Is protein folding problem really a NP-complete one ? First investigations

To determine the 3D conformation of proteins is a necessity to understand their functions or interactions with other molecules. It is commonly admitted that, when proteins fold from their primary linear structures to their final 3D conformations, they tend to choose the ones that minimize their free energy. To find the 3D conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a NP complete one. More precisely, to determine the backbone structure of the protein using the low resolution models (2D HP square and 3D HP cubic), by finding the conformation that minimize free energy, is intractable exactly. Both the proof of NP-completeness and the 2D prediction consider that acceptable conformations have to satisfy a self-avoiding walk (SAW) requirement, as two different amino acids cannot occupy a same position in the lattice. It is shown in this document that the SAW requirement considered when proving NP-completeness is different from the SAW requirement used in various prediction programs, and that they are different from the real biological requirement. Indeed, the proof of NP completeness and the predictions in silico consider conformations that are not possible in practice. Consequences of this fact are investigated in this research work.Comment: Submitted to Journal of Bioinformatics and Computational Biology, under revie

Finite volume analysis of reinforced concrete structure cracking using a thermo-plastic-damage model

This paper proposes modifications to the phenomenological model formulation called CDPM2, developed by Grassl et al. [1]. The proposed modifications are designed to enhance model performance with coupling to temperature effects. A very strong coupling between nonlinear elasticity, plasticity, nonlocal damage evolution and temperature gradient is used to simulate arbitrary crack propagation. The use of FVM to model solid damage is a numerical challenge. This approach presents some advantages such as: ensuring that discretization is conservative even when the geometry is changing; providing a simple formulation that can be obtained directly from a difference method; and employing unstructured meshes. Most authors have neglected the nonlinearity of concrete in the elastic domain from the start of loading to the plastic domain. In this paper we confirm that concrete rheology is not linear even under low loading. Also, since the so-called fracture energy is a key parameter needed to determine the size of cracks and how they propagate in space, we consider that the fracture energy is both material and geometrical parameter dependent. For this reason, we developed a new approach which includes adaptive mesh, nonlinear rheology and thermal effects to re-calculate fracture energy at each time step. Many authors use a constant value obtained from experiments to calculate fracture energy; others use a numerical correlation. In this study, the fracture energy parameter is not constant and can vary with temperature or/and with a change in geometry due to concrete failure. As is well known, the mesh quality of complex geometries is very important for making accurate predictions. A new meshing tool was developed using the C++ programming language. This tool is faster, more accurate and produces a high-quality structured mesh. The predictions obtained were compared to a wide variety of experimental data and showed good agreement

Dynamics of electrons in the quantum Hall bubble phases

In Landau levels N > 1, the ground state of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field evolves from a Wigner crystal for small filling of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as the filling increases, to a modulated stripe state near half filling. In this work, we show that these first-order phase transitions between the bubble states lead to measurable discontinuities in several physical quantities such as the density of states and the magnetization of the 2DEG. We discuss in detail the behavior of the collective excitations of the bubble states and show that their spectra have higher-energy modes besides the pinned phonon mode. The frequencies of these modes, at small wavevector k, have a discontinuous evolution as a function of filling factor that should be measurable in, for example, microwave absorption experiments.Comment: 13 pages, 7 figures. Corrected typos in eqs. (38),(39),(40

Skyrme and Wigner crystals in graphene

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu$ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.Comment: 14 pages with 11 figure

Solitonic Excitations in Linearly Coherent Channels of Bilayer Quantum Hall Stripes

In some range of interlayer distances, the ground state of the two-dimensional electron gas at filling factor nu =4N+1 with N=0,1,2,... is a coherent stripe phase in the Hartree-Fock approximation. This phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study this gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton-antisoliton excitation energy is lower than the corresponding Hartree-Fock electron-hole pair energy. We compare our results with estimates of the transport gap obtained from a field-theoretic model valid in the limit of slowly varying pseudospin textures.Comment: 15 pages, 8 figure

Dynamical matrix of two-dimensional electron crystals

In a quantizing magnetic field, the two-dimensional electron (2DEG) gas has a rich phase diagram with broken translational symmetry phases such as Wigner, bubble, and stripe crystals. In this paper, we derive a method to get the dynamical matrix of these crystals from a calculation of the density response function performed in the Generalized Random Phase Approximation (GRPA). We discuss the validity of our method by comparing the dynamical matrix calculated from the GRPA with that obtained from standard elasticity theory with the elastic coefficients obtained from a calculation of the deformation energy of the crystal.Comment: Revised version published in Phys. Rev. B. 12 pages with 11 postscripts figure