R-3 Repository :: Browsing by Author "Zhang, Ming"

Browsing by Author "Zhang, Ming"

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A Set of Convolution Identities Relating the Blocks of Two Dixon Resultant Matrices
(1999-06-16) Chionh, Eng-Wee; Goldman, Ronald; Zhang, Ming
Resultants for bivariate polynomials are often represented by the determinants of very big matrices. Properly grouping the entries of these matrices into blocks is a very effective tool for studying the properties of these resultants. Here we derive a set of convolution identities relating the blocks of two Dixon bivariate resultant representations.
Computing and Updating Molecular Conformations Using the Atomgroup Local Frames Method
(2001-05-11) Kavraki, Lydia E.; Zhang, Ming
Efficiently maintaining molecular conformations is important for molecular modeling and protein engineering. This paper reviews the widely used simple rotations scheme, simple local frames method, and introduces a new atom group local frames method for maintaining the molecular conformation changes due to the changes of torsional angles. The simple rotations scheme applies a sequence of rotations to update all atom positions. The order of the updates is important and some bookkeeping of the atom positions is necessary. Numeric errors can accumulate as rotations around the bonds are repeated. The simple local frames method builds local frames at the bonds, and relational matrices between parents and children frames are constructed. The atom positions are computed by chaining series of such matrices. No bookkeeping is necessary and numeric errors do not accumulate upon rotations. Multiple local frames are needed at a bond if it has more than one child. This paper introduces a new atom group local frames method to efficiently maintain molecular conformations. A single local frame is attached to each atom group. Bookkeeping is not necessary and numeric errors do not accumulate upon rotations. This method also provides lazy evaluations for atom positions. Thus, the conformational maintenance cost is greatly reduced, especially when many conformations are generated and updated such as in a minimization process.
Design of All-dielectric Metasurfaces for Vacuum Ultraviolet Applications
(2020-12-04) Zhang, Ming; Nordlander, Peter
The last decade witnessed a surge in applications of all-dielectric metasurfaces. Compared to traditional plasmonic materials, low-loss, high-refractive-index dielectric materials can generate strong local electric field enhancement while maintaining low optical absorption, thus providing new possibilities in various applications, such as imaging, nonlinear generation, and biosensing. In this thesis, we explore the potential of all-dielectric metasurfaces in two aspects. In the first part of this thesis, we demonstrate two novel nonlinear all-dielectric metasurface designs in the vacuum ultraviolet (VUV) region: a titanium dioxide (TiO2) metasurface that provides enhanced third harmonic generation at 185 nm by an anapole resonance near the fundamental wavelength of 555 nm, and an ultracompact zinc oxide (ZnO) metalens that effectively converts a 394-nm wave into converging 197-nm light via second harmonic generation. In the second part of the thesis, we introduce a new automated nanodevice design (inverse design) platform based on the discrete dipole approximation method (DDA) and optimization theories. With given performance metrics, this computational platform is capable of efficiently searching for optimal nanodevice geometries without intensive human labor, thus illustrating a promising strategy for designing large-scale, multifunctional all-dielectric metasurfaces.
Finding Solutions of the Inverse Kinematics Problems in Computer-aided Drug Design
(2002-01-25) Kavraki, Lydia E.; Zhang, Ming
The efficient computation of low-energy molecular conformations is of critical importance to problems ranging from protein folding to computer-assisted drug design. Despite the growing number of papers on three-dimensional conformational search, several questions remain open. In this paper we investigate one such question relating to molecular inverse kinematics problems. In these problems we are given an initial conformation of a molecule and the target positions of some feature atoms of the molecule. We wish to automatically compute a new conformation of the molecule that brings the feature atoms to their target positions. We first show how to derive a system of polynomial equations from the geometric constraints of the feature atoms. In contrast with previous work, we do not attempt to solve the system of equations directly, which is computationally expensive. Instead, we adopt a technique based on the Groebner basis from algebraic geometry and develop a novel subdivision algorithm to approximate the real solutions. The approximated solutions can then be used as the starting conformations for existing(heuristic) energy minimization procedures that try to satisfy the target positions of feature atoms and reduce the overall energy of the conformation. To our knowledge, this is the first time that a rigorous algebraic methodology has been used to approximate molecular inverse kinematics solutions and the first time that a subdivision algorithm has been developed to efficiently locate the solutions.
Harmonic light-generating metasurface
(2022-11-15) Semmlinger, Michael; Tseng, Ming-lun; Yang, Jian; Zhang, Ming; Tsai, Din Ping; Dong, Liangliang; Ahmadivand, Arash; Nordlander, Peter; Halas, Naomi Jean; Rice University; William Marsh Rice University; Academia Sinica; United States Patent and Trademark Office
A harmonic light-generating metasurface includes a base substrate and a plurality of structures, that include nonlinear material, that are disposed in a pattern on a surface of the base substrate. Each structure of the plurality of structures individually supports a magnetic dipole mode. An electromagnetic field enhancement of the magnetic dipole mode induces generation of a harmonic signal by the plurality of structures. Alternatively, a harmonic light-generating metasurface, includes a base substrate, a supporting substrate that includes a nonlinear material, and a plurality of paired structures disposed in a pattern on a surface of the supporting substrate. Each paired structure, of the plurality of paired structures, collectively supports a toroidal dipole mode. An electromagnetic field enhancement of the toroidal dipole mode penetrates the supporting substrate to induce generation of a harmonic signal by the supporting substrate.
Hybrid Dixon Resultants
(1998-05-13) Chionh, Eng-Wee; Goldman, Ronald; Zhang, Ming
Dixon [1908] describes three distinct homogeneous determinant representations for the resultant of three bivariate polynomials of bidegree(m,n). These Dixon resultants are the determinants of matrices of orders 6mn, 3mn and 2mn, and the entries of these matrices are respectively homogeneous of degrees 1, 2, and 3 in the coefficients of the original three polynomial equations. Here we mix and match columns from these three Dixon matrices to construct a large assortment of new hybrid determinant representations of orders ranging from 2mn to 6mn for the resultant of three bivariate polynomials of bidegree (m,n).
Metal-organic frameworks tailor the properties of aluminum nanocrystals
(AAAS, 2019) Robatjazi, Hossein; Weinberg, Daniel; Swearer, Dayne F.; Jacobson, Christian; Zhang, Ming; Tian, Shu; Zhou, Linan; Nordlander, Peter; Halas, Naomi J.
Metal-organic frameworks (MOFs) and metal nanoparticles are two classes of materials that have received considerable recent attention, each for controlling chemical reactivities, albeit in very different ways. Here, we report the growth of MOF shell layers surrounding aluminum nanocrystals (Al NCs), an Earth-abundant metal with energetic, plasmonic, and photocatalytic properties. The MOF shell growth proceeds by means of dissolution-and-growth chemistry that uses the intrinsic surface oxide of the NC to obtain the Al3+ ions accommodated into the MOF nodes. Changes in the Al NC plasmon resonance provide an intrinsic optical probe of its dissolution and growth kinetics. This same chemistry enables a highly controlled oxidation of the Al NCs, providing a precise method for reducing NC size in a shape-preserving manner. The MOF shell encapsulation of the Al NCs results in increased efficiencies for plasmon-enhanced photocatalysis, which is observed for the hydrogen-deuterium exchange and reverse water-gas shift reactions.
Plasmonic Photocatalysis of Nitrous Oxide into N2 and O2 Using Aluminum–Iridium Antenna–Reactor Nanoparticles
(American Chemical Society, 2019) Swearer, Dayne F.; Robatjazi, Hossein; Martirez, John Mark P.; Zhang, Ming; Zhou, Linan; Carter, Emily A.; Nordlander, Peter; Halas, Naomi J.; Laboratory for Nanophotonics
Photocatalysis with optically active “plasmonic” nanoparticles is a growing field in heterogeneous catalysis, with the potential for substantially increasing efficiencies and selectivities of chemical reactions. Here, the decomposition of nitrous oxide (N2O), a potent anthropogenic greenhouse gas, on illuminated aluminum–iridium (Al–Ir) antenna–reactor plasmonic photocatalysts is reported. Under resonant illumination conditions, N2 and O2 are the only observable decomposition products, avoiding the problematic generation of NOx species observed using other approaches. Because no appreciable change to the apparent activation energy was observed under illumination, the primary reaction enhancement mechanism for Al–Ir is likely due to photothermal heating rather than plasmon-induced hot-carrier contributions. This light-based approach can induce autocatalysis for rapid N2O conversion, a process with highly promising potential for applications in N2O abatement technologies, satellite propulsion, or emergency life-support systems in space stations and submarines.
The Block Structure of Three Dixon Resultants and Their Accompanying Transformation Matrices
(1999-06-16) Chionh, Eng-Wee; Goldman, Ronald; Zhang, Ming
Dixon [1908] introduces three distinct determinant formulations for the resultant of three bivariate polynomials of bidegree (m,n) . The first technique applies Sylvester's dialytic method to construct the resultant as the determinant of a matrix of order 6mn . The second approach uses Cayley's determinant device to form a more compact representation for the resultant as the determinant of a matrix of order 2mn . The third method employs a combination of Cayley's determinant device with Sylvester's dialytic method to build the resultant as the determinant of a matrix of order 3mn . Here relations between these three resultant formulations are derived and the structure of the transformations between these resultant matrices is investigated. In particular, it is shown that these transformation matrices all have similar, simple, upper triangular, block symmetric structures and the blocks themselves have elegant symmetry properties. Elementary entry formulas for the transformation matrices are also provided. In light of these results, the three Dixon resultant matrices are reexamined and shown to have natural block structures compatible with the block structures of the transformation matrices. These block structures are analyzed here and applied along with the block structures of the transformation matrices to simplify the calculation of the entries of the Dixon resultants of order 2mn and 3mn and to make these calculations more efficient by removing redundant computations.
Titanium Dioxide Metasurface for Vacuum Ultraviolet Third-harmonic Generation
(2019-11-26) Zhang, Ming; Nordlander, Peter
Vacuum ultraviolet (VUV) light, in the wavelength regime between 100nm and 200nm, is of long-lasting interest in both academia and industry for its strong photon energy and efficient absorption in most common materials. However, a simple and robust way of VUV light generation remains to be found. In this thesis, I report a titanium dioxide (TiO2) all-dielectric metasurface that enables light generation at 185nm through photonic resonance enhanced third-harmonic generation (THG). Both theoretical analysis and experimental measurements of the metasurface are presented in detail. A multi-step model to calculate generated THG strength is demonstrated. In addition, I include a heat transfer model to analyze the thermal effect of the high input laser power on THG power dependence. A nonlinear signal enhancement factor of 180 compared to an unpatterned TiO2 thin film is reported in the experiment. Finally, the possibility to further enhance the conversion efficiency of the device by using a reflective structure and redesigning the structure geometry through inverse design is also discussed in the simulation aspect.
Topics in resultants and implicitization
(2000) Zhang, Ming; Goldman, Ron
Resultants are computational tools for determining whether or not a system of polynomials has a common root without actually solving for the roots of these equations. Resultants can also be used to solve for the common roots of polynomial systems. Classical resultants are typically represented as determinants whose entries are polynomials in the coefficients of the original polynomials in the system. The work in this dissertation on classical resultants focuses on bivariate polynomials. It is shown that bivariate resultants can be represented as determinants in a variety of innovative ways and that these various formulations are interrelated. Remarkable internal structures in these resultant matrices are exposed. Based on these structures, efficient computational algorithms for calculating the entries of these resultant matrices are developed. Sparse resultants are used for solving systems of sparse polynomials, where classical resultants vanish identically and hence fail to give any useful information about the common roots of the sparse polynomials. Nevertheless, sparse polynomial systems frequently appear in surface design. Sparse resultants are usually represented as GCDs of a collection of determinants. These GCDs are extremely awkward for symbolic computation. Here a new way is presented to construct sparse resultants as single determinants for a large collection of sparse systems of bivariate polynomials. An important application of both classical and sparse resultants in geometric modeling is implicitization. Implicitization is the process of converting surfaces from parametric form into algebraic form. Classical resultant methods fail when a rational surface has base points. The method of moving quadrics, first introduced by Professor Tom Sederberg at Brigham Young University, is known empirically to successfully implicitize rational surfaces with base points. But till now nobody has ever been able to give a rigorous proof of the validity of this technique. The first proof of the validity of this method when the surfaces have no base points is provided in this dissertation.
Transformations and Transitions from the Sylvester to the Bezout Resultant
(1999-06-17) Chionh, Eng-Wee; Goldman, Ronald; Zhang, Ming
A simple matrix transformation linking the resultant matrices of Sylvester and Bezout is derived. This transformation matrix is then applied to generate an explicit formula for each entry of the Bezout resultant, and this entry formula is used, in turn, to construct an efficient recursive algorithm for computing all the entries of the Bezout matrix. Hybrid resultant matrices consisting of some columns from the Sylvester matrix and some columns from the Bezout matrix provide natural transitions from the Sylvester to the Bezout resultant, and allow as well the Bezout construction to be generalized to two polynomials of different degrees. Such hybrid resultants are derived here, employing again the transformation matrix from the Sylvester to the Bezout resultant.

Browsing by Author "Zhang, Ming"

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