model was derived based on
overall experimental observations, with the IED process itself being built
directly on three experimental facts, a) electric charges present with all
material particles, b) an accelerated charge generates electromagnetic waves
according to Maxwell's equations and Planck energy equation and c) source
motion produces Doppler effect. A set of well-known basic particle equations
and properties become predictable based on first principles solutions for the
IED process; several key solutions achieved are outlined, including the de
Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass,
Einstein mass-energy relation, Newton's law of gravity, single particle self
interference, and electromagnetic radiation and absorption; these equations and
properties have long been broadly experimentally validated or demonstrated. A
specific solution also predicts the Doebner-Goldin equation which emerges to
represent a form of long-sought quantum wave equation including gravity. A
critical review of the key experiments is given which suggests that the IED
process underlies the basic particle equations and properties not just
sufficiently but also necessarily.Comment: Presentation at the 27th Int Colloq on Group Theo Meth in Phys, 200
New Relations for Gauge-Theory Amplitudes
We present an identity satisfied by the kinematic factors of diagrams
describing the tree amplitudes of massless gauge theories. This identity is a
kinematic analog of the Jacobi identity for color factors. Using this we find
new relations between color-ordered partial amplitudes. We discuss applications
to multi-loop calculations via the unitarity method. In particular, we
illustrate the relations between different contributions to a two-loop
four-point QCD amplitude. We also use this identity to reorganize gravity tree
amplitudes diagram by diagram, offering new insight into the structure of the
KLT relations between gauge and gravity tree amplitudes. This can be used to
obtain novel relations similar to the KLT ones. We expect this to be helpful in
higher-loop studies of the ultraviolet properties of gravity theories.Comment: 40 pages, 7 figures, RevTex, v2 minor correction
Landau-Zener-Stuckelberg Interferometry of a Single Electron Charge Qubit
We perform Landau-Zener-Stuckelberg interferometry on a single electron GaAs
charge qubit by repeatedly driving the system through an avoided crossing. We
observe coherent destruction of tunneling, where periodic driving with specific
amplitudes inhibits current flow. We probe the quantum dot occupation using a
charge sensor, observing oscillations in the qubit population resulting from
the microwave driving. At a frequency of 9 GHz we observe excitation processes
driven by the absorption of up to 17 photons. Simulations of the qubit
occupancy are in good agreement with the experimental data.Comment: Related papers at http://pettagroup.princeton.ed
Frequency-Dependent Current Noise through Quantum-Dot Spin Valves
We study frequency-dependent current noise through a single-level quantum dot
connected to ferromagnetic leads with non-collinear magnetization. We propose
to use the frequency-dependent Fano factor as a tool to detect single-spin
dynamics in the quantum dot. Spin precession due to an external magnetic and/or
a many-body exchange field affects the Fano factor of the system in two ways.
First, the tendency towards spin-selective bunching of the transmitted
electrons is suppressed, which gives rise to a reduction of the low-frequency
noise. Second, the noise spectrum displays a resonance at the Larmor frequency,
whose lineshape depends on the relative angle of the leads' magnetizations.Comment: 12 pages, 15 figure
Cost-effective intervention thresholds against osteoporotic fractures based on FRAX® in Switzerland
Summary: FRAX-based cost-effective intervention thresholds in the Swiss setting were determined. Assuming a willingness to pay at 2× Gross Domestic Product per capita, an intervention aimed at reducing fracture risk in women and men with a 10-year probability for a major osteoporotic fracture at or above 15% is cost-effective. Introduction: The fracture risk assessment algorithm FRAX® has been recently calibrated for Switzerland. The aim of the present analysis was to determine FRAX-based fracture probabilities at which intervention becomes cost-effective. Methods: A previously developed and validated state transition Markov cohort model was populated with Swiss epidemiological and cost input parameters. Cost-effective FRAX-based intervention thresholds (cost-effectiveness approach) and the cost-effectiveness of intervention with alendronate (original molecule) in subjects with a FRAX-based fracture risk equivalent to that of a woman with a prior fragility fracture and no other risk factor (translational approach) were calculated based on the Swiss FRAX model and assuming a willingness to pay of 2 times Gross Domestic Product per capita for one Quality-adjusted Life-Year. Results: In Swiss women and men aged 50years and older, drug intervention aimed at decreasing fracture risk was cost-effective with a 10-year probability for a major osteoporotic fracture at or above 13.8% (range 10.8% to 15.0%) and 15.1% (range 9.9% to 19.9%), respectively. Age-dependent variations around these mean values were modest. Using the translational approach, treatment was cost-effective or cost-saving after the age 60years in women and 55 in men who had previously sustained a fragility fracture. Using the latter approach leads to considerable underuse of the current potential for cost-effective interventions against fractures. Conclusions: Using a FRAX-based intervention threshold of 15% for both women and men should permit cost-effective access to therapy to patients at high fracture probability based on clinical risk factors and thereby contribute to further reduce the growing burden of osteoporotic fractures in Switzerlan
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