There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

The uncatalyzed atomic dissociation of water requires breaking of a strong O–H bond with an enthalpy of 494 kJ mol−1, which necessitates the understanding and designing of appropriate catalysts. Here we employ transition state theory within quantum chemical density functional theory to understand the role of metal-oxide inorganic complexes in the OH → O + H process, the most important reaction in water oxidation. We study the effect of (a) chemical bonding in different M4O4 (M = Mn, Co) cubane complexes, (b) heterocubane geometry containing Ca, in addition to a transition metal ion, (c) dimensionality by considering both three-dimensional and two-dimensional geometry of the oxometallic unit, and (d) connectivity between two oxometallic cubane units, corner shared versus edge shared geometry. Analysis of our density functional theory based calculations singles out a robust microscopic quantity among various plausible and competing factors, which elucidates the important role of metal–oxygen covalency at the oxidized site. The M–O bonding strength inversely determines the strength of the O–H bond, and thus the energy required for OH dissociation. This provides one with an important microscopic design principle for a metal-oxide complex catalyst responsible for water oxidation.

/pdf/role-of-oxometallic-complex-on-oh-dissociation-during-water-4ah29mqwej.pdf

Role of oxometallic complex on OH dissociation during water oxidation: A microscopic insight from DFT study

We have studied the electronic structure of the spin-$1∕2$ quantum magnet TiOCl by polarization-dependent momentum-resolved photoelectron spectroscopy. From that, we confirm the quasi-one-dimensional nature of the electronic structure along the crystallographic $b$ axis and find no evidence for sizable phonon-induced orbital fluctuations as the origin for the noncanonical phenomenology of the spin-Peierls transition in this compound. A comparison of the experimental data to our own $\\mathrm{LDA}+\\mathrm{U}$ and Hubbard model calculations reveals a striking lack of understanding regarding the quasi-one-dimensional electron dispersions in the normal state of this compound.

Electronic structure of the spin-1/2 quantum magnet TiOCI

By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the energy of the so-called axial-orbital as the essential, material-dependent parameter. It is uniquely related to the range of the intra-layer hopping. It controls the Cu 4s-character, influences the perpendicular hopping, and correlates with the observed Tc at optimal doping. We explain its dependence on chemical composition and structure, and present a generic tight-binding model.

Band-structure trend in cuprates and correlation with Tc,max

Employing grand canonical Monte-Carlo and molecular dynamics simulations, the viscoelastic response of trapped fluid under molecularly thin confinement by walls having different wall–fluid interaction strengths, is investigated. With increase in slit asymmetry, given by the ratio of interaction strengths of the wall having strong wall–fluid interaction to that of the wall with weak wall–fluid interaction, a crossover in effective density of the fluid film, from rarer (R) to denser (D) than the bulk density is observed. Upon increasing asymmetry further, the dense fluid (F) layers undergo bond-orientational (S) ordering. The variation of viscoelastic relaxation time with scaled asymmetry shows a universal behavior, independent of slit width, with two distinct regimes. Below a critical value of asymmetry, the viscoelastic relaxation time is a slowly varying function of asymmetry, comparable with the structural relaxation time. Beyond the critical asymmetry, on the other hand, viscoelastic response time shows a sharp increase upon increasing asymmetry, deviating markedly from the structural relaxation time. Interestingly the critical asymmetry value is found to correlate with R to D crossover. The microscopic origin of the two-regime universal behavior of viscoelastic response time is found to stem from the fact that below critical asymmetry, the overall viscoelastic behaviour of the slit is dominated by that of the fast relaxing layer close to the weakly attracting surface, while above the critical asymmetry, the relaxation behaviour is guided by the dense fluid layer adjacent to the strongly attracting wall. In vicinity of fluid to ordering transition, the loss and storage moduli merge for low frequencies as in gel-like mechanical behaviour. The storage modulus takes over the loss modulus in the phase co-existence region even before the long ranged order sets in. Our findings bear important implications for fluid transport in hetero-structured geometry in nanotechnology.

Viscoelastic response of fluid trapped between two dissimilar van der Waals surfaces

(TaSe$_4$)$_3$I, a compound belonging to the family of quasi-one-dimensional transition-metal tetrachalcogenides, has drawn significant attention due to a recent report on possible coexistence of two antagonistic phenomena, superconductivity and magnetism below 2.5~K (Bera et. al, arXiv:2111.14525). Here, we report a structural phase transition of the trimerized phase at temperature, $T~\simeq$~145~K using Raman scattering, specific heat, and electrical transport measurements. The temperature-dependent single-crystal X-ray diffraction experiments establish the phase transition from a high-temperature centrosymmetric to a low-temperature non-centrosymmetric structure, belonging to the same tetragonal crystal family. The first-principle calculation finds the aforementioned inversion symmetry-breaking structural transition to be driven by the hybridization energy gain due to the off-centric movement of the Ta atoms, which wins over the elastic energy loss.

Tanusri Saha-Dasgupta

Papers

Role of oxometallic complex on OH dissociation during water oxidation: A microscopic insight from DFT study

Electronic structure of the spin-1/2 quantum magnet TiOCI

Band-structure trend in cuprates and correlation with Tc,max

Viscoelastic response of fluid trapped between two dissimilar van der Waals surfaces

Centrosymmetric-noncentrosymmetric Structural Phase Transition in Quasi one-dimensional compound, (TaSe$_4$)$_3$I