Repository of works by Caltech published authors.
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Elastic wave velocities of lunar samples at high pressures and their geophysical implications - Kanamori, Hiroo; Nur, Amos; Chung, D. H.; Simmons, Gene
Ultrasonic measurement of P and S velocities of Apollo 11 lunar samples 10020, 10057 and
10065 to 5 kbar pressure at room temperature shows a pronounced increase of velocity (as much as
twofold) for the first 2 kbar. The travel times predicted from the velocity-depth curve of sample
10057 are consistent with the results of the Apollo 12 seismic experiments. At pressures below 200
bar, the samples are highly attenuating; for both P and S waves, the value of Q is about 10.
Herbivore enamel carbon isotopic composition and the environmental context of Ardipithecus at Gona, Ethiopia - Levin, Naomi E.; Simpson, Scott W.; Quade, Jay; Cerling, Thure E.; Frost, Stephen R.
Ardipithecus fossils found in late Miocene and early Pliocene deposits in the Afar region of Ethiopia, along with Sahelanthropus tchadensis from Chad and Orrorin tugenensis from Kenya, are among the earliest known human ancestors and are considered to be the predecessors to the subsequent australopithecines (Australopithecus anamensis and Australopithecus afarensis). Current paleoenvironmental reconstructions suggest a wooded habitat for both Ardipithecus kadabba and Ardipithecus ramidus but more open and varied environments for other hominids living in Africa during the late Miocene and early Pliocene. To further evaluate the environmental context of Ardipithecus, we present stable carbon isotope data of 182 fossil...
Phase Transitions and Mantle Mixing: Effects of Three-Dimensionality and Temperature-Dependent Viscosity, and Relationship to Observational Constraints - Tackley, Paul J.
In recent years there has been much interest in the question of mantle layering induced by
the endothermic phase transition at 670 km depth, and a partially or intermittently layered
mantle characterized by accumulation of downwellings in the transition zone and catastrophic
avalanches into the lower mantle has been indicated by several numerical studies. Now that this
basic pattern has been established, the challenge is to better constrain how the model results
relate to convection with the actual Earth, by (1) improving the realism of numerical models,
including such effects as three-dimensionality (3-D) and temperature-dependent viscosity, and
(2) relating the theoretical results to a wider range of...
Regionalized Variations in Upper Mantle Temperature - Tralli, D. M.; Ita, J. J.
P and S velocities obtained from tau-p inversion of International Seismological Centre (ISC)
travel-time data (Tralli and Johnson, 1986) are used to construct upper mantle seismic parameter
profiles for oceanic regions categorized according to the square-root of crustal age and
continental regions ranging from active to stable. The radial resolution of velocity anomalies is
about 75 km, with a 5 by 5 degree surface tectonic regionalization. The confidence bounds on the
velocities are used to place corresponding bounds on the seismic parameter, defined as the ratio
of bulk modulus to density and easily determined from P and S velocities at a common depth.
Seismic Resolution of the Earth's Outermost Core in Relation to Lower Mantle Heterogeneity - Garnero, Edward J.; Helmberger, Donald V.
Issues concerning resolution of seismically determined outermost core properties are presented.
Particular attention is given to effects of both large and small scale lower mantle heterogeneity
on seismic phases most commonly used for determining outermost core properties. The family
of SmKS waves, which travel as S in the mantle, P in the core, reflecting (m-1) times at the
underside of the core-mantle boundary (CMB), are the outer core's equivalent to upper mantle
multiple S waves (S, SS, SSS, ... ), and are well-suited for studying outermost core structure.
The higher multiples of SmKS have outer core wave paths restricted to the outermost few
hundred km of the...
Layering in the Mantle: To Be Or Not To Be - Ita, Joel; Anderson, Don L.; King, Scott; Stixrude, Lars
One of the most perplexing and compelling problems in deep Earth geophysics is the possibility
of mantle layering induced dynamically by the presence of the endothermic spinel to Perovskitite
plus magnesiumüstite phase transition, a change in bulk composition or a change in viscosity
between the upper and lower mantle, or any combination of these. Recent models of mantle
convection indicate that the Clapeyron slope of the phase transition (-3 ± lMPa/K) is strong
enough to produce a dynamically layered mantle. One key feature common to these studies
is that the variation of thermal expansively with depth is assumed to be near that found by
Chopelas and Boehler...
"Hotspots"; Uppermantle or Deep-Mantle Phenomena? - Anderson, Don L.
Large igneous provinces (LIPs) such as continental flood basalt (CFB) and oceanic plateau basalt
(OPB) provinces are usually attributed to the arrival of giant plume heads from deep mantle
thermal plumes. Thermal instability in D" is the usually mentioned mechanism. The difficulties
with this mechanism include the effects of internal heating, background mantle convection,
upper mantle phase changes, pressure dependent thermodynamic properties (low a, high lattice
conductivity in D"), cold downwellings and lack of a mechanism for fixing locations. In the
mantle, upwellings are expected to be broad and to be seriously affected by both endothermic
and exothermic phase changes, plate motions and by dense cold downwellings.,...
Radiation Defect-Induced Lattice Contraction of InP - Wie, C. R.; Jones, T.; Tombrello, T. A.; Vreeland, T., Jr.; Xiong, F.; Zhu, Z.; Burns, G.; Dacol, F. H.
We studied the lattice strain induced in the MeV ion bombarded InP crystals and the annealing behaviors of lattice strain, Raman line shift, and linewidth. The lattice spacing for the planes parallel to the surface decreases as a result of irradiation, and amounts to a strain of −0.061% for (100) face, −0.056% for (110) face, and −0.050% for (111) face for 15 MeV Cl bombarded samples to a dose of 1.25E15 ions/cm^2. The negative lattice strain, Raman line shift, and line width completely recover at 450°C, and show a major recovery stage at 250°C – 350°C.
MCMC methods for integer least-squares problems - Hassibi, Babak; Dimakis, Alexandros G.; Papailiopoulos, Dimitris
We consider the problem of finding the least-squares solution to a system of linear equations where the unknown vector has integer entries (or, more precisely, has entries belonging to a subset of the integers), yet where the coefficient matrix and given vector are comprised of real numbers. Geometrically, this problem is equivalent to finding the closest lattice point to a given point and is known to be NP hard. In communication applications, however, the given vector is not arbitrary, but is a lattice point perturbed by some noise vector. Therefore it is of interest to study the computational complexity of...
Anytime reliable codes for stabilizing plants over erasure channels - Sukhavasi, Ravi Teja; Hassibi, Babak
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in problems of distributed control and networked control systems. Although the work of Schulman and Sahai over the past two decades, and their development of the notions of “tree codes” and “anytime capacity”, provides the theoretical framework for studying such problems, there has been scant practical progress in this area because explicit constructions of tree codes with efficient encoding and decoding did not exist. To stabilize an unstable plant driven by bounded noise over a noisy channel one needs real-time encoding...
The Mojave-Sonora megashear — Field and analytical studies leading to the conception and evolution of the hypothesis - Anderson, Thomas H.; Silver, Leon T.
The megashear hypothesis is based upon reconnaissance geologic and geochronologic studies conducted principally from 1968 until 1974 in northwestern Sonora, Mexico. Our research incorporated U-Pb isotopic analyses of more than 70 zircon populations separated from 33 Precambrian rock samples with field relations and maps based upon structural and stratigraphic measurements. The results delineate a region known as the Caborca block and further reveal that the block is a principal element of an unexpected, discordant pattern of Proterozoic basement provinces. The Mojave-Sonora megashear was conceived in an effort to explain: (1) the unexpected pattern of two Proterozoic crystalline provinces with distinct...
Jurassic rocks in Sonora, Mexico: Relations to the Mojave-Sonora megashear and its inferred northwestward extension - Anderson, Thomas H.; Rodríguez-Castañeda, José Luis; Silver, Leon T.
The Mojave-Sonora megashear constitutes a regional boundary between lithologically distinct Jurassic assemblages of different ages. North of the Mojave-Sonora megashear, arc-related volcanic, volcaniclastic, and clastic rocks, intruded by plutons (175–160 Ma) compose part of the Middle Jurassic (commonly ca. 175 Ma) igneous province, previously recognized in Arizona and California. Distinct domains among Jurassic igneous rocks in northern Sonora are: (1) southern Papago, a region where pre-Jurassic rocks are unknown, (2) Nogales-Cananea-Nacozari, where Jurassic rocks are underlain by 1.7–1.4 Ga crystalline basement, and (3) Mojave-Sonora, where strata, including Oxfordian beds, along the north side of the Mojave-Sonora megashear are commonly strongly...
Molecular Manipulator: Dynamic Design Criteria - Jaramillo-Botero, Andrés
This entry reviews the literature on the creation of nanometer-scale spatial positioners, from a kinematic and
dynamic standpoint, as one of the basic building blocks for an atomic-scale manipulator (to arrange
differently functionalized molecular building blocks into a lattice or any other nanometer-scale object in a
specified and complex pattern, it is necessary to introduce positional control).
Origin of the modern Chiapanecan Volcanic arc in southern México inferred from thermal models - Manea, Vlad C.; Manea, Marina
In southern México, the subducting Cocos slab drastically changes its geometry: from a flat slab in central México to a ∼45° dip angle beneath Chiapas. Also, the currently active volcanic arc, the modern Chiapanecan volcanic arc, is oblique and situated far inland from the Middle America trench, where the slab depth is ∼200 km. In contrast, the Central America volcanic arc is parallel to the Middle America trench, and the slab depth is ∼100 km. A two-dimensional steady-state thermomechanical model explains the calc-alkaline volcanism by high temperature (∼1300 °C) in the mantle wedge just beneath the Central America volcanic arc...
On the Mechanisms of Particulate Media Compaction - Vreeland, T.; Prinz, F. B.
Powder handling operations can produce segregation of particles when sufficient vibratory
motion occurs. A benefit of this segregation could be the removal of some foreign particles,
while the segregation can be a detriment when a uniform mixture of particles is desired.
Segregation effects are discussed as well as the beneficial aspect of using a vibratory
component of loading which can produce green compacts of more uniform distention than that
produced by quasi-static pressing.
Dynamic consolidation of green compacts using strong shock waves can produce void-free
material with strong interparticle bonds. The kinetics and energetics of the shock consolidation
of ductile powders is discussed, with the objective of modeling...
A Stieltjes transform approach for studying the steady-state behavior of random Lyapunov and Riccati recursions - Vakili, Ali; Hassibi, Babak
In this paper we study the asymptotic eigenvalue distribution of certain random Lyapunov and Riccati recursions that arise in signal processing and control. The analysis of such recursions has remained elusive when the system and/or covariance matrices are random. Here we use transform techniques (such as the Stieltjes transform and free probability) that have gained popularity in the study of large random matrices. While we have not yet developed a full theory, we do obtain explicit formula for the asymptotic eigendistribution of certain classes of Lyapunov and Riccati recursions, which well match simulation results. Generalizing the results to arbitrary classes...
Approximate capacity region of the two-pair bidirectional Gaussian relay network - Sezgin, Aydin; Khajehnejad, M. Amin; Avestimehr, A. Salman; Hassibi, Babak
We study the capacity of the Gaussian two-pair fullduplex directional (or two-way) relay network with a single-relay supporting the communication of the pairs. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We propose a novel transmission technique which is based on a specific superposition of lattice codes and random Gaussian codes at the source nodes. The relay attempts to decode the Gaussian codewords and the superposition of the lattice codewords of each pair. Then it forwards this information to all users. We analyze the achievable rate of this...
On the distribution of indefinite quadratic forms in Gaussian random variables - Al-Naffouri, Tareq Y.; Hassibi, Babak
In this work, we propose a transparent approach to evaluating the CDF of indefinite quadratic forms in Gaussian random variables and ratios of such forms. This quantity appears in the analysis of different receivers in communication systems and in various applications in signal processing. Instead of attempting to find the pdf of this quantity as is the case in many papers in literature, we focus on finding the CDF. The basic trick that we implement is to replace inequalities that appear in the CDF calculations with the unit step function and replace the latter with its Fourier transform. This produces...
The Kalman Like Particle Filter: Optimal Estimation With Quantized Innovations/Measurements - Sukhavasi, Ravi Teja; Hassibi, Babak
We study the problem of optimal estimation using quantized innovations, with application to distributed estimation over sensor networks. We show that the state probability density conditioned on the quantized innovations can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resulting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far...
Weighted compressed sensing and rank minimization - Oymak, Samet; Khajehnejad, M. Amin; Hassibi, Babak
We present an alternative analysis of weighted ℓ_1 minimization for sparse signals with a nonuniform sparsity model, and extend our results to nuclear norm minimization for matrices with nonuniform singular vector distribution. In the case of vectors, we find explicit upper bounds for the successful recovery thresholds, and give a simple suboptimal weighting rule. For matrices, the thresholds we find are only implicit, and the optimal weight selection requires an exhaustive search. For the special case of very wide matrices, the relationship is made explicit and the optimal weight assignment is the same as the vector case. We demonstrate through...