Repository of works by Caltech published authors.
Type = Report or Paper
Mostrando recursos 1 - 20 de 2,491
Affine Grassmannians and the geometric Satake in mixed characteristic - Zhu, Xinwen
We endow the set of lattices in Q_p^n with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
Non-abelian Hodge theory for algebraic curves in characteristic p - Chen, Tsao-Hsien; Zhu, Xinwen
Let G be a reductive group over an algebraically closed field of positive
characteristic. Let C be a smooth projective curve over k. We give a
description of the moduli space of flat G-bundles in terms of the moduli space
of G-Higgs bundles over the Frobenius twist C' of C. This description can be
regarded as the non-abelian Hodge theory for curves in positive characteristic.
Recent erosion in the San Gabriel Mountains - Brown, William M., III; Taylor, Brent D.
Recently the Environmental Quality Laboratory at the California Institute of Technology and the Shore Processes Laboratory at Scripps Institution of Oceanography have undertaken a joint project to study the natural sediment budget in coastal southern California. This budget
includes inland erosion which under natural conditions provides sand sized material to nourish the beaches along the shoreline. The San Gabriel Mountains near Los Angeles are an important natural source of sand for beach nourishment. However, the intense urbanization along the base of these mountains have required the advent of extensive flood control structures which significantly reduce the natural transport of sediments from...
Sediment Management for Southern California Mountains, Coastal Plains, and Shoreline - Taylor, Brent D.; Brown, William M.; Brownlie, William R.
The Environmental Quality Laboratory at Caltech and the Shore Processes Laboratory at Scripps Institution of Oceanography have jointly undertaken a study of regional sediment balance problems in coastal southern California (see map in Figure 1). The overall objective in this study is to define specific alternatives in sediment management that may be implemented to alleviate existing sediment imbalance problems (e.g. inland debris disposal, local shoreline erosion) and possible future problems that have not yet manifested themselves. These alternatives will be identified through a consideration of economic, legal, and institutional issues as well as an analysis of governing
physical processes and engineering...
Equilibrium as a Conceptual Framework for an Integrated, Synergistic Introductory Course in Chemistry and Physics - Luca, Oana R.
Teachers of introductory chemistry face the reality of outdated curricula and decreased student interest. The retention rates of students in the sciences remain troubling and the need to revisit course content and teaching methods has become increasingly apparent. A more general course framework developed on the principles of scientific teaching and active learning with relevant examples will perhaps allow students to embrace both chemistry and physics as relevant and inextricably linked disciplines. The present article proposes an integrated curriculum of chemistry and physics at the introductory level, based on the overarching conceptual framework of equilibrium with a focus on energy,...
SIMPle Dark Matter: Self-Interactions and keV Lines - Boddy, Kimberly K.; Feng, Jonathan L.; Kaplinghat, Manoj; Shadmi, Yael; Tait, Timothy M. P.
We consider a simple supersymmetric hidden sector: pure SU(N) gauge theory. Dark matter is
made up of hidden glueballinos with mass mX and hidden glueballs with mass near the confinement
scale Λ. For m_X ~ 1 TeV and Λ ~ 100 MeV, the glueballinos freeze out with the correct relic density
and self-interact through glueball exchange to resolve small-scale structure puzzles. An immediate
consequence is that the glueballino spectrum has a hyperfine splitting of order Λ^2/m_X ~ 10 keV.
We show that the radiative decays of the excited state can explain the observed 3.5 keV X-ray line
signal from clusters of galaxies, Andromeda, and the Milky...
Precision Timing Measurements for High Energy Photons - Anderson, Dustin; Apreysan, Artur; Duarte, Javier; Newman, Harvey; Pena, Cristian; Ronzhin, Anatoly; Spiropulu, M.; Trevor, Jason; Xie, Si; Zhu, Ren-Yuan
Particle colliders operating at high luminosities present challenging environments for high energy physics event reconstruction and analysis. We discuss how timing information, with a precision on the order of 10 ps, can aid in the reconstruction of physics events
under such conditions. We present calorimeter based timing measurements from test beam experiments in which we explore the
ultimate timing precision achievable for high energy photons or electrons of 10 GeV and above. Using a prototype calorimeter
consisting of a 1.7 x 1.7 x 1.7 cm^3 LYSO crystal cube, read out by micro-channel plate PMTs (MCP-PMTs), we demonstrate a
time resolution of (33.5 ± 2.1)...
On Baryogenesis and nn-Oscillations - Herrmann, Enrico
We study a simple model where color sextet scalars violate baryon number at tree level but do not give rise to proton decay. In particular, we include one light and two heavy sextets with ΔB=2 baryon number violating interactions that induce neutron anti-neutron oscillations. This setup also suggests an intimate connection to the generation of the observed baryon asymmetry in the Universe via the out of equilibrium decay of the heavy sextet scalars at around 10^(14) GeV. The large SU(3)-color charges of the scalar fields involved in generating the baryon asymmetry motivate us to study potentially significant washout effects. We...
Experimental determination of the microscopic origin of magnetism in parent iron pnictides - Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Gomes, K.; Yazdani, A.; Chen, G. F.; Luo, J. L.; Wang, N. L.; Hasan, M. Z.
Like high T_c cuprates, the newly discovered iron based superconductors lie in
close proximity to a magnetically ordered parent phase. However, while the
magnetic order in parent cuprates is known to derive from a spin-spin local
superexchange interaction, a plethora of experiments including neutron
scattering have so far been unable to conclusively resolve whether a local
moment Heisenberg description applies in parent iron based compounds, or
whether magnetism arises from a collective SDW order instability. These two
alternatives can in principle be distinguished by measuring the low energy
momentum-resolved bulk-representative electronic structure of the magnetically
ordered phase. Using a combination of polarization dependent ARPES and STM, we
have isolated the...
Tail Bounds for All Eigenvalues of a Sum of Random Matrices - Gittens, Alex A.; Tropp, Joel A.
This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in [Tro11c] that yields both
upper and lower bounds on each eigenvalue of a sum of random self-adjoint matrices. This machinery is used
to derive eigenvalue analogs of the classical Chernoff, Bennett, and Bernstein bounds.
Two examples demonstrate the efficacy of the minimax Laplace transform. The first concerns the effects of column sparsification on the spectrum of a matrix with orthonormal rows. Here, the behavior of the singular values can be described in terms of coherence-like quantities. The second
example addresses the question of relative accuracy...
Error Bounds for Random Matrix Approximation Schemes - Gittens, A.; Tropp, J. A.
Randomized matrix sparsification has proven to be a fruitful technique for producing
faster algorithms in applications ranging from graph partitioning to semidefinite programming. In
the decade or so of research into this technique, the focus has been—with few exceptions—on
ensuring the quality of approximation in the spectral and Frobenius norms. For certain graph
algorithms, however, the ∞→1 norm may be a more natural measure of performance.
This paper addresses the problem of approximating a real matrix A by a sparse random matrix
X with respect to several norms. It provides the first results on approximation error in the ∞→1
and ∞→2 norms, and it uses a result...
Anatomy of the Amplituhedron - Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto; Trnka, Jaroslav
We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the
integrand of scattering amplitudes in planar N = 4 SYM theory. We do so by
introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally...
Herschel HIFI observations of O_2 toward Orion: special conditions for shock enhanced emission - Chen, Jo-Hsin; Goldsmith, Paul F.; Viti, Serena; Snell, Ronald; Lis, Dariusz C.; Benz, Arnold; Bergin, Edwin; Black, John; Caselli, Paola; Encrenaz, Pierre; Falgarone, Edith; Goicoechea, Javier R.; Hjalmarson, Åke; Hollenbach, David; Kaufman, Michael; Melnick, Gary; Neufeld, David; Pagani, Laurent; van der Tak, Floris; Van Dishoeck, Ewine; Yildiz, Umut A.
We report observations of molecular oxygen (O_2) rotational transitions at 487 GHz, 774 GHz, and 1121 GHz toward Orion Peak A. The O_2 lines at 487 GHz and 774 GHz are detected at velocities of 10-12 km s^(-1) with line widths ~3 km s^(-3); however, the transition at 1121 GHz is not detected. The observed line characteristics, combined with the results of earlier observations, suggest that the region responsible for the O_2 emission is ≃9" (6x10^(16) cm) in size, and is located close to the H_2 Peak 1 position (where vibrationally-excited H_2 emission peaks), and not at Peak A, 23"...
Dispersion of Long-Period Love Waves in a Spherical Earth - Kovach, Robert L.; Anderson, Don L.
Periods of torsional eigenvibrations have been computed for heterogeneous
spheres corresponding to a variety of Earth models, and
the periods of oscillation are used to calculate phase and group
velocities for the fundamental and first higher modes of Love waves.
A comparison is made between velocities for different spherical
models, with the velocities calculated by use of equivalent flat Earth
structures. The comparison shows that (1) the effect of sphericity
on fundamental-mode Love waves is more complicated than for
Rayleigh waves because of the efficient channeling of waves by low-velocity
layers, and (2) the first higher Love mode is more affected
by curvature than the fundamental mode. The variation with...
Influence of Aerosol Scattering on the Retrieval of CO_2 Mixing Ratios: A Case Study Using Measurements from the California Laboratory for Atmospheric Remote Sensing (CLARS) - Zhang, Qiong; Natraj, Vijay; Li, King-Fai; Shia, Run-Lie; Fu, Dejian; Pongetti, Thomas J.; Sander, Stanley P.; Yung, Yuk L.
Column abundances of greenhouse gases in the Los Angeles (LA) basin have recently been measured in the near-infrared spectral region using the California Laboratory for Atmospheric Remote Sensing Fourier Transform Spectrometer (CLARS-FTS) deployed at Mt. Wilson, California since August 2011. In the presence of haze, aerosol scattering causes a variable bias in the measured slant column densities (SCDs). We apply an analytic radiative transfer model and a numerical two-stream model to estimate the impact of neglecting aerosol scattering on the CO_2 and O_2 SCDs operationally retrieved from CLARS-FTS measurements. A retrieval scheme has been developed, and tested using synthetic data....
Pressure Line Broadening and Feasibility of CO_2 Profile Retrieval using Near Infrared Observations of an Absorption Line - Shia, Run-Lie; Kuai, Le; Line, Michael R.; Trauger, John T.; Yung, Yuk L.
Analytic expressions are derived for the transmittance and reflectance of sunlight and
their Jacobians for an absorption line with Lorentz line broadening. Rodgers information analysis
is applied to calculate the information content, the degrees of freedom and the averaging kernel
for a simple atmospheric model to investigate the feasibility of retrieving the profile of CO_2
using near-infrared (NIR) measurements over a single absorption line. The results have
implications for the design of future space instruments with high spectral resolution and high
signal to noise ratios to obtain global scale information on the CO_2 vertical distribution which is
important for inferring the sources, sinks, and transport of CO_2.
Non-Axisymmetric Flows on Hot Jupiters with Oblique Magnetic Fields - Batygin, Konstantin; Stanley, Sabine
Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace Alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly-ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework....
Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases - Geraedts, Scott D.; Motrunich, Olexei I.
We study a topological phase of interacting bosons in (3+1) dimensions which is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model which realizes this phase and which can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a...
MORE THAN SMART: A Framework to Make the Distribution Grid More Open, Efficient and Resilient - De Martini, Paul
This paper is the result of a series of workshops with industry, government and nonprofit leaders focused on helping guide future utility investments
and planning for a new distributed generation system. The distributed grid is the final stage in the delivery of electric power linking electricity
sub-stations to customers. To date, no state has initiated a comprehensive effort that includes the planning,
design-build and operational requirements for large
scale integration of DER into state-wide distributed
generation systems. This paper provides a framework and guiding principles for how to initiate such a
system and can be used to implement California law
AB 327 passed in 2013 requiring investor...