Folding of lattice protein model chains with fixed ends

Using Monte Carlo simulations, we have studied the folding dynamics and thermodynamics of geometricall yconstrained lattice protein model chains. The constraints are realized by fixing one or both terminals of the chains. By comparing the results with that of the free-end chains, we find that the folding behaviours of the end-constralned chains are not completely similar to that of the free-end chains. Both kinds of constraints on the chain ends affect the folding dynamics of the chains: i.e., the folding rate, but not the thermodynamics. The thermodynamic behaviour of the one-end-fixed chains shows less difference from that of the free-end chains, while the thermodynamic behaviour of the two-end-fixed chains has obvious difference from that of the free-end chains. The origin of these differences comes from the differences of the ergodicitv of the chains in the conformational space.     

Bound state solutions of d-dimensional Schrdinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial.We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions.Numerical results are also computed for the energy spectrum and the potentials.     

Formation of fundamental solitons in the two-dimensional nonlinearSchrödinger equation with a lattice potential

We consider self-trapping of 2D solitons in the model based on theGross-Pitaevskii/nonlinear Schrödinger equation with the self-attractivecubic nonlinearity and a periodic potential of the optical-lattice (OL)type. It is known that this model may suppress the collapse, giving rise toa family of stable fundamental solitons. Here, we report essential dynamical featuresof self-trapping of the fundamental solitons from input configurations oftwo types, with vorticity 0 or 1. We identify regions in the respectiveparameter spaces corresponding to the formation of the soliton, collapse,and decay. A noteworthy result is the self-trapping of stable fundamentalsolitons in cases when the input norm essentially exceeds the collapsethreshold. We also compare predictions of the dynamical variationalapproximation with direct numerical simulations.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

First principles calculations of Cd and Zn chalcogenides with modified Becke–Johnson density potential

In this work, we present first principles calculations based on a full potential linear augmented plane-wave method (FP-LAPW) to calculate structural and electronic properties of CdX and ZnX (X = S, Se, Te) based II–VI chalcogenides. First principles calculations using the local density approximation (LDA) and the related generalized gradient approximation (GGA) lead to a severe underestimate of the band gap. The proposed model uses various exchange–correlation potentials (LSDA, GGA and MBJLDA) to determine band gaps and structural properties of semiconductors. We show that using modified Becke–Johnson (MBJLDA) density potential leads to a better agreement with experimental data for band gaps of Cd and Zn based semiconductors.     

Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique,this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However,when the conditions for boundedness of the perturbed solution are satisfied,then the Bose-Einstein condensates are Lyapunov-stable.     

Thermoelectric properties of nano-granular indium–tin-oxide within modified electron filtering model with chemisorption-type potential barriers

In this work, an approach to the numerical study of the thermoelectric parameters of nanoscale indium tin oxide (ITO, Sn content<10 at%) based on an electron filtering model (EFM) was developed. Potential barriers at grain boundaries were assumed to be responsible for a filtering effect. In the case of the dominant inelastic scattering of electrons, the maximal distance between potential barriers was limited in this modified model. The algorithm for such characteristic length calculation was proposed, and its value was evaluated for ITO. In addition, the contributions of different scattering mechanisms (SMs) in electron transport were examined. It was confirmed that in bulk ITO, the scattering on polar optical phonons (POPs) and ionized impurities dominates, limiting electron transport. In the framework of the filtering model, the basic thermoelectric parameters (i.e., electrical conductivity, mobility, Seebeck coefficient, and power factor (PF)) were calculated for ITO in the temperature range of 100–500 °C as a function of potential barrier height. The results demonstrated a sufficient rise of the Seebeck coefficient with an increase in barrier height and specific behavior of PF. It was found that PF is very sensitive to barrier height, and at its optimal value for granular ITO, it may exceed the PF for bulk ITO by 3–5 times. The PF maximum was achieved by band bending, slightly exceeding Fermi energy. The nature of surface potential barriers in nano-granular ITO with specific grains is due to the oxygen chemisorption effect, and this can be observed despite of the degeneracy of the conduction band (CB). This hypothesis and the corresponding calculations are in good agreement with recent experimental studies [Brinzari et al. Thin Solid Films 552 (2014) 225].     

Darboux–Bäcklund transformation and explicit solutions to a hybrid lattice of the relativistic Toda lattice and the modified Toda lattice

The relativistic Toda lattice and the modified Toda lattice are two important discrete integrable equations. In this paper, we investigate a hybrid lattice equation of the two lattice equations. Darboux–Bäcklund transformation and explicit solutions to the hybrid lattice equation are constructed.     

Discrete integrable couplings associated with modified Korteweg——de Vries lattice and two hierarchies of discrete soliton equations

A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg--de Vries (m-KdV) lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.     

Electronic structure engineering of ZnO with the modified Becke–Johnson exchange versus the classical correlation potential approaches

In this study, we report investigations of structural and electronic properties of ZnO in wurtzite (WZ), rock salt (RS) and zinc-blende (ZB) phases. Calculations have been done with full-potential linearized augmented plane wave plus local orbital method developed within the frame work of Density Functional Theory (DFT). For structural properties investigations, Perdew and Wang proposed local density approximations (LDA) and Perdew et al. proposed generalized gradient approximations (GGA) have been applied. Where for electronic properties in addition to these, Tran–Blaha modified Becke–Johnson (mBJ) potential has been used. Our computed band gap values of ZnO in WZ and ZB phases with mBJ potential are significantly improved compared to those with LDA and GGA; however, in RS phase, energy gap is significantly overestimated compared to experimental measurements. The Zn-d band was found to be more narrower with mBJ potential than that of LDA and GGA. On the other hand, our evaluated crystal field splitting energy values overestimate the experimental values.     

Electric–magnetic duality of lattice systems with topological order

We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define electromagnetic (EM) duality for all of Kitaev?s quantum double models based on discrete gauge theories with Abelian and non-Abelian groups, and identify its natural habitat as a new class of topological models based on Hopf algebras. We interpret these as extended string-net models, whereupon Levin and Wen?s string-nets, which describe all intrinsic topological orders on the lattice with parity and time-reversal invariance, arise as magnetic and electric projections of the extended models. We conjecture that all string-net models can be extended in an analogous way, using more general algebraic and tensor-categorical structures, such that EM duality continues to hold. We also identify this EM duality with an invertible domain wall. Physical applications include topology measurements in the form of pairs of dual tensor networks.     

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.     

Impurity states in a cylindrical quantum dot with the modified Pöschl-Teller potential

We study impurity states in a cylindrical quantum dot with two confining potentials: in the direction of cylinder axis modified Pöschl-Teller potential and in radial direction parabolic potential. Studies of impurity states are performed in the frames of variational method and by using numerical methods, the dependences of the particle energy on the geometrical parameters of the cylindrical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential wall are revealed.     

Impurity states in a spherical quantum dot with a modified P?schel-Teller potential

Quantum states and energy levels of an electron in a spherical quantum dot with a modified P?schel-Teller potential are studied. Analytical expressions for the wave function and energy of particle in the absence of impurity are obtained. Within the framework of variational method the impurity states are studied and by using numerical methods the dependences of the particle energy on the parameters of the spherical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential well are revealed.     

Relaxation processes and mobility of electrons in a semiconductor quantum well with the modified Pöschl-teller confining potential

Relaxation processes and mobility of electrons in a semiconductor quantum well are studied. The modified Pöschl-Teller potential is used as a confining potential. Scattering rates due to impurity ions, acoustic and piezoacoustic phonons are calculated taking into account the screening of scattering potentials by charge carriers. It is shown that when degenerate electrons are scattered by acoustic phonons, the dependence of scattering rate on electron wave number ν_ac(k) is almost linear. At small k, the acoustic phonon piezoelectric scattering rate of degenerate electrons increases with k, and then it decreases slightly when k > 8 × 10⁷ m⁻¹. The ionized impurity scattering rate of degenerate electrons does not depend on temperature, is directly proportional to the electron density, and decreases with increasing k. Dependences of electron mobility on surface ion density and temperature are studied. It is shown that in the case of non-degenerate or slightly degenerate electron gas, a maximum appears in the temperature dependence of the mobility, and the screening effect is negligible. The screening significantly increases the mobility of electrons in the case of high degeneration. Obtained results are applied to GaAs-based quantum wells.     

Cluster calculations of the interactions of μ+ with lattice defects in Li

Using the Hartree-Fock Roothaan scheme we have carried out molecular cluster calculations to study the interaction of positive muon with host metal atoms and intrinsic lattice defects in lithium. The total ground state energies of the clusters are calculated selfconsistently for various assumed impurity-host configurations. From the minimum in the total energy curve, we are able to determine the equilibrium lattice constant, the relaxation of first near neighbors around the impurity, the binding energy of the muon to a lattice trap and the activation energy for muon diffusion. Extension of the present method to treat ⁺-defect complexes in other metallic hosts are discussed.     

First-principles calculations of the stibnite at the level of modified Becke–Johnson exchange potential

The demand for cheaper, nontoxic and earth-abundant materials as absorbing layer for solar cell is immensely needed to replace scarce, toxic and expensive one. In this regard, chalcogenide materials have considerably attracted the attention of a lot of researchers because of showing a great potential for different applications. Stibnite (Sb₂S₃), a chalcogenide binary material is considerably investigated for exploiting its potential for different energy technologies being a less toxic, abundantly available, stable and efficient, which are the fundamentals for sustainability as well as to realize the dream of green energy. In this study, theoretical calculations of the structural, electronic and optical properties of stibnite (Sb₂S₃) crystal structure are presented using the full potential (FP) linearized augmented plane wave (LAPW) framed within density functional theory (DFT). To incorporate the exchange-correlation part in the total energy functional, besides the local density approximation (LDA), Wu-Cohen parameterized generalized gradient approximation (WC-GGA), Perdew–Burke–Ernzerhof parameterized generalized gradient approximation (PBE-GGA), and Perdew–Burke–Ernzerhof generalized gradient approximation for solids and surfaces (PBEsol-GGA) are used for the calculations of the structural parameters, where the Trans-Blaha approach of the modified Becke–Johnson (TB-mBJ) potential is used to get more reliable results for the fundamental band gap energy value. These calculations are performed by involving spin-orbit coupling (SOC) contribution. Additionally, optical properties, such as imaginary and real parts of the dielectric function, optical conductivity, absorption coefficient, refractive index, reflectivity, and electron energy loss function are analyzed. Our first-principles calculations show that Wu-Cohen GGA (WC-GGA) reproduces results for lattice parameters comparable to the experimental measurements. The obtained results of the band gap energy and optical properties with TB-mBJ potential are also closer to the experimental data and, endorse its potentiality for the photovoltaics applications.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator(HFSS)simulation.General wave vectors in the first Briliouin zone are derived.The relative band gap as a function of air-filling factor and background material is investigated,respectively,and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy.These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Disjointness of β-KMS states with different chemical potential

The disjointness of -KMS states with different chemical potential is proved. Accordingly, states with different chemical potential are in different superselection sectors so that the chemical potential is a classical observable.     

Investigation of ultra—thin ferromagnetic films with a simple cubic lattice

Using Green‘s function method,we investigate ferromagnetic films with a simple cubic lattice containing up to ten monolayers.The Hamiltonian includes the Heisenberg exchange term,surface anisotropy (SA) and dipole interaction (DI).We calculate the magnetization as a function of temperature and film thickness,and we analyse the behaviour of spin canting.The result is in agreement with experiments.We calculate phase diagrams of SA versus DI to show the conditions under which spontaneous magnetization can occur.As a special case,we discuss the Heisenberg model without SA and DI.