27,065 research outputs found
Injection locking of two frequency-doubled lasers with 3.2 GHz offset for driving Raman transitions with low photon scattering in Ca
We describe the injection locking of two infrared (794 nm) laser diodes which
are each part of a frequency-doubled laser system. An acousto-optic modulator
(AOM) in the injection path gives an offset of 1.6 GHz between the lasers for
driving Raman transitions between states in the hyperfine split (by 3.2 GHz)
ground level of Ca. The offset can be disabled for use in
Ca. We measure the relative linewidth of the frequency-doubled beams
to be 42 mHz in an optical heterodyne measurement. The use of both injection
locking and frequency doubling combines spectral purity with high optical
power. Our scheme is applicable for providing Raman beams across other ion
species and neutral atoms where coherent optical manipulation is required.Comment: 3 pages, 3 figure
Atypical late-time singular regimes accurately diagnosed in stagnation-point-type solutions of 3D Euler flows
We revisit, both numerically and analytically, the finite-time blowup of the
infinite-energy solution of 3D Euler equations of stagnation-point-type
introduced by Gibbon et al. (1999). By employing the method of mapping to
regular systems, presented in Bustamante (2011) and extended to the
symmetry-plane case by Mulungye et al. (2015), we establish a curious property
of this solution that was not observed in early studies: before but near
singularity time, the blowup goes from a fast transient to a slower regime that
is well resolved spectrally, even at mid-resolutions of This late-time
regime has an atypical spectrum: it is Gaussian rather than exponential in the
wavenumbers. The analyticity-strip width decays to zero in a finite time,
albeit so slowly that it remains well above the collocation-point scale for all
simulation times , where is the singularity time.
Reaching such a proximity to singularity time is not possible in the original
temporal variable, because floating point double precision ()
creates a `machine-epsilon' barrier. Due to this limitation on the
\emph{original} independent variable, the mapped variables now provide an
improved assessment of the relevant blowup quantities, crucially with
acceptable accuracy at an unprecedented closeness to the singularity time:
$T^*- t \approx 10^{-140}.
Against Game Theory
People make choices. Often, the outcome depends on choices other people make. What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers an answer, one based on games of strategy such as chess and checkers: the chooser considers the choices that others will make and makes a choice that will lead to a better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily modified) is bad at predicting behavior. But instead of abandoning classical game theory, those in the social sciences have mounted a rescue operation under the name of “behavioral game theory.” Its main tool is to propose systematic deviations from the predictions of game theory, deviations that arise from character type, for example. Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we can correct our predictions accordingly, and so get it right. There are two problems with this rescue operation, each of them is fatal. (1) For a chooser, contemplating the range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models useless for modeling human thought or human behavior in general. (2) Modeling deviations are helpful only if the deviations are consistent, so that scientists (and indeed decision makers) can make predictions about future choices on the basis of past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging candidates
Can We Build Behavioral Game Theory?
The way economists and other social scientists model how people make interdependent decisions is through the theory of games. Psychologists and behavioral economists, however, have established many deviations from the predictions of game theory. In response to these findings, a broad movement has arisen to salvage the core of game theory. Extant models of interdependent decision-making try to improve their explanatory domain by adding some corrective terms or limits. We will make the argument that this approach is misguided. For this approach to work, the deviations would have to be consistent. Drawing in part on our experimental results, we will argue that deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In turn, the problem of finding an equilibrium strategy is not easier but rather is exponentially more difficult. It does not seem that game theory can be repaired by adding corrective terms (such as consideration of personal characteristics, social norms, heuristic or bias terms, or cognitive limits on choice and learning). In what follows, we describe new methods for investigating interdependent decision-making. Our experimental results show that people do not choose consistently, do not hold consistent beliefs, and do not in general align actions and beliefs. We will show that experimental choices are inconsistent in ways that prevent us from drawing general characterizations of an individual’s choices or beliefs or of the general population\u27s choices and beliefs. A general behavioral game theory seems a distant and, at present, unfulfilled hope
Use of cohesive elements in fatigue analysis
Cohesive laws describe the resistance to incipient separation
of material surfaces. A cohesive finite element
is formulated on the basis of a particular cohesive
law. Cohesive elements are placed at the boundary
between adjacent standard volume finite elements
to model fatigue damage that leads to fracture at the
separation of the element boundaries per the cohesive
law. In this work, a cohesive model for fatigue
crack initiation is taken to be the irreversible loadingunloading
hysteresis that represents fatigue damage
occuring due to cyclic loads leading to the initiation of
small cracks. Various cohesive laws are reviewed and
one is selected that incorporates a hysteretic cyclic
loading that accounts for energetic dissipative mechanisms.
A mathematical representation is developed
based on an exponential effective load-separation cohesive
relationship. A three-dimensional cohesive element
is defined using this compliance relationship integrated
at four points on the mid-surface of the area
element. Implementation into finite element software
is discussed and particular attention is applied to numerical
convergence issues as the inflection point between
loading and 'unloading in the cohesive law is
encountered. A simple example of a displacementcontrolled
fatigue test is presented in a finite element
simulation. Comments are made on applications of
the method to prediction of fatigue life for engineering
structures such as pressure vessels and piping
Scalable simultaneous multi-qubit readout with 99.99% single-shot fidelity
We describe single-shot readout of a trapped-ion multi-qubit register using
space and time-resolved camera detection. For a single qubit we measure
0.9(3)x10^{-4} readout error in 400us exposure time, limited by the qubit's
decay lifetime. For a four-qubit register (a "qunybble") we measure an
additional error of only 0.1(1)x10^{-4} per qubit, despite the presence of 4%
optical cross-talk between neighbouring qubits. A study of the cross-talk
indicates that the method would scale with negligible loss of fidelity to
~10000 qubits at a density <~1 qubit/um^2, with a readout time ~1us/qubit.Comment: 4 pages, 3 figures; simulations added to fig.3, with some further
text and figure revisions. Main results unchanged
- …