Independent Amplitudes Research Articles

Higher-order analysis of crack tip fields in elastic power-law hardening materials

A higher-order asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode I. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K 1, K 2 and K 5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K 1, K 2 and K 4. It is found that appropriate choices of K 2 and K 4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

Isospin-symmetry breaking in the πN system

There are only two independent isospin amplitudes for pion-nucleon scattering if isospin is assumed to be a good symmetry. In those cases in which isospin symmetry is broken (but time-reversal symmetry is valid), six more are needed to express an on-shell amplitude and two more to express an off-shell amplitude or potential. An independent set of these operators is constructed and analyzed.

X-ray crystal structure of DL-aspartic acid-β-hydroxamic acid (N-hydroxyasparagine) monohydrate

The structure of DL-aspartic acid-β-hydroxamic acid (N-hydroxyasparagine, Asp-β-ha) monohydrate C4H10N2O5 (HOOCCH(NH2)CH2C(O)NHOH×H2O) has been determined by single-crystal X-ray diffraction methods. The crystals are orthorhombic:P21nb(C 2v 9 ),a=9.690(2),b=8.936(2),c=8.118(2) A,Z=4. The structure has been solved by direct phase determination methods, and refined to an R value of 0.026 for 797 nonzero independent amplitudes. The molecule of the title compound exists in the structure as a zwitterion,−OOCCH(NH 3 + )CH2C(O)NHOH. The crystal structure is stabilized by intermolecular O⋯H-N and O⋯H-O hydrogen bonds involving amino groups, carboxyl groups and water molecules.

Nearly spherical vesicle shapes calculated by use of spherical harmonics : axisymmetric and nonaxisymmetric shapes and their stability

A theoretical approach to determine nearly spherical shapes of phospholipid vesicles is developed. The method is general in the sense that it does not depend on any symmetry restrictions. Equilibrium shapes are assumed to correspond to the minimum of the membrane bending elastic energy at constant values of the membrane area, the vesicle volume and the difference of areas of the two leaflets of the phospholipid bilayer. The bending energy and the constraints are expanded up to fourth order terms in the deviation from a sphere, and in the subsequent calculations all terms up to the third order are included. The deviation is expressed as a series of spherical harmonics. It sis shown that the stability of the solutions can be tested by inspecting the eigenvalues of the matrix of second derivatives of the bending energy with respect to independent amplitudes of spherical harmonics expansion. The method is applied to the calculation of axisymmetric and nonaxisymmetric shapes, and the influences of different approximations are discussed. It is shown that at variations of the leaflet area difference stable oblate and stable prolate shapes are transformed into each other in a continuous manner.

Bonn nucleon-nucleon meson exchange model with a relativistic quark-gluon annihilation potential.

The full Bonn potential, combined with a relativistic quark-gluon annihilation potential, is compared with recent NN\ifmmode\bar\else\textasciimacron\fi{} polarization data from LEAR and with measured differential cross sections (elastic and charge exchange) below ${\mathit{p}}_{\mathrm{lab}}$=800 MeV/c. It is demonstrated within this approach that a careful analysis of pp\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}pp\ifmmode\bar\else\textasciimacron\fi{}(EL) and pp\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}nn\ifmmode\bar\else\textasciimacron\fi{}(CEX), at the same energy, in terms of the five independent helicity amplitudes can be used to selectively test specific boson exchange contributions to NN\ifmmode\bar\else\textasciimacron\fi{} scattering. The charge-exchange differential cross section in forward direction is particularly sensitive to the one-pion-exchange potential in this model. This feature could be used to see if recent attempts to fit NN data with a much softer \ensuremath{\pi}NN form factor can be made compatible with NN\ifmmode\bar\else\textasciimacron\fi{} data.

Non-linear structural vibrations under combined multi-frequency parametric and external excitations

A system of second order equations with weak quadratic and cubic non-linearities is considered. Simultaneous parametric and external (forcing) excitations act on the system, each including multiple harmonic components with independent amplitudes, frequencies and phases. Attention is focused on resonances involving two frequencies from one of the excitations and one frequency from the other. Results are obtained by the method of multiple scales. Figures are presented which illustrate the behavior of the steady state response amplitude as a function of the excitation amplitudes and the relative values of the excitation frequencies.

COUPLED NONLINEAR SCHRÖDINGER EQUATIONS ARISING IN FIBRE OPTICS

For systems with weak dispersion and cubic nonlinearity, the equation governing fluctuations in amplitude of a signal is usually taken to be the cubic Schro'dinger equation. Consequently, this equation appears in the fibre optics literature. However, in axially symmetric waveguides, modes of propagation occur in pairs which have identical dispersion relations. Analysis of a 'single-mode' optical fibre shows that a general quasi-monochromatic signal is governed by two coupled cubic SchrCdinger equations describing the interaction between the two independent complex amplitudes. Some exact solutions of this coupled system are discussed, including single-soliton solutions describing either linearly-polarized or circularly-polarized signals. Numerical results showing interaction between linearly-polarized solitons of differing polarization angles are also presented, indicating that after the collision the signal separates into two self-similar solutions which are more general than the usual soliton.

X-ray crystallographic determination of the structure and conformation of 7-(1-acetoxy-1-methylethyl)-4a-methyl-octahydro-2(3H)-naphthalenone

The crystal structure of 7-(1-acetoxy-1-methylethyl)-4a-methyl-octahydro-2(3H)-naphthalenone, C16H24O3 has been determined by X-ray diffraction. The crystals are orthorhombic, P212121,a=5.938(2),b=12.081(4),c=21.607(7) A,Z=4. The structure was solved by direct methods, and refined to an R value of 0.062 for 1013 nonzero independent amplitudes. Ring A has the C(6)β distorted sofa conformation whereas the B ring possesses the slightly deformed chair conformation. The side chain in the C(10) position isα oriented in relation to the plane of the B ring.

Factorization and selection rules of operator product algebras in conformal field theories

Factorization of the operator product algebra in conformal field theory into independent left and right components is investigated. For those theories in which factorization holds we propose an ansatz for the number of independent amplitudes which appear in the fusion rules, in terms of the crossing matrices of conformal blocks in the plane. This is proved to be equivalent to a recent conjecture by Verlinde. The monodromy properties of the conformal blocks of 2-point functions on the torus are investigated. The analysis of their short-distance singularitities leads to a precise definition of Verlinde's operations.

Constraints from the Drell-Hearn-Gerasimov sum rule in chiral models of composite fermions.

We analyze a dispersion relation for a spin-flip Compton amplitude in a chiral model of composite quarks and leptons. We discuss the asymptotic behavior of the amplitude and show under what conditions the Drell-Hearn-Gerasimov sum rule holds. Using a small-mass expansion we derive a consistency condition that relates the photoproduction cross sections for different helicities. We show that this condition suggests the existence of higher-spin excited fermions, as well as relations among a priori independent photoproduction amplitudes.

Structure and IR spectroscopic behaviour of 1,8-bis-(dimethylamino)naphthalene 2,4-dinitroimidazolate

The crystal structure of 1,8-bis(dimethylamino)naphthalene (DMAN) 2,4-dinitroimidazolate, C 17H 20N 6O 4, has been determined by X-ray diffraction. The crystals are monoclinic, P2 1/ c, a = 13.426(4), b = 10.465(3), c = 15.915(4) », β = 126.12(4)°, Z = 4. The structure was solved by direct methods, and refined to an R value of 0.033 for 2291 non-zero independent amplitudes. The [NN⋯N] + bridges of 2.606(3) » with ∠NHN = 160(3)° are characterized by an asymmetric proton density distribution. The IR protonic absorption is located in two regions at about 650 and 1950 cm −1 showing relatively small intensity. The isotopic ratio ν(NHN/ν(NDN) for the low frequency region is almost unity. It seems that hydrogen bonds in protonated DMAN are characterized by a flat asymmetric single minimum potential for the proton motion.

A Statistical Model for Indoor Multipath Propagation

The results of indoor multipath propagation measurements using 10 ns, 1.5 GHz, radarlike pulses are presented for a medium-size office building. The observed channel was very slowly time varying, with the delay spread extending over a range up to about 200 ns and rms values of up to about 50 ns. The attenuation varied over a 60 dB dynamic range. A simple statistical multipath model of the indoor radio channel is also presented, which fits our measurements well, and more importantly, appears to be extendable to other buildings. With this model, the received signal rays arrive in clusters. The rays have independent uniform phases, and independent Rayleigh amplitudes with variances that decay exponentially with cluster and ray delays. The clusters, and the rays within the cluster, form Poisson arrival processes with different, but fixed, rates. The clusters are formed by the building superstructure, while the individual rays are formed by objects in the vicinities of the transmitter and the receiver.

Helicity-amplitude relations for vector-meson production from a skyrmion model.

Mattis has derived six relations among the partial-wave amplitudes for the reaction $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\rho}N$. From these relations we deduce that the six independent helicity amplitudes for the $t$-channel isospin-0 reaction may be simply expressed in terms of one unknown function. This leads to definite predictions for the $\ensuremath{\rho}$-meson density matrix and the absence of nucleon polarization effects, which can be tested directly, without recourse to partial-wave analysis.

Symmetric, Lorentz invariant NN amplitude: Yukawa representation.

Previous work on the general representation of NN scattering amplitudes in the full Dirac space of two nucleons is extended to allow a simple realization of the generalized Pauli principle. New kinematic covariants are found which are linearly independent and which have simple particle exchange symmetries. This permits a representation in which all invariant amplitudes are even or odd with respect to interchange of initial state four-momenta or interchange of final state four-momenta for on-mass-shell kinematics. When parity invariance, charge symmetry, and time-reversal invariance are taken into consideration, it is found that for each isospin state there are 56 independent amplitudes for off-mass-shell kinematics, 50 independent amplitudes for quasipotential kinematics, and 44 independent amplitudes for on-mass-shell kinematics. A relativistic meson exchange model is used to calculate the invariant amplitudes for on-mass-shell kinematics, and the resulting amplitudes are fit by sums of Yukawa terms. The analysis provides complete sets of Feynman invariant amplitudes for 200, 500, and 800 MeV NN scattering.

Generalized gauge independence and the physical limitations on the von Neumann measurement postulate

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields.

Combined use of the CALKUL method and N = 1 supersymmetry to calculate QCD six-parton processes

Concise expressions are presented for the two independent helicity amplitudes of the subprocess 4g2q. The result has been derived using the improved CALKUL method and is given in terms of spinor inner products in manifestly covariant and crossing symmetric forms. Changing the color factors of the quarks from the fundamental to the adjoint representation we obtain the helicity amplitudes of the four-gluon-two-gluino subprocess. Simple N = 1 supersymmetric relations have been found which express the helicity amplitudes of the six gluon parton process in terms of the helicity amplitudes of the 4g2 g process. In this way we have avoided the direct calculation of 220 Feynman diagrams. Gauge invariance and the validity of the supersymmetric relations have been tested with an independent numerical calculation.

Simple tests for CP or P violation by sequential decays: V1V2 modes with decays into l-barAlB and/or q-barAqB.

In a \ensuremath{\varphi}J, JJ, or J\ensuremath{\Upsilon} decay channel sin 2\ensuremath{\varphi} and/or sin \ensuremath{\varphi} terms in the azimuthal distribution would imply that P and CP separately are violated. Similarly in a \ensuremath{\varphi}${Z}^{0}$, ${\mathrm{JZ}}^{0}$, ${Z}^{0}$${Z}^{0}$, or ${W}^{+}$${W}^{\mathrm{\ensuremath{-}}}$ decay channel sin 2\ensuremath{\varphi} terms would imply that CP is violated. For these latter modes there are several distinct \ensuremath{\alpha} and \ensuremath{\gamma} signatures for CP violation. Analogous signatures for expected P violation occur in a charged \ensuremath{\varphi}${W}^{\ifmmode\pm\else\textpm\fi{}}$, ${\mathrm{JW}}^{\ifmmode\pm\else\textpm\fi{}}$, or ${Z}^{0}$${W}^{\ifmmode\pm\else\textpm\fi{}}$ decay channel. Stronger tests for violations occur when the two vector bosons are identical and the X has odd spin because for J=1 (g1) there are only two (three) independent amplitudes. For X of spin 0 many signatures and consistency checks are tabulated for (i) the violation of both P invariance and CP invariance in a \ensuremath{\varphi}${\ensuremath{\rho}}^{0}$, \ensuremath{\varphi}\ensuremath{\varphi}, ${K}^{\mathrm{*}+}$${K}^{\mathrm{*}\mathrm{\ensuremath{-}}}$, \ensuremath{\varphi}J, JJ, or J\ensuremath{\Upsilon} decay channel, for (ii) the violation of CP invariance in a \ensuremath{\varphi}${Z}^{0}$, ${\mathrm{JZ}}^{0}$, ${Z}^{0}$${Z}^{0}$, or ${W}^{+}$${W}^{\mathrm{\ensuremath{-}}}$ decay channel, and for (iii) the expected violation of P invariance in a charged \ensuremath{\varphi}${W}^{\ifmmode\pm\else\textpm\fi{}}$, ${\mathrm{JW}}^{\ifmmode\pm\else\textpm\fi{}}$, or ${Z}^{0}$${W}^{\ifmmode\pm\else\textpm\fi{}}$ decay channel.

Combined use of the CALKUL method and N = 1 supersymmetry to calculate QCD six-parton processes

Concise expressions are presented for the two independent helicity amplitudes of the subprocess 4g2q. The result has been derived using the improved CALKUL method and is given in terms of spinor inner products in manifestly covariant and crossing symmetric forms. Changing the color factors of the quarks from the fundamental to the adjoint representation we obtain the helicity amplitudes of the four-gluon-two-gluino subprocess. Simple N = 1 supersymmetric relations have been found which express the helicity amplitudes of the six gluon parton process in terms of the helicity amplitudes of the 4g2g process. In this way we have avoided the direct calculation of 220 Feynman diagrams. Gauge invariance and the validity of the supersymmetric relations have been tested with an independent numerical calculation.

Complete amplitude and cross section structure of one-loop contributions toe + e ??q $$\bar q$$ g

We calculate theO(α 2 ) one-loop contributions to the seven (inn≠4) independent invariant amplitudes describinge + e −→q $$\bar q$$ g in massless QCD. After folding with theO(α 1/2 ) Born term contribution we obtain the nine independentO(α 2 ) structure functions that describe the parity-conserving and parity-violating contributions toe + e −→q $$\bar q$$ g. We use dimensional regularization to control infrared and ultraviolet divergencies.

Crystal and molecular structure of glycinehydroxamic acid

Glycinehydroxamic acid, C2H6N2O2 (NH2CH2C(O)NHOH), was synthesized and its crystal and molecular structure determined by single-crystal X-ray diffraction methods. The crystals are monoclinic:P21/c C2h5, No. 14),a=5.682(2),b=7.133(2),c=9.540(3) A,β=104.38(4)°,Z=4. The structure has been solved by direct phase determination methods, and refined to anR value of 0.042 for 633 nonzero independent amplitudes. The molecule of the title compound exists in the structure as a zwitterion, NH3+-CH2-C(O)-N-OH. The hydroxamate group is planar and the Nα (amino) atom, from the glycine part of the molecule, deviates by 1.43 A from the best molecular plane defined by O(1), N(1), C(1), and O(2) atoms, respectively.