Phanish Suryanarayana's blog
https://imechanica.org/blog/53762
enTorsional moduli of transition metal dichalcogenide nanotubes from first principles
https://imechanica.org/node/25132
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1065">Nanotubes</a></div><div class="field-item odd"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item even"><a href="/taxonomy/term/6074">torsion analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/458">Young's modulus</a></div><div class="field-item even"><a href="/taxonomy/term/7488">poisson ratio</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><strong>Abstract</strong></span></p>
<p><span>We calculate the torsional moduli of single-walled transition metal dichalcogenide (TMD) nanotubes using </span><span>ab initio</span><span> density functional theory (DFT). Specifically, considering forty-five select TMD nanotubes, we perform symmetry-adapted DFT calculations to calculate the torsional moduli for the armchair and zigzag variants of these materials in the low-twist regime and at practically relevant diameters. We find that the torsional moduli follow the trend: MS</span><span>2</span><span> > MSe</span><span>2</span><span> > MTe</span><span>2</span><span>. In addition, the moduli display a power law dependence on diameter, with the scaling generally close to cubic, as predicted by the isotropic elastic continuum model. In particular, the shear moduli so computed are in good agreement with those predicted by the isotropic relation in terms of the Young's modulus and Poisson's ratio, both of which are also calculated using symmetry-adapted DFT. Finally, we develop a linear regression model for the torsional moduli of TMD nanotubes based on the nature/characteristics of the metal-chalcogen bond, and show that it is capable of making reasonably accurate predictions.</span></p>
<p><a href="https://doi.org/10.1088/1361-6528/abf59c">https://doi.org/10.1088/1361-6528/abf59c</a><span><br /></span></p>
</div></div></div>Tue, 27 Apr 2021 15:37:51 +0000Phanish Suryanarayana25132 at https://imechanica.orghttps://imechanica.org/node/25132#commentshttps://imechanica.org/crss/node/25132Flexoelectricity in atomic monolayers from first principles
https://imechanica.org/node/25004
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/978">Flexoelectricity</a></div><div class="field-item odd"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item even"><a href="/taxonomy/term/12922">Atomic monolayers</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Abstract</p>
<p><span>We study the flexoelectric effect in fifty-four select atomic monolayers using </span><em>ab initio</em><span> Density Functional Theory (DFT). Specifically, considering representative materials from each of the Group III monochalcogenides, transition metal dichalcogenides (TMDs), Groups IV, III–V, and V monolayers, Group IV dichalcogenides, Group IV monochalcogenides, transition metal trichalcogenides (TMTs), and Group V chalcogenides, we perform symmetry-adapted DFT simulations to calculate transversal flexoelectric coefficients along the principal directions at practically relevant bending curvatures. We find that the materials demonstrate linear behavior and have similar coefficients along both principal directions, with values for TMTs being up to a factor of five larger than those of graphene. In addition, we find electronic origins for the flexoelectric effect, which increases with monolayer thickness, elastic modulus along the bending direction, and sum of polarizability of constituent atoms.</span></p>
<p><a href="https://doi.org/10.1039/D0NR07803D">https://doi.org/10.1039/D0NR07803D</a></p>
</div></div></div>Tue, 09 Mar 2021 17:25:48 +0000Phanish Suryanarayana25004 at https://imechanica.orghttps://imechanica.org/node/25004#commentshttps://imechanica.org/crss/node/25004Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles
https://imechanica.org/node/25003
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/978">Flexoelectricity</a></div><div class="field-item odd"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item even"><a href="/taxonomy/term/12922">Atomic monolayers</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Abstract</p>
<p><span>We present a formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of </span><span>radial polarization</span><span> to make the coefficient a well-defined quantity for uniform bending deformations. We use the framework to calculate the flexoelectric coefficient for group IV atomic monolayers using density functional theory. We find that graphene's coefficient is significantly larger than previously reported, with a charge transfer mechanism that differs from other members of its group.</span></p>
<p><span><a href="https://doi.org/10.1103/PhysRevMaterials.5.L030801">https://doi.org/10.1103/PhysRevMaterials.5.L030801</a></span><span><br /></span></p>
</div></div></div>Tue, 09 Mar 2021 17:23:39 +0000Phanish Suryanarayana25003 at https://imechanica.orghttps://imechanica.org/node/25003#commentshttps://imechanica.org/crss/node/25003Real-space density functional theory adapted to cyclic and helical symmetry: Application to torsional deformation of carbon nanotubes
https://imechanica.org/node/24859
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3371">DFT</a></div><div class="field-item odd"><a href="/taxonomy/term/6428">symmetry</a></div><div class="field-item even"><a href="/taxonomy/term/13031">Helical</a></div><div class="field-item odd"><a href="/taxonomy/term/7835">Cyclic</a></div><div class="field-item even"><a href="/taxonomy/term/469">torsion</a></div><div class="field-item odd"><a href="/taxonomy/term/139">Carbon nanotube</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><strong><span>Abstract</span></strong></span></p>
<p><span>We present a cyclic and helical symmetry-adapted formulation and large-scale parallel implementation of real-space Kohn-Sham density functional theory for one-dimensional (1D) nanostructures, with application to the mechanical and electronic response of carbon nanotubes subject to torsional deformations. Specifically, employing a semilocal exchange correlation and a local formulation of the electrostatics, we derive symmetry-adapted variants for the energy functional, variational problem governing the electronic ground state, Kohn-Sham equations, atomic forces, and axial stress, all posed on the fundamental domain. In addition, we develop a representation for twisted nanotubes of arbitrary chirality within this framework. We also develop a high-order finite-difference parallel implementation capable of performing accurate cyclic and helical symmetry-adapted Kohn-Sham calculations in both the static and dynamic settings, and verify it through numerical tests and comparisons with established codes. We use this implementation to perform twist-controlled simulations for a representative set of achiral and chiral carbon nanotubes, in both the small and large deformation regimes. In the linear regime, we find that the torsional moduli are proportional to the cube of the diameter; metallic nanotubes undergo metal-insulator transitions; and both the band gap as well as effective mass of charge carriers are proportional to the shear strain and sine of three times the chiral angle. In the nonlinear regime, we find that there is significant Poynting effect, particularly at the ultimate strain, the value of which is determined by the chiral angle; torsional deformations provide a possible mechanism for the irreversible phase transformation from armchair to zigzag nanotubes; and both the band gap as well as effective mass have an oscillatory behavior, with the period for metal-insulator transitions being inversely proportional to the square of the diameter and sine of three times the chiral angle. Wherever available, the results are in good agreement with experimental observations and measurements. Overall, this opens an avenue for the highly accurate and efficient first-principles study of 1D nanostructures that have cyclic and/or helical symmetry, as well as their response to torsional deformations.</span></p>
<p><span><a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.035101" target="_blank" rel="noopener noreferrer">https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.035101</a></span></p>
</div></div></div>Tue, 12 Jan 2021 23:43:25 +0000Phanish Suryanarayana24859 at https://imechanica.orghttps://imechanica.org/node/24859#commentshttps://imechanica.org/crss/node/24859Bending moduli for forty-four select atomic monolayers from first principles
https://imechanica.org/node/24502
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/12921">Bending modulus</a></div><div class="field-item odd"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item even"><a href="/taxonomy/term/12922">Atomic monolayers</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>We calculate bending moduli along the principal directions for forty-four select atomic monolayers using </span><span>ab initio</span><span> density functional theory (DFT). Specifically, considering representative materials from each of Groups IV, III–V, V monolayers, Group IV monochalcogenides, transition metal trichalcogenides, transition metal dichalcogenides and Group III monochalcogenides, we utilize the recently developed Cyclic DFT method to calculate the bending moduli in the practically relevant but previously intractable low-curvature limit. We find that the moduli generally increase with thickness of the monolayer, while spanning three orders of magnitude between the different materials. In addition, structures with a rectangular lattice are prone to a higher degree of anisotropy relative to those with a honeycomb lattice. Exceptions to these trends are generally a consequence of unusually strong/weak bonding and/or significant structural relxation related effects.</span></p>
<p><span><a href="https://iopscience.iop.org/article/10.1088/1361-6528/aba2a2">https://iopscience.iop.org/article/10.1088/1361-6528/aba2a2</a></span></p>
</div></div></div>Mon, 10 Aug 2020 16:17:22 +0000Phanish Suryanarayana24502 at https://imechanica.orghttps://imechanica.org/node/24502#commentshttps://imechanica.org/crss/node/24502Postdoctoral positions at Georgia Institute of Technology
https://imechanica.org/node/22761
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/73">job</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>There are two openings for the position of post-doctoral scholar starting immediately for the US Department of Energy (DOE) Computational Chemical Sciences (CCS) project titled “SPARC-X: Quantum simulations at extreme scale — reactive dynamics from first principles” at Georgia Institute of Technology. This is a four year interdisciplinary research project being led by Phanish Suryanarayana, Andrew J Medford, Edmond Chow, and Polo Chau in collaboration with John E Pask (LLNL). The objective of this research is to develop SPARC-X: a computational framework for performing Kohn-Sham Density Functional Theory (DFT) calculations that scale linearly with the number of atoms in the system, leveraging machine-learning and petascale/exascale parallel computers to study chemical phenomena at unprecedented length and time scales. The position will involve interaction with leading researchers from a range of fields including electronic structure theory, numerical methods, high-performance computing, data visualization, and computational catalysis and will help prepare candidates for a range of future careers including academia, national laboratories, or industry.</p>
<p>Qualifications:<br /> 1) Ph.D. in any scientific or engineering discipline.<br /> 2) Significant expertise in C/C++, MPI programming, and scientific computing.<br /> 3) Knowledge of electronic structure theories and calculations.<br /> 4) Experience in software development including version control, testing, and documentation.</p>
<p>It is a three year research position, subject to funding and performance. Interested applicants should send a copy of their latest CV (with list of references, publications, and software development experience) to Phanish Suryanarayana (<a href="mailto:phanish.suryanarayana@ce.gatech.edu">phanish.suryanarayana@ce.gatech.edu</a>) or Andrew J Medford (<a href="mailto:ajm@gatech.edu">ajm@gatech.edu</a>) with the subject line: Postdoc DOE CCS 2018.</p>
</div></div></div>Mon, 15 Oct 2018 15:30:28 +0000Phanish Suryanarayana22761 at https://imechanica.orghttps://imechanica.org/node/22761#commentshttps://imechanica.org/crss/node/22761Journal Club for July 2018: Mechanics using Quantum Mechanics
https://imechanica.org/node/22476
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Phanish Suryanarayana</p>
<p>Georgia Institute of Technology</p>
<p><strong>1. Introduction and Motivation</strong></p>
<p>Over the past few decades, Density Functional Theory (DFT) developed by Hohenberg, Kohn, and Sham [1,2] has been extensively used for understanding and predicting a wide array of material behavior, including their electronic, mechanical, thermal, and optical properties [3-6]. The tremendous popularity of DFT---free from any empirical parameters by virtue of its origins in the first principles of quantum mechanics---stems from its high accuracy to cost ratio when compared to other such ab-initio theories. However, the efficient and accurate solution of the DFT problem still remains a formidable task. In particular, the orthogonality constraint on the Kohn-Sham orbitals in combination with the substantial number of basis functions required per atom results in a cubic scaling with respect to the number of atoms that is accompanied by a large prefactor. Furthermore, the need for orthogonality gives rise to substantial amount of global communication in parallel computations, which hinders parallel scalability. Consequently, the size of physical systems accessible to DFT has been severely restricted to hundreds of atoms, which has limited the use of DFT in mechanics related applications.</p>
<p>In this journal club, I will outline efforts that enable the application of DFT based ab-initio calculations to three mechanics related problems: (i) study of materials under extreme conditions; (ii) study of the effect of mechanical deformations on the electronic properties of nanostructures, and their interaction with applied electrical and magnetic fields; and (iii) study of crystal defects, interactions betweem them, and interaction with macroscopic deformations. Note that this discussion will focus solely on Kohn-Sham DFT, and will try to provide a general overview, details of which (along with a more comprehensive review of literature) can be found in the cited references.</p>
<p><strong>2. SPARC: Simulation Package for Ab-initio Real-space Calculations</strong></p>
<p>Traditional methods for DFT utilize the plane-wave basis [7-9]. However, the non-locality of plane-waves makes them unsuitable for the development of approaches that scale O(N) with respect to the number of atoms, and makes parallelization over modern large-scale, distributed-memory computer architectures particularly challenging. Furthermore, they cannot be made compatible with non-traditional symmetries like cyclic and helical. Finally, the need for periodic boundary conditions limits their effectiveness in the study of non-periodic and localized systems such as defects. To overcome these limitations and therefore make DFT calculations amenable to the aforementioned mechanics related applications, we have developed a new real-space formulation and parallel implementation of DFT referred to as SPARC [10,11], which is able to outperform state-of-the-art implementations (typically developed by large teams of researchers over a couple of decades) by up to an order of magnitude or more, e.g., Fig. 1. In addition to mechanics, it is expected that SPARC will significantly impact a number of other fields such as materials science, physics, and chemistry.</p>
<p><span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0010465517300711-gr15a.jpg" alt="" height="233" /></span><span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0010465517300711-gr15b.jpg" alt="" height="235" /></span><br /><span id="download-image"></span></p>
<p>Figure 1: Comparison of the performance of SPARC with other well-established plane-wave and real-space codes for representative aluminum systems with a vacancy [11].</p>
<p><strong>3. SQDFT: Ab-intio framework for materials under extreme conditons</strong></p>
<p>In order to overcome the critical cubic-scaling bottleneck with respect to system size, much research in the past two decades has been devoted to the development of linear-scaling solution strategies for DFT [12,13]. Rather than calculate the orthonormal Kohn-Sham orbitals, these techniques directly determine the quantities of interest with linear-scaling cost by exploiting the nearsightedness of matter. Though these efforts have yielded significant advances, there are a number of limitations. In particular, the accuracy and stability of linear-scaling methods remain ongoing concerns due to the need for additional computational parameters, subtleties in determining sufficient numbers and/or centers of localized orbitals, limitations of underlying basis sets, and calculation of accurate atomic forces, as required for structural relaxation and molecular dynamics simulations. In addition, efficient large-scale parallelization poses a significant challenge due to complex communications patterns and load balancing issues. Finally, and perhaps most importantly, the assumption of a band gap in the electronic structure makes these methods inapplicable to metallic systems. </p>
<p>High temperature calculations present additional challenges for DFT. These include the need for a significantly larger number of orbitals to be computed, as the number of partially occupied states increases, and need for more diffuse orbitals, as higher-energy states become less localized. Consequently, cubic-scaling methods as well as local-orbital based linear-scaling methods have very large prefactors, which makes them unsuitable for the study of materials under extreme conditions. In order to overcome these limitations, in the framework provided by the SPARC formulation and implementation, we have recently developed a linear-scaling DFT formulation and implementation referred to as SQDFT [14-16], whose cost actually decreases with increasing temperature. Furthermore, it can efficiently scale up to a hundred thousands computational processors (e.g., Fig. 2), and is therefore able to simulate systems whose sizes are two orders of magnitude larger than previously feasible. SQDFT is currently being utilized to study a variety of materials systems at extreme conditions, with applications in geomechanics.</p>
<p><span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0010465517304022-gr4a.jpg" alt="" height="252" /></span><span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0010465517304022-gr4b.jpg" alt="" height="256" /></span></p>
<p>Figure 2: Parallel scaling of SQDFT, with straight lines in the strong scaling representing ideal scaling [16].</p>
<p> </p>
<p><strong>4. Symmetry-adapted DFT: Ab-initio framework for systems with non-traditional symmetries</strong></p>
<p>Nanostructures have tremendous number of applications, including energy harvesting, efficient power transmission, curing terminal diseases, and design of materials with high specific strength. Therefore, the development of techniques that enable the systematic design and discovery of novel nanostructures with tailored properties is of tremendous interest. Unfortunately, current experimental approaches are generally time consuming, expensive and typically rely on empirical insight. Further, accurate computational techniques like DFT are unable to characterize complex nanostructures and systematically traverse the enormous configurational space because of their large computational expense. This is mainly a consequence of their inability to exploit non-traditional symmetries that are typically present in nanostructures displaying exotic and novel properties. In order to overcome this, in the framework provided by SPARC, we are currently developing a novel DFT framework---based on the notion of objective structures [17]---that is compatible with all the symmetry groups, which will not only provide tremendous simplification in the characterization of nanostructures, but will also accelerate the design of new nanostructures by allowing the use of symmetry to parameterize the configurational space of nanostructures. </p>
<p>As first steps towards achieving this goal, we have developed Cyclic DFT [18] and Helical DFT [19] in the framework provided by the SPARC formulation, which can exploit the cyclic and helical symmetries present in the system to tremendously reduce the computational cost. Since uniform bending deformations can be associated with cyclic symmetry and uniform torsional deformations can be associated with helical symmetry, Cyclic and Helical DFT provide an elegant route to the ab-initio study of bending and torsion in nanostructures (e.g., Fig. 3). Ab-initio simulations of this nature are unprecedented and well outside the scope of any other systematic first principles method in existence. For example, Cyclic DFT was recently employed to study the properties of a 2 micron sized nanostructure, which is up to two orders of magnitude larger than state-of-the-art [20]. Cyclic and Helical DFT are currently being used to study the interaction of mechanical deformations with electric and magneic fields in nanostructures. Also, it is being used to study biological systems with helical symmetry.</p>
<p> </p>
<p> <span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0022509616303684-gr5.jpg" alt="Fig. 5" width="606" height="233" /></span></p>
<p> Figure 3: <span id="cap0025">Results for bending of a silicene nanoribbon [18]. (a) Electron density contour. (b) Cyclic band structure. </span></p>
<p> </p>
<p><strong>5. Course-grained DFT: Ab-initio framework for the study of crystal defects</strong></p>
<p>Crystal defects, though present in relatively minute concentrations, play a significant role in determining material properties. This necessitates an accurate characterization of defects at physically relevant defect concentrations (parts per million), which represents a unique challenge since both the electronic structure of the defect core as well as the long range elastic field need to be resolved simultaneously. Since routine DFT calculations are limited to hundreds of atoms, this represents a truly challenging open problem. In order to solve this, we have developed a method to coarse-grain DFT (in the framework provided by the SPARC and SQDFT formulations) that is solely based on approximation theory, without the introduction of any new equations and resultant spurious physics [21,22]. This work has opened an avenue for the study of extended crystal defects using DFT, which represents a vital step towards understanding the deformation and failure mechanisms in solids. We are currently utilizing this framework to characterize dislocations, the interactions between them, and their interaction with macroscopic fields (e.g. strain). Such studies provide an avenue for the use of constitutive laws based on first principles in higher-scale simulations (e.g. dislocation dynamics).</p>
<p> </p>
<p><span id="download-image"><img src="https://ars.els-cdn.com/content/image/1-s2.0-S0022509612001949-gr9.jpg" alt="" height="300" /></span></p>
<p> </p>
<p>Figure 4: Electron density contours on the mid and edge planes of sodium calculated using coarse-grained DFT [21]</p>
<p> </p>
<p><strong>6. Concluding Remarks</strong></p>
<p>There is great potential and scope for the the use of quantum-mechanical methods like DFT in mechanics related applications. Unfortunately, many of these require system sizes that are well beyond the capabilities of traditional DFT formulations and implementations. Development of methods such as those described above have the potential to open new and exciting avenues for the routine use of ab-initio methods like DFT in mechanics.<br /> </p>
<p> </p>
<p><strong>References</strong></p>
<p>[1] Hohenberg, P. and Kohn, W., 1964. Inhomogeneous electron gas. Physical review, 136(3B), p.B864.<br />[2] Kohn, W. and Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects. Physical review, 140(4A), p.A1133.<br />[3] Jones, R.O. and Gunnarsson, O., 1989. The density functional formalism, its applications and prospects. Reviews of Modern Physics, 61(3), p.689.<br />[4] Baroni, S., De Gironcoli, S., Dal Corso, A. and Giannozzi, P., 2001. Phonons and related crystal properties from density-functional perturbation theory. Reviews of Modern Physics, 73(2), p.515.<br />[5] Marques, M.A. and Gross, E.K., 2004. Time-dependent density functional theory. Annu. Rev. Phys. Chem., 55, pp.427-455.<br />[6] Jones, R.O., 2015. Density functional theory: Its origins, rise to prominence, and future. Reviews of modern physics, 87(3), p.897.</p>
<p>[7] Gonze, X., Beuken, J.M., Caracas, R., Detraux, F., Fuchs, M., Rignanese, G.M., Sindic, L., Verstraete, M., Zerah, G., Jollet, F. and Torrent, M., 2002. First-principles computation of material properties: the ABINIT software project. Computational Materials Science, 25(3), pp.478-492.<br />[8] Kresse, G. and Furthmüller, J., 1996. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical review B, 54(16), p.11169.<br />[9] Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I. and Dal Corso, A., 2009. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of physics: Condensed matter, 21(39), p.395502.<br />[10] Ghosh, S. and Suryanarayana, P., 2017. SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters. Computer Physics Communications, 212, pp.189-204.<br />[11] Ghosh, S. and Suryanarayana, P., 2017. SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems. Computer Physics Communications, 216, pp.109-125.</p>
<p>[12] [12] Goedecker, S., 1999. Linear scaling electronic structure methods. Reviews of Modern Physics, 71(4), p.1085.<br />[13] Bowler, D.R. and Miyazaki, T., 2012. Methods in electronic structure calculations. Reports on Progress in Physics, 75(3), p.036503.<br />[14] Suryanarayana, P., 2013. On spectral quadrature for linear-scaling density functional theory. Chemical Physics Letters, 584, pp.182-187.<br />[15] Pratapa, P.P., Suryanarayana, P. and Pask, J.E., 2016. Spectral Quadrature method for accurate O (N) electronic structure calculations of metals and insulators. Computer Physics Communications, 200, pp.96-107.<br />[16] Suryanarayana, P., Pratapa, P.P., Sharma, A. and Pask, J.E., 2018. SQDFT: Spectral Quadrature method for large-scale parallel O (N) Kohn–Sham calculations at high temperature. Computer Physics Communications, 224, pp.288-298.</p>
<p>[17] James, R.D., 2006. Objective structures. Journal of the Mechanics and Physics of Solids, 54(11), pp.2354-2390.<br />[18] Banerjee, A.S. and Suryanarayana, P., 2016. Cyclic Density Functional Theory: A route to the first principles simulation of bending in nanostructures. Journal of the Mechanics and Physics of Solids, 96, pp.605-631.<br />[19] Banerjee, A.S. and Suryanarayana, P., 2018. Ab initio framework for simulating systems with helical symmetry: formulation, implementation and applications to torsional deformations in nanostructures. In preparation.<br />[20] Ghosh, S., Banerjee, A.S. and Suryanarayana, P., 2018. Density Functional Theory in cylindrical coordinates: Ab-initio simulations of nanomaterials with uniform curvature. In preparation</p>
<p>[21] Suryanarayana, P., Bhattacharya, K. and Ortiz, M., 2013. Coarse-graining Kohn–Sham density functional theory. Journal of the Mechanics and Physics of Solids, 61(1), pp.38-60.<br />[22] Ponga, M., Bhattacharya, K. and Ortiz, M., 2016. A sublinear-scaling approach to density-functional-theory analysis of crystal defects. Journal of the Mechanics and Physics of Solids, 95, pp.530-556.</p>
</div></div></div>Sun, 01 Jul 2018 21:45:29 +0000Phanish Suryanarayana22476 at https://imechanica.orghttps://imechanica.org/node/22476#commentshttps://imechanica.org/crss/node/22476Bloch wave framework for structures with nonlocal interactions: Application to the design of origami acoustic metamaterials
https://imechanica.org/node/22391
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/9589">origami</a></div><div class="field-item odd"><a href="/taxonomy/term/12078">Bloch wave analysis</a></div><div class="field-item even"><a href="/taxonomy/term/1117">design</a></div><div class="field-item odd"><a href="/taxonomy/term/6924">acoustic metamaterials</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><strong><span>Abstract</span></strong></span></p>
<p><span>We present a generalized Bloch wave framework for the dynamic analysis of structures with </span><span>nonlocal</span><span> interactions and apply it to the design of origami acoustic </span><span>metamaterials</span><span>. Specifically, we first </span><span>discretize</span><span> the origami structures using a customized structural bar-and-hinge model that minimizes the degrees of freedom in the associated unit cell, while being sufficiently accurate to capture the behavior of interest. Next, observing that this </span><span>discretization</span><span> results in </span><span>nonlocal</span><span> structural interactions---the stiffness matrix has </span><span>nonzeros</span><span> between nodes that are not nearest neighbors due to the coupled deformations arising during folding or bending---we generalize the standard Bloch wave approach used in structural analysis to enable the study of such systems. Utilizing this framework, choosing the geometry of the unit cell as well as the folded state of the structure as design variables, we design </span><span>tunable</span><span> and programmable </span><span>Miura</span><span>-</span><span>ori</span><span> and </span><span>eggbox </span><span><em>strips</em>, </span><span><em>sheets</em>, and </span><span><em>composites</em> that are large band, low frequency acoustic switches. In doing so, we find that the number of </span><span>bandgaps</span><span> in the sheets is significantly smaller than their strip counterparts and also occur at relatively higher frequencies, a limitation which is overcome by considering composite structures that have individual panels made of different materials. Overall, we have found origami structures to be ideal candidates as acoustic </span><span>metamaterials</span><span> for noise control, vibration isolation, impact absorption, and wave guides.</span></p>
<p><span>This paper has been published in JMPS: <a href="https://www.sciencedirect.com/science/article/pii/S0022509618303089">https://www.sciencedirect.com/science/article/pii/S0022509618303089</a></span></p>
</div></div></div>Mon, 28 May 2018 15:24:10 +0000Phanish Suryanarayana22391 at https://imechanica.orghttps://imechanica.org/node/22391#commentshttps://imechanica.org/crss/node/22391Postdoctoral Position at Georgia Institute of Technology
https://imechanica.org/node/20289
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/73">job</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>There is an opening for a post-doctoral position in Prof. Phanish Suryanarayana’s group starting October/November 2016. The objective of the research project is to develop a new parallel formulation and implementation of Density Functional Theory (DFT) for large-scale calculations, and then apply it to lithium-ion battery anode-electrolyte systems.</p>
<p>Qualifications:<br />1) Ph.D. in any scientific or engineering discipline.<br />2) Significant expertise in C/C++, MPI programming, and scientific computing.<br />3)An ideal candidate will also have knowledge of electronic structure theories and calculations.</p>
<p>Interested applicants should send a copy of their latest CV (with list of references) to <a href="mailto:phanish.suryanarayana@ce.gatech.edu">phanish.suryanarayana@ce.gatech.edu</a> with the subject line: Postdoc DFT 2016</p>
</div></div></div>Sun, 11 Sep 2016 03:48:31 +0000Phanish Suryanarayana20289 at https://imechanica.orghttps://imechanica.org/node/20289#commentshttps://imechanica.org/crss/node/20289Cyclic density functional theory: A route to the first principles simulation of bending in nanostructures
https://imechanica.org/node/20288
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Recent article published in JMPS (Amartya S. Banerjee and Phanish Suryanarayana): <a href="http://www.sciencedirect.com/science/article/pii/S0022509616303684 ">http://www.sciencedirect.com/science/article/pii/S0022509616303684 </a><br /></p><p id="authorab00101" class="title"><strong>Abstract <br /></strong></p>
<p id="sp0050">We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) — a self-consistent first principles simulation method for nanostructures with cyclic symmetries. Using arguments based on Group Representation Theory, we rigorously demonstrate that the Kohn-Sham eigenvalue problem for such systems can be reduced to a fundamental domain (or cyclic unit cell) augmented with cyclic-Bloch boundary conditions. Analogously, the equations of electrostatics appearing in Kohn-Sham theory can be reduced to the fundamental domain augmented with cyclic boundary conditions. By making use of this symmetry cell reduction, we show that the electronic ground-state energy and the Hellmann-Feynman forces on the atoms can be calculated using quantities defined over the fundamental domain. We develop a symmetry-adapted finite-difference discretization scheme to obtain a fully functional numerical realization of the proposed approach. We verify that our formulation and implementation of Cyclic DFT is both accurate and efficient through selected examples.</p>
<p id="sp0055">The connection of cyclic symmetries with uniform bending deformations provides an elegant route to the ab-initio study of bending in nanostructures using Cyclic DFT. As a demonstration of this capability, we simulate the uniform bending of a silicene nanoribbon and obtain its energy-curvature relationship from first principles. A self-consistent ab-initio simulation of this nature is unprecedented and well outside the scope of any other systematic first principles method in existence. Our simulations reveal that the bending stiffness of the silicene nanoribbon is intermediate between that of graphene and molybdenum disulphide — a trend which can be ascribed to the variation in effective thickness of these materials. We describe several future avenues and applications of Cyclic DFT, including its extension to the study of non-uniform bending deformations and its possible use in the study of the nanoscale flexoelectric effect.</p>
</div></div></div>Sun, 11 Sep 2016 01:09:47 +0000Phanish Suryanarayana20288 at https://imechanica.orghttps://imechanica.org/node/20288#commentshttps://imechanica.org/crss/node/20288Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems
https://imechanica.org/node/19209
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10897">Linear systems of equations; Fixed-point iteration; Jacobi method; Anderson extrapolation; Nonsymmetric matrix; Poisson equation; Helmholtz equation; Parallel computing</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Abstract<br /></p><p id="sp0140">We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson-Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-ups that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. Overall, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0021999115007585">http://www.sciencedirect.com/science/article/pii/S0021999115007585</a></p>
</div></div></div>Sun, 06 Dec 2015 01:02:16 +0000Phanish Suryanarayana19209 at https://imechanica.orghttps://imechanica.org/node/19209#commentshttps://imechanica.org/crss/node/19209Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations
https://imechanica.org/node/18880
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10752">Linear systems of equations</a></div><div class="field-item odd"><a href="/taxonomy/term/10753">fixed-point iterations</a></div><div class="field-item even"><a href="/taxonomy/term/6602">ab-initio calculations</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Abstract<br /></p><p id="spar0015">We present a variant of the restarted Pulay's Direct Inversion in the Iterative Subspace (DIIS) method for efficiently and robustly accelerating the convergence of fixed-point iterations. Specifically, we propose a simple modification of DIIS without any additional parameters, which we refer to as the r-Pulay method. We demonstrate the efficacy of r-Pulay in the context of the Jacobi iteration for solving large linear systems of equations, as well as in the Self Consistent Field (SCF) approach for Density Functional Theory (DFT) calculations. Overall, we find r-Pulay to be an attractive version of the restarted DIIS method.</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0009261415004480">http://www.sciencedirect.com/science/article/pii/S0009261415004480</a></p>
</div></div></div>Tue, 22 Sep 2015 03:35:30 +0000Phanish Suryanarayana18880 at https://imechanica.orghttps://imechanica.org/node/18880#commentshttps://imechanica.org/crss/node/18880Ab initio strain engineering of graphene: opening bandgaps up to 1 eV
https://imechanica.org/node/18506
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/671">graphene</a></div><div class="field-item odd"><a href="/taxonomy/term/8540">strain engineering</a></div><div class="field-item even"><a href="/taxonomy/term/4465">density functional theory</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Abstract</p>
<p>We employ electronic structure calculations based on Density Functional Theory (DFT) to strain engineer graphene's bandgap. Specifically, working in the finite deformation setting, we traverse the three-dimensional in-plane strain space to determine states capable of opening significant bandgaps in graphene. We find that biaxial strains comprising of tension in the zigzag direction and compression in the armchair direction are particularly effective at tuning graphene's electronic properties, with resulting bandgaps of up to 1 eV. Notably, we ascertain that a 11% strain in the zigzag direction in combination with −20% in the armchair direction produces a bandgap of approximately 1 eV. We also establish that uniaxial and isotropic biaxial strains of up to ±20% are incapable of opening bandgaps, while shear strains of ±20% can introduce bandgaps of around 0.4 eV.</p>
<p><a href="http://pubs.rsc.org/en/content/articlelanding/2015/ra/c5ra03422a#!divAbstract">http://pubs.rsc.org/en/content/articlelanding/2015/ra/c5ra03422a#!divAbs...</a></p>
</div></div></div>Sat, 27 Jun 2015 01:49:05 +0000Phanish Suryanarayana18506 at https://imechanica.orghttps://imechanica.org/node/18506#commentshttps://imechanica.org/crss/node/18506A very interesting, inspiring article
https://imechanica.org/node/17853
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span id="OBJ_PREFIX_DWT4922_com_zimbra_url" class="Object"><a href="http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty" target="_blank">http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty</a></span></p>
</div></div></div>Wed, 28 Jan 2015 21:42:59 +0000Phanish Suryanarayana17853 at https://imechanica.orghttps://imechanica.org/node/17853#commentshttps://imechanica.org/crss/node/17853Augmented Lagrangian formulation of Orbital-Free Density Functional Theory
https://imechanica.org/node/17011
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1269">electronic structure</a></div><div class="field-item odd"><a href="/taxonomy/term/3371">DFT</a></div><div class="field-item even"><a href="/taxonomy/term/10009">real-space</a></div><div class="field-item odd"><a href="/taxonomy/term/10010">Augmented Lagrangian</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><strong>Abstract</strong></span></p>
<p>We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.</p>
<p>The published article can be found here: <a href="http://www.sciencedirect.com/science/article/pii/S0021999114004860">http://www.sciencedirect.com/science/article/pii/S0021999114004860</a></p>
<p>A preprint is available on arXiv: <a href="http://arxiv.org/abs/1405.6456">http://arxiv.org/abs/1405.6456</a></p>
</div></div></div>Mon, 11 Aug 2014 18:12:25 +0000Phanish Suryanarayana17011 at https://imechanica.orghttps://imechanica.org/node/17011#commentshttps://imechanica.org/crss/node/17011Coarse-graining Kohn-Sham Density Functional Theory
https://imechanica.org/node/15676
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/412">coarse-graining</a></div><div class="field-item odd"><a href="/taxonomy/term/3280">defects</a></div><div class="field-item even"><a href="/taxonomy/term/4465">density functional theory</a></div><div class="field-item odd"><a href="/taxonomy/term/9319">Kohn-Sham</a></div><div class="field-item even"><a href="/taxonomy/term/9320">Linear-scaling</a></div><div class="field-item odd"><a href="/taxonomy/term/9321">Gauss quadrature</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Article published in Journal of the Mechanics and Physics of Solids</p>
<p>Abstract: We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.</p>
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The published version of this manuscript can be found at: <a href="http://www.sciencedirect.com/science/article/pii/S0022509612001949" target="_blank">http://www.sciencedirect.com/science/article/pii/S0022509612001949</a>
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</div></div></div>Thu, 21 Nov 2013 23:03:43 +0000Phanish Suryanarayana15676 at https://imechanica.orghttps://imechanica.org/node/15676#commentshttps://imechanica.org/crss/node/15676