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Several of NASA missions (TESS, JWST, WFIRST, etc.) and mission concepts (LUVOIR, HabEx, and OST) emphasize the exploration and characterization of exoplanets, and the study of the interstellar medium. We anticipate that a much broader set of chemical environments exists on exoplanets, necessitating data from a correspondingly broader set of chemical reactions. Similarly, the conditions that exist in astrophysical environments are very different from those traditionally probed in laboratory chemical kinetics studies. These are areas where quantum mechanical theory, applied to important reactions via well-validated chemical kinetics models, can fill a critical knowledge gap. Quantum chemical calculations are also introduced to study interior of planets, photochemical escape, and many critical chemical pathways (e.g. prebiotic environments, contaminations, etc.) After years of development of the relevant quantum chemical theories and significant advances in computational power, quantum chemical simulations have currently matured enough to describe real systems with an accuracy that competes with experiments. These approaches, therefore, have become the best possible alternative in many circumstances where performing experiments is too difficult, too expensive, or too dangerous, or simply not possible. In this white paper, several existing quantum chemical studies supporting exoplanetary science, planetary astronomy, and astrophysics are described, and the potential positive impacts of improved models associated with scientific goals of missions are addressed. In the end, a few recommendations from the scientific community to strengthen related research efforts at NASA are provided.

We study a variation of offline Dial-a-Ride, where each request has not only a source and destination, but also a revenue that is earned for serving the request. We investigate this problem for the uniform metric space with uniform revenues. While we present a study on a simplified setting of the problem that has limited practical applications, this work provides the theoretical foundation for analyzing the more general forms of the problem. Since revenues are uniform the problem is equivalent to maximizing the number of served requests. We show that the problem is NP-hard and present a 2/3 approximation algorithm. We also show that a natural generalization of this algorithm has an approximation ratio at most 7/9.

Several of NASA missions (TESS, JWST, WFIRST, etc.) and mission concepts (LUVOIR, HabEx, and OST) emphasize the exploration and characterization of exoplanets, and the study of the interstellar medium. We anticipate that a much broader set of chemical environments exists on exoplanets, necessitating data from a correspondingly broader set of chemical reactions. Similarly, the conditions that exist in astrophysical environments are very different from those traditionally probed in laboratory chemical kinetics studies. These are areas where quantum mechanical theory, applied to important reactions via well-validated chemical kinetics models, can fill a critical knowledge gap. Quantum chemical calculations are also introduced to study interior of planets, photochemical escape, and many critical chemical pathways (e.g. prebiotic environments, contaminations, etc.) After years of development of the relevant quantum chemical theories and significant advances in computational power, quantum chemical simulations have currently matured enough to describe real systems with an accuracy that competes with experiments. These approaches, therefore, have become the best possible alternative in many circumstances where performing experiments is too difficult, too expensive, or too dangerous, or simply not possible. In this white paper, several existing quantum chemical studies supporting exoplanetary science, planetary astronomy, and astrophysics are described, and the potential positive impacts of improved models associated with scientific goals of missions are addressed. In the end, a few recommendations from the scientific community to strengthen related research efforts at NASA are provided.

Modelling of mantle flows with sharp viscosity contrasts in a viscoelastic medium is a challenging computational problem in geodynamics because of its multiple-scale nature in space and time. We have employed a recently developed adaptive multilevel wavelet collocation algorithm to study the dynamics of a small rising diapir interacting with a stiff lithosphere in a Maxwell viscoelastic mantle. In this kinematic model we have prescribed the upward velocity of the diapir and then we need to integrate in time onlythe momentum equation governing the temporal evolution of the pressure, stress andvelocity components, which together constitute a sixth-order system in time. The total number of collocation points did not exceed 104, compared to more than 106 gridpoints using conventional evenly spaced grid methods. The viscosity of the diapir is10−4 times lower than that of the surrounding mantle, while the viscosity of the thinlithosphere, about 5-10 per cent of the entire layer depth, is 104-108 times stiffer than the ambient mantle. Our results demonstrate the efficacy of wavelets to capture thesharp gradients of the stress and pressure fields developed in the diapiric impingement process. The interaction of the viscoelastic lithosphere with therisingviscoelastic diapir results in the localization of stress within the lithosphere. The magnitude of the stress fields can reach around 100-300 MPa. Our simple kinematic model shows clearly that viscoelasticity canpotentially play an important role in the dynamics of thelithosphere, especially concerning the potential severage of the lithosphere by mantle upwellings

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990., Title as it appears in the M.I.T. Graduate List, June 1990: High-frequency dielectric constant and conductivity of fluids and fluid-saturated rocks at high pressure., Includes bibliographical references (leaves 124-127)., by David J. Yuen., M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990., Title as it appears in the M.I.T. Graduate List, June 1990: High-frequency dielectric constant and conductivity of fluids and fluid-saturated rocks at high pressure., Includes bibliographical references (leaves 124-127)., by David J. Yuen., M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990., Title as it appears in the M.I.T. Graduate List, June 1990: High-frequency dielectric constant and conductivity of fluids and fluid-saturated rocks at high pressure., Includes bibliographical references (leaves 124-127)., by David J. Yuen., M.S.

We give a hyperelliptic formulation of the Ansatz of D'Hoker and Phong. We give an explicit family of binary invariants, one for each genus, that satisfies this hyperelliptic Ansatz. We also prove that this is the unique family of weight eight binary forms over the theta group on the hyperelliptic locus that satisfies this Ansatz. Futhermore, we prove that this solution may also be obtained by applying Thomae's map to multivalued Siegel modular forms of Grushevsky and making certain choices of roots.

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

We derive optimal bidding strategies for a global bidder who participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always place non-zero bids in all available auctions, provided there are no budget constraints. With a budget, however, the optimal strategy is to bid locally if this budget is equal or less than the valuation. Furthermore, for a wide range of valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions if all auctions are identical. Moreoever, we address markets with both sequential and simultaneous auctions, non-identical auctions, and the allocative efficiency of the market. Finally, by combining analystical and simulation results, we analyse equilibrium strategies in case of several global bidders. However, a stable solution is then only found if there are local bidders as well.

We derive optimal bidding strategies for a global bidder who participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always place non-zero bids in all available auctions, provided there are no budget constraints. With a budget, however, the optimal strategy is to bid locally if this budget is equal or less than the valuation. Furthermore, for a wide range of valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions if all auctions are identical. Moreoever, we address markets with both sequential and simultaneous auctions, non-identical auctions, and the allocative efficiency of the market. Finally, by combining analystical and simulation results, we analyse equilibrium strategies in case of several global bidders. However, a stable solution is then only found if there are local bidders as well.

Runge gave the ring of genus three Siegel modular forms as a quotient ring, 3=hJ(3)i. R3 is the genus three ring of code polynomials and J(3) is the di®erence of he weight enumerators for the e8 © e8 and d+ 6 codes. Freitag and Oura gave a degree 24 elation, R(4) , of the corresponding ideal in genus four; R(4) is also a linear combination of eight enumerators. We take another step toward the ring of Siegel modular forms in genus our. We explain new techniques for computing with Siegel modular forms and actually ompute six new relations, classifying all relations through degree 32. We show that the local odimension of any irreducible component de¯ned by these known relations is at least 3 and hat the true ideal of relations in genus four is not a complete intersection. Also, we explain ow to generate an in¯nite set of relations by symmetrizing ¯rst order theta identities and ive one example in degree 32. We give the generating function of R5 and use it to reprove esults of Nebe [25] and Salvati Manni [37].

by Yuen, David., Thesis (M.B.A.)--Chinese University of Hong Kong, 1988., Bibliography: leaves 40-41., http://library.cuhk.edu.hk/record=b5885893, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Modelling of mantle flows with sharp viscosity contrasts in a viscoelastic medium is a challenging computational problem in geodynamics because of its multiple-scale nature in space and time. We have employed a recently developed adaptive multilevel wavelet collocation algorithm to study the dynamics of a small rising diapir interacting with a stiff lithosphere in a Maxwell viscoelastic mantle. In this kinematic model we have prescribed the upward velocity of the diapir and then we need to integrate in time onlythe momentum equation governing the temporal evolution of the pressure, stress andvelocity components, which together constitute a sixth-order system in time. The total number of collocation points did not exceed 104, compared to more than 106 gridpoints using conventional evenly spaced grid methods. The viscosity of the diapir is10−4 times lower than that of the surrounding mantle, while the viscosity of the thinlithosphere, about 5-10 per cent of the entire layer depth, is 104-108 times stiffer than the ambient mantle. Our results demonstrate the efficacy of wavelets to capture thesharp gradients of the stress and pressure fields developed in the diapiric impingement process. The interaction of the viscoelastic lithosphere with therisingviscoelastic diapir results in the localization of stress within the lithosphere. The magnitude of the stress fields can reach around 100-300 MPa. Our simple kinematic model shows clearly that viscoelasticity canpotentially play an important role in the dynamics of thelithosphere, especially concerning the potential severage of the lithosphere by mantle upwellings