Extension Of Potential Research Articles

Extension of the Lennard-Jones potential: Theoretical investigations into rare-gas clusters and crystal lattices of He, Ne, Ar, and Kr using many-body interaction expansions

The many-body expansion ${V}_{\mathrm{int}}={\ensuremath{\sum}}_{ilj}{V}^{(2)}({r}_{ij})+{\ensuremath{\sum}}_{iljlk}{V}^{(3)}({r}_{ij},{r}_{ik},{r}_{jk})+\ensuremath{\cdots},$ in terms of interaction potentials between rare-gas atoms converges fast at distances $rg{r}_{\mathit{HS}}$, with ${r}_{\mathit{HS}}$ being the hard-sphere radius at the start of the repulsive wall of the interaction potential. Hence, for the solid state where the minimum distance is always above ${r}_{\mathit{HS}}$, a reasonable accuracy is already obtained for the lattice parameters and cohesive energies of the rare-gas elements using precise two-body terms. All tested two-body potentials show a preference of the hcp over the fcc structure. We demonstrate that this is always the case for the Lennard-Jones potential. We extend the Lennard-Jones potential to obtain analytical expressions for the lattice parameters, cohesive energy, and bulk modulus using the solid-state parameters of Lennard-Jones and Ingham [Proc. R. Soc. London, Ser. A 107, 636 (1925)], which we evaluate up to computer precision for the cubic lattices and hcp. The inclusion of three-body terms does not change the preference of hcp over fcc, and zero-point vibrational effects are responsible for the transition from hcp to fcc as shown recently by Rosciszewski et al. [Phys. Rev. B 62, 5482 (2000)]. More precisely, we show that it is the coupling between the harmonic modes which leads to the preference of fcc over hcp, as the simple Einstein approximation of moving an atom in the static field of all other atoms fails to describe this difference accurately. Anharmonicity corrections to the crystal stability are found to be small for argon and krypton. We show that at pressures higher than $15\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ three-body effects become very important for argon and good agreement is reached with experimental high-pressure density measurements up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, where higher than three-body effects become important. At high pressures we find that fcc is preferred over the hcp structure. Zero-point vibrational effects for the solid can be successfully estimated from an extrapolation of the cluster zero-point vibrational energies with increasing cluster size $N$. For He, the harmonic zero-point vibrational energy is predicted to be always above the potential energy contribution for all cluster sizes up to the solid state at structures obtained from the two-body force. Here anharmonicity effects are very large which is typical for a quantum solid.

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.

A variational method from the variance of energy

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second order extension of the gaussian effective potential.

Biology and management of relapsed acute myeloid leukaemia

Disease relapse remains the major cause of treatment failure in adults with acute myeloid leukaemia (AML). This reflects both the failure of current salvage regimens and the absence of effective strategies to secure long-term disease-free survival in those patients who achieve a second remission. Recent progress in understanding the pathogenesis of relapsed disease has enabled the identification of a variety of dysregulated molecular pathways and these now provide a rational basis for the design of novel targeted therapies. At the same time, advances in allogeneic stem-cell transplantation have permitted the extension of the curative potential of allografting to patients in whom it was previously contraindicated. As a result, a range of novel drug and transplant therapies has become available in patients with relapsed AML, and it is realistic to anticipate that a co-ordinated assessment of their clinical and biological impact will provide the basis for the design of future, more effective treatments in relapsed disease.

Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for , and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.

Dispersion relations for cylindrical bending motions of polarized piezoceramic bimorph plates with two facing edges free

Dispersion relations of thin parallel bimorph plates with polarized piezoceramics are obtained by using Hamilton’s principle. The coupled variational equations for piezoceramic bimorph plates are derived with the thin plate theory and the extension of electric potential in the thickness direction, which are valid for low frequency range. More specifically, coupled differential equations as well as dispersion relations subject to homogeneous natural-type boundary conditions on the two facing side-edges are derived for the cylindrical bending motions of both fully electroded and unelectroded bimorph plates of which surfaces are free from applied traction for both cases; the derivations are made through the expansions of mechanical displacements in the thickness co-ordinate with plane stress assumptions at major surfaces in the manner of Mindlin and of electric potential with vanishing second order components of electric potentials at major surfaces in the manner of Tiersten. Relations between the deflection gradient of fully electroded bimorph plate and the induced electric current are obtained. The complexity due to the additional inclusion of differential equations for the electric potential components may be alleviated through the reductions of the coupled differential equations. As an illustrative example, dispersion relations for the aforementioned four cases of bimorph plates composed of PZT5 are obtained. The dispersion curves are depicted and compared each other, and some differences and similarities are discussed.

Hybrid diatomics-in-molecules-based quantum mechanical/molecular mechanical approach applied to the modeling of structures and spectra of mixed molecular clusters Arn(HCl)m and Arn(HF)m.

A new hybrid QM/DIM approach aimed at describing equilibrium structures and spectroscopic properties of medium size mixed molecular clusters is developed. This methodology is applied to vibrational spectra of hydrogen chloride and hydrogen fluoride clusters with up to four monomer molecules embedded in argon shells Arn(H(Cl/F))m (n = 1-62, m = 1-4). The hydrogen halide complexes (QM part) are treated at the MP2/aug-cc-pVTZ level, while the interaction between HX molecules and Ar atoms (MM part) is described in terms of the semiempirical DIM methodology, based on the proper mixing between neutral and ionic states of the system [Grigorenko et al., J. Chem. Phys. 104, 5510 (1996)]. A detailed analysis of the resulting topology of the QM/DIM potential energy (hyper-)surface in the triatomic subsystem Ar-HX reveals more pronounced nonadditive atomic induction and dispersion contributions to the total interaction energy in the case of the Ar-HCl system. An extension of the original analytical DIM-based potential in the frame of the present model as well as the current limitations of the method are discussed. A modified algorithm for the gradient geometry optimization, along with partly analytical force constant matrix evaluation, is developed to treat large cages of argon atoms around molecular clusters. Calculated frequency redshifts of HX stretching vibrations in the mixed clusters relative to the isolated hydrogen-bonded complexes are in good agreement with experimental findings.

Hydrolytic and transglycosylation reactions of N-acyl modified substrates catalysed by β- N-acetylhexosaminidases

The hydrolytic and transglycosylation capabilities of 35 fungal β- N-acetylhexosaminidases with p-nitrophenyl 2-amino-2-deoxy-β- d-glucopyranoside and its four N-acyl derivatives (CHO, COCH 2OH, COCH 2CH 3, COCF 3) as substrates were tested. The preparation of four novel p-nitrophenyl disaccharides from these unnatural substrates catalysed by enzymes from Aspergillus oryzae, Penicillium oxalicum and Talaromyces flavus represents a considerable extension of the synthetic potential of glycosidases.

A symmetric boundary element method for the Stokes problem in multiple connected domains

AbstractWe consider a symmetric Galerkin boundary element method for the Stokes problem with general boundary conditions including slip conditions. The boundary value problem is reformulated as Steklov–Poincaré boundary integral equation which is then solved by a standard approximation scheme. An essential tool in our approach is the invertibility of the single layer potential which requires the definition of appropriate factor spaces due to the topology of the domain. Here we describe a modified boundary element approach to solve Dirichlet boundary value problems in multiple connected domains. A suitable extension of the standard single layer potential leads to an operator which is elliptic on the original function space. Copyright © 2003 John Wiley & Sons, Ltd.

Spectral statistics of rectangular billiards with localized perturbations

The form factor K(τ) is calculated analytically to the order τ3 as well as numerically for a rectangular billiard perturbed by a δ-like scatterer with an angle independent diffraction constant, D. The cases where the scatterer is at the centre and at a typical position in the billiard are studied. The analytical calculations are performed in the semiclassical approximation combined with the geometrical theory of diffraction. Non-diagonal contributions are crucial and are therefore taken into account. The numerical calculations are performed for a self-adjoint extension of a δ-function potential. We calculate the angle-dependent diffraction constant for an arbitrary perturbing potential U(r), that is large in a finite but small region (compared to the wavelength of the particles that, in turn, is small compared to the size of the billiard). The relation to the idealized model of the δ-like scatterer is formulated. The angle-dependent diffraction constant is used for the analytic calculation of the form factor to the order τ2. If thescatterer is at a typical position, the form factor is found to reduce (in this order) to the one found for angle independent diffraction. If the scatterer is at the centre, the large degeneracy in the lengths of the orbits involved leads to an additional small contribution to the form factor, resulting from the angle dependence of the diffraction constant. The robustness of the results is discussed.

Length of magnetic field lines in turbulent plasmas.

An estimation of the length of any magnetic field line in a two-dimensional periodic magnetohydrodynamic problem is provided. This is done by using some classical function theory results on the analytic extension of the vector potential. The essential parameter, the maximum of this extension, may be analyzed in the case of turbulent plasmas by admitting the Iroshnikov-Kraichnan statistics, establishing in this way a relation between the length of any magnetic field line and the energy dissipation scale. (c) 2002 American Institute of Physics.

Aminopyrimidines as Electron-Rich Azadienes: Extension of the Synthetic Potential of Hetero Diels-Alder Reactions under Acidic Conditions

By addition of a catalytic amount of a strong acid and selection of the appropriate solvent, the cycloaddition reactions of dimethyl acetylenedicarboxylate (DMAD) to 6-aminopyrimidine derivatives drastically changed their course leading to new products, pyrrolo[3,4-c]pyridines, which were different from those obtained in the absence of acid. This change was interpreted on the basis of acid interception of the non-isolable adducts formed by initial hetero Diels-Alder cycloaddition between the reactants.

Transfer of the human telomerase reverse transcriptase(TERT) gene into T lymphocytes results in extension of replicative potential

AbstractIn most human somatic cells telomeres progressively shorten with each cell division eventually leading to chromosomal instability and cell senescence. The loss of telomere repeats with cell divisions may also limit the replicative life span of antigen-specific T lymphocytes. Recent studies have shown that the replicative life span of various primary human cells can be prolonged by induced expression of the telomerase reverse transcriptase (hTERT) gene. To test whether introduction of hTERT can extend the life span of primary human T lymphocytes, naive CD8+ T lymphocytes were transfected with retroviral vectors containing the hTERTgene. Transduced T-cell clones expressed high levels of telomerase and either maintained or elongated their telomere lengths upon culture for extended periods of time. Two of the transduced subclones retained a normal cloning efficiency for more than 170 population doublings (PDs). In contrast, T-cell clones transfected with control vectors exhibited progressive telomere length shortening and stopped proliferation at around 108 PDs. Telomerase-positive T clones had a normal 46,XY karyotype, maintained their cytotoxic properties, and showed very little staining for the apoptotic marker annexin-V. These results indicate that ectopic hTERT gene expression is capable of extending the replicative life span of primary human CD8+cytotoxic T lymphocytes.

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. VI. The helium dimer (He2) revisited

A recent computation of the helium dimer interaction potential for intermediate distances (2 ≤ R/a0 ≤ 15) using the (explicitly correlated) r12-MR-ACPF (averaged coupled-pair functional) method [GDANITZ, R. J., 1999, Molec. Phys., 96, 1423] is extended to larger basis sets. Calculations including a large atom centred [11 s8p6d5f4g3h2ilk] set show that the convergence of the energy with respect to enlargement of the basis set has previously been considerably underestimated. The extension of the Pk potential (292.75 ± 0.01, −10.980 ± 0.004 and −4.620 = ± 0.002 K at R = 4, 5.6 and 7 a0) to distances between 2.5 and 15a0 (Pk*)is close to a recent potential of van Mourik and Dunning [1999, J. Chem. Phys., 111, 9248] and it is believed to be the most accurate available. It gives rise to 4He2 molecular constants of (R) = 46.4 ± 1.4 Å and D0 = 1.67 ± 0.11 mK.

ChemInform Abstract: Aminopyrimidines as Electron‐Rich Azadienes: Extension of the Synthetic Potential of Hetero Diels—Alder Reactions under Acidic Conditions.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Electrochemical oxidation of poly(3,4-ethylenedioxythiophene) — “in situ” conductivity and spectroscopic investigations

Electrochemical oxidation of poly(3,4-ethylenedioxythiophene) (PEDOT) is investigated by cyclic voltammetry combined with “in situ” conductivity measurements, UV-vis–NIR and Raman spectroelectrochemical studies. The results seem to indicate that the doping can be adequately described by a heterogeneous “two-phase” model in which the doped conducting phase grows on the expense of the undoped, neutral phase. The extension of the scanning potential to 1400 mV vs. Ag/AgCl leads to a finite potential window of PEDOT conductivity — the phenomenon reported for the first time in the case of PEDOT. The existence of this potential window can be rationalized within the framework of the “two-phase” model of electrochemical doping, assuming the coexistence of percolating conductive and insulating networks. Doping induced changes in Raman spectra of PEDOT indicate that, unlike in other polythiophenes, the ground state of the neutral polymer is quinoid in nature whereas upon doping it is transformed into the benzenoid one.

Genes involved in the control of cellular proliferative potential.

Evidence that control of cellular proliferative potential may be linked to telomere length, along with data indicating that other factors may also be involved, will be reviewed. According to the telomere hypothesis of senescence, the sequential loss of telomeric repeat DNA that occurs during the replication of normal somatic cells eventually dictates the onset of the permanently nonreplicative state known as senescence. Many immortalized cells express telomerase, a ribonucleoprotein enzyme that replaces the telomeric DNA that would otherwise be lost due to replication. However, some immortalized human cells may avoid telomeric shortening without using telomerase. The mechanism involved is currently unknown, but other eukaryotes are able to replace telomeric DNA through (1) recombination and copy switching or (2) retrotransposition. Human fibroblasts that lose p53 function proliferate a limited number of times beyond the population-doubling level at which their normal counterparts become senescent. Lack of functional retinoblastoma (Rb) protein (or equivalent events, such as loss of p16INK4 function, resulting in abrogation of Rb regulatory activity) also permits a temporary extension of proliferative potential. The p53 and pRb effects are additive, indicating that they exert their control on proliferative potential separately. The temporary life span extension associated with loss of p53 and/or Rb pathway function is accompanied by continued telomere shortening. The proliferation arrest that eventually ensues in p53-minus cells or in p53-minus/Rb-minus cells may be regarded as terminal proliferation arrest states serving as a backup to senescence. p53-minus/Rb-minus cells cannot proliferate further unless they acquire the ability to prevent telomeric shortening. Somatic cell hybridization and microcell-mediated chromosome transfer experiments indicate that immortalization involves the loss of function of other, as yet unidentified, genes; some of these may normally repress telomerase expression in somatic cells.

Quantum molecular dynamics of large systems beyond separable approximation: The configuration interaction classical separable potential method

A nonseparable method for time-dependent quantum simulations of large polyatomic systems is presented and applied to the dynamics of the I2Ar17 cluster, following electronic excitation of the iodine molecule. The new method is an extension of the classical separable potential (CSP) approximation, in which the evolution of each mode is governed by a time-dependent mean potential due to the other modes and the total wave packet is a product of single mode wave functions. The computational effectiveness of the CSP approach stems from the use of classical molecular dynamics (MD) trajectories, carried out at the outset of the procedure, for obtaining the effective single-mode potentials. The present method generalizes the CSP scheme by a configuration interaction (CI) treatment, in which the total wave packet is represented as a linear combination of separable terms, with coefficients determined from the time-dependent Schrodinger equation. The single mode wave functions for each configuration are propagated along effective potentials that are generated using individual classical trajectories. The classical MD simulation is also used for simplifying the dynamical equations for the CI coefficients. Thus, the selection of correlations that are included quantum mechanically is guided by classical mechanics, which is the basis for the computational efficiency of this approach. The CI wave packet for the I2Ar17 system with 51 vibrational degrees of freedom was propagated for 500 fs following I2 (B←X) excitation. About 1500 configurations proved sufficient for convergence of the CI series. The separable approximation to the wave function holds for 60 fs and begins to break down upon the first collision of the iodine atoms with argons. After the second iodine-argon collision this breakdown is almost complete, and at t=500 fs the CSP term represents less than 5% of the correlated wave packet. Both absorption and resonance Raman spectra are, however, well described by the separable CSP method, since they are determined within the first 60 fs. The CI-CSP method offers very good accuracy due to inclusion of important correlation effects between different modes, while remaining computationally feasible for systems up to 100 degrees of freedom and more.

Metallic superlattices: quasi two-dimensional playground for hydrogen

Hydrogen in superlattices, whose constituents have different hydrogen affinities, comprises a new class of hydrogen absorbing materials. The period of the absorption potential can be made as small as two monolayers, which implies highly anisotropic host mediated hydrogen–hydrogen (H–H) interactions. As the correlation between the hydrogen atoms can be influenced in an almost arbitrary way, it is possible to create an ensemble whose nature is neither three- nor two-dimensional, but something in between. By changing the strain state of the constituents, the interaction between the hydrogen atoms in vanadium can be changed from being attractive (for biaxial tensile strain) to repulsive (for biaxial compressive strain). This has been observed experimentally for, e.g., 2 nm vanadium layers in Mo–V and Fe–V superlattices. The biaxial strain state is shown to have a gigantic effect on the hydrogen induced lattice expansion. By changing the strain state from tensile to compressive, in ≈2 nm V layers, the hydrogen induced lattice expansion is altered by a factor of ten. This feature is expected to affect the diffusion properties of hydrogen in these structures dramatically. The principal orientation of the crystal axis of the host material, with respect to the boundary planes, is found to have large impact on the host mediated H–H interactions. The theoretical understanding of hydrogen in quasi-two-dimensional potentials is still rudimentary, and more theoretical and experimental work is required for a detailed understanding of these problems. In the present work, we will treat the implications of the extension and amplitude of the hydrogen absorption potential, and we will demonstrate the existence and impact of weak and strong modulation of the host potential on the hydrogen uptake. The influence of the strain state on the hydrogen absorption and the host mediated H–H interactions will also be treated, and we will show that the phase diagram can, in some cases, be altered in a controllable way.

A molecular dynamics study of a bi-disperse liquid crystal mixture using a generalized Gay-Berne potential

We report results from a constant NVE molecular dynamics simulation of a 50:50 mixture of Gay-Berne rods with axial ratios of 35 to 1 and 3 to 1. The simulation makes use of a recently developed extension of the Gay-Berne potential which allows simulation of non-equivalent anisotropic molecules with attractive interactions. There is clear evidence of pre-smectic ordering in the nematic phase. The system undergoes a well defined transition from the nematic phase to a randomly mixed smectic phase. There is some local compositional ordering within the smectic layers but no evidence of demixing. In both the nematic and smectic phases it is found that the longer molecules have a higher [S] order parameter than the shorter molecules. This difference in order parameter is at its greatest a little below the isotropic-nematic transition temperature and decreases as the smectic phase is approached.