Papers by Marek Grabowski
Physical Review A, 1985
Quasiperiodic (incommensurate) patterns consisting of an array of solitous are found in a convect... more Quasiperiodic (incommensurate) patterns consisting of an array of solitous are found in a convecting nematic fluid subjected to spatially periodic forcing. The solitons are regions of local compression of the convective rolls and are well described by solutions to the sine-Gordon equation. The commensurate-incommensurate transition is continuous for weak forcing, but becomes discontinuous as the forcing amplitude increases. This behavior indicates the existence of a tricritical point on the phase transition line.
Journal of structural and functional genomics, Jan 2, 2016
The period 2000-2015 brought the advent of high-throughput approaches to protein structure determ... more The period 2000-2015 brought the advent of high-throughput approaches to protein structure determination. With the overall funding on the order of $2 billion (in 2010 dollars), the structural genomics (SG) consortia established worldwide have developed pipelines for target selection, protein production, sample preparation, crystallization, and structure determination by X-ray crystallography and NMR. These efforts resulted in the determination of over 13,500 protein structures, mostly from unique protein families, and increased the structural coverage of the expanding protein universe. SG programs contributed over 4400 publications to the scientific literature. The NIH-funded Protein Structure Initiatives alone have produced over 2000 scientific publications, which to date have attracted more than 93,000 citations. Software and database developments that were necessary to handle high-throughput structure determination workflows have led to structures of better quality and improved i...
Numerical reevaluation of the formulas yield corrections to Fig. 3 and the lower panel of Fig. 4,... more Numerical reevaluation of the formulas yield corrections to Fig. 3 and the lower panel of Fig. 4, as shown here. In Fig.
Journal of Magnetism and Magnetic Materials, May 1, 2020
Abstract We examine a magnetic moment subject to a static external magnetic field and a time depe... more Abstract We examine a magnetic moment subject to a static external magnetic field and a time dependent driving magnetic field. Taking the system in the highly anisotropic limit, like that of a thin film, we lower the complexity of the system so that it may be analyzed for transitions to chaos analytically using the Melnikov method. Guided by the calculation of the Melnikov bifurcation functions we computationally calculated the Lyapunov characteristic exponents for several lines in parameter space and find that the Melnikov method is a good predictor of chaotic motion for sufficiently small external fields. Motion plots and Poincare sections are also plotted for several parameter space points to observe the transitions to and from chaos around the calculated Melnikov bifurcations functions.
Modern Physics Letters A, 1994
An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg s=1/2... more An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg s=1/2 spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferromagnetic and antiferromagnetic sectors are briefly discussed.
Journal of Physics A: Mathematical and General, 1995
We examine a simple heuristic test of integrability for quantum chains. This test is applied to a... more We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearestneighbor interactions and a multiparameter family of spin-1/2 models generalizing the XYZ chain, with next-to-nearest neighbor interactions and bond alternation. Within the latter family we determine all the integrable models with an o(2) symmetry.
Journal of Physics A: Mathematical and General, 1996
We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial bo... more We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial boundary conditions. The general structure of these charges consists of a bulk part, whose density is identical to that of a periodic chain, and a boundary part. In contrast with the periodic case, only the charges corresponding to the interactions of even number of spins exist for the open chain. Hence, there are half as many charges in the open case as in the closed case. For the open spin-1/2 XY chain, we derive the explicit expressions of all the charges. For the open spin-1/2 XXX chain, several lowest order charges are presented and a general method of obtaining the boundary terms is indicated. In contrast with the closed case, the XXX charges cannot be described in terms of a Catalan tree pattern.
Journal of Mathematical Physics, 1995
A class of quantum chains possessing a family of local conserved charges with a Catalan tree patt... more A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, w e h a v e identied such a structure in the integrable SU(N)-invariant c hains. In the present w ork we nd sucient conditions for the existence of a family of charges with this structure in terms of the underlying algebra. Two additional systems with a Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ model with = 1. The other is a new octonionic isotropic chain, generalizing the Heisenberg model. This system provides an interesting example of an innite family of noncommuting local conserved quantities.
Journal of Magnetism and Magnetic Materials, 2019
Abstract We examine a magnetic moment subject to a static external magnetic field and a time depe... more Abstract We examine a magnetic moment subject to a static external magnetic field and a time dependent driving magnetic field. Taking the system in the highly anisotropic limit, like that of a thin film, we lower the complexity of the system so that it may be analyzed for transitions to chaos analytically using the Melnikov method. Guided by the calculation of the Melnikov bifurcation functions we computationally calculated the Lyapunov characteristic exponents for several lines in parameter space and find that the Melnikov method is a good predictor of chaotic motion for sufficiently small external fields. Motion plots and Poincare sections are also plotted for several parameter space points to observe the transitions to and from chaos around the calculated Melnikov bifurcations functions.
npj Systems Biology and Applications, 2016
Systems Biology has established numerous approaches for mechanistic modeling of molecular network... more Systems Biology has established numerous approaches for mechanistic modeling of molecular networks in the cell and a legacy of models. The current frontier is the integration of models expressed in different formalisms to address the multi-scale biological system organization challenge. We present MUFINS (MUlti-Formalism Interaction Network Simulator) software, implementing a unique set of approaches for multi-formalism simulation of interaction networks. We extend the constraint-based modeling (CBM) framework by incorporation of linear inhibition constraints, enabling for the first time linear modeling of networks simultaneously describing gene regulation, signaling and whole-cell metabolism at steady state. We present a use case where a logical hypergraph model of a regulatory network is expressed by linear constraints and integrated with a Genome-Scale Metabolic Network (GSMN) of mouse macrophage. We experimentally validate predictions, demonstrating application of our software in an iterative cycle of hypothesis generation, validation and model refinement. MUFINS incorporates an extended version of our Quasi-Steady State Petri Net approach to integrate dynamic models with CBM, which we demonstrate through a dynamic model of cortisol signaling integrated with the human Recon2 GSMN and a model of nutrient dynamics in physiological compartments. Finally, we implement a number of methods for deriving metabolic states from~omics data, including our new variant of the iMAT congruency approach. We compare our approach with iMAT through the analysis of 262 individual tumor transcriptomes, recovering features of metabolic reprogramming in cancer. The software provides graphics user interface with network visualization, which facilitates use by researchers who are not experienced in coding and mathematical modeling environments.
Studies in Applied Mathematics, 2018
The inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger-t... more The inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger-type systems whose reductions include two equations that model certain hyperfine spin F = 1 spinor Bose-Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four-component fermionic condensates. In addition, the general behavior of the soliton solutions for all four reductions is analyzed in detail, and some novel solutions are presented.
Scientific Reports, 2017
We show here how to create macroscopic quantum states in a semiconductor device: a chain of InAs ... more We show here how to create macroscopic quantum states in a semiconductor device: a chain of InAs quantum dots embedded in an InP nanowire. Filling the nanowire with 4 electrons per dot creates a synthetic spin-one chain, with four-fold degenerate topological ground state protected by a Haldane gap. The four states correspond to two spin-½ quasiparticles localised at the ends of the macroscopic wire. The quasiparticle spins are mapped onto a robust, macroscopic, singlet-triplet qubit. These predictions are supported by a microscopic theory and extensive numerical simulations.
Physical Review E, 1997
We study the spatial pattern formation and emerging long range correlations in a model of three s... more We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a truncation approximation and supported by computer simulations, reveal emergent strategies of survival for minority agents based on selection of patterns. Minority agents exhibit defensive clustering and cooperative behavior close to phase transitions.
Physical Review B, 1991
We investigate the tunneling of carriers in a quasi-one-dimensional array of semimagnetic quantum... more We investigate the tunneling of carriers in a quasi-one-dimensional array of semimagnetic quantum dots. The large magnetopolaron e8'ects due to the exchange interaction of carriers with magnetic ions result in a transmission via solitonlike electronic states. The intensity-dependent transmission coe%cient shows the opening of intensity-dependent gaps in the transmission spectrum.
Surface Science, 1990
ABSTRACT
Journal of Magnetism and Magnetic Materials, 2009
We examine the motion of a spin subject to a static external field, dynamic demagnetizing fields,... more We examine the motion of a spin subject to a static external field, dynamic demagnetizing fields, and a relatively weak oscillatory driving field. More specifically, we study the initial transient behavior just after all these fields are turned on and present analytic calculations based on an approximation scheme for the motion of the spin. We find that two modes-a mode at the driving frequency and a mode at the natural resonant frequency-play an important role in the initial transient. Because of the nonlinear nature of the spin equations of motion, one also finds, only in the initial transient, modes with doubled frequencies of the initial two modes and modes involving the sum and difference frequencies of the initial two modes. We also examine large amplitude transients in specific cases through numerical calculations.
Journal of Magnetism and Magnetic Materials, 1987
A possible novel mechanism for superconductivity in heavy fermlon systems is proposed The Coqblln... more A possible novel mechanism for superconductivity in heavy fermlon systems is proposed The Coqblln-Schneffer model [or a Kondo-hke impurity Is studied in the limit of large spin degeneracy The effective dynamical mteractmn between conduction electrons mediated by spin fluctuations is calculated and shown to be attractive at fimte frequencies
Physical Review B, 2013
We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag e... more We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Möbius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Möbius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings.
A novel, purely dynamical spin-fluctuation-mediated pairing interaction is proposed and examined.... more A novel, purely dynamical spin-fluctuation-mediated pairing interaction is proposed and examined. This interaction is extracted from the Coqblin-Schrieffer model for a single Kondo-like localised moment. The resulting superconducting transition temperature is estimated and shown to scale with the Kondo temperature in a quite unusual way. A possible application of the proposed mechanism to heavy-fermion systems is discussed. Over the years various theoretical models for purely electronic pairing interactions leading to superconductivity have been proposed to replace phonons as the mediating bosons between two electrons forming a Cooper pair. The recent discovery of super-conductivity in the heavy-fermion compounds [l] (for a review of the present status see [2]) has renewed interest in these models due to the possibility that the heavy-fermion superconductors are the first known systems with pairing driven by electron-electron interactions. (For a review of the theoretical situation see [ 3 ] .) In spite of considerable theoretical efforts, there are still [3] many more open questions than convincing answers about the pairing mechanisms and transition temperatures of heavy-fermion superconductors. Most attempts to calculate T, have borrowed heavily from methods originally developed for ordinary superconductors or for 'He, and much of the uncertainty and controversy centres [3] on the viability of these transplanted techniques and approximations. In this Letter I propose a novel, spin-fluctuation-mediated, pairing interaction and calculate the associated supercon-ducting transition temperature. To understand the basic nature of spin-fluctuation-mediated interactions I have adopted [4] a very simple model of heavy-fermion systems. Consider a number of magnetic impurities (localised f electrons) immersed in a metallic matrix (conduction electrons). Conduction band electrons of the metal can screen out the impurity moment antiferromagnetically, and below the Kondo temperature TK the fully compensated local moments acts as a scattering centre for conduction electrons. The intuitive picture of this scattering process can be described as follows. A conduction electron polarises the spin cloud around the impurity and a second electron passing by at a later time is affected by the antiferromagnetic spin fluctuations induced by the first electron. An effective electron-electron interaction mediated by these fluctuations thus results. This interaction is local in space but strongly retarded in time. Such purely dynamical interactions were shown [5] to be very effective in leading to superconducting instabilities.
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Papers by Marek Grabowski