Elastic analysis of pin joints in plates under some combined pin and plate loads

Joints are primary sources of weakness in structures. Pin joints are very common and are used where periodic disassembly of components is needed. A circular pin in a circular hole in an infinitely large plate is an abstraction of such a pin joint. A two-dimensional plane-stress analysis of such a configuration is carried out, here, subjected to pin-bearing and/or biaxial-plate loading. The pin is assumed to be rigid compared to the plate material. For pin load the reactive stresses at the edges of the infinite plate tend to zero though their integral over the external boundary equals to the pin load. The pin-hole interface is unbonded and so beyond some load levels the plate separates from the pin and the extent of separation is a non-linear function of load level. The problem is solved by inverse technique where the extent of contact is specified and the causative loads are evaluated directly. In the situations where combined load is acting the separation-contact zone specification generally needs two parameters (angles) to be specified. The present report deals with analysing such a situation in metallic (or isotropic) plates. Numerical results are provided for parametric representation and the methodology is demonstrated.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A Molecular Dynamics Study

Molecular dynamics (MD) simulations are reported for an anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) and CH3(CH2)15N+(CH3) ions in a layered solid, CdPS3. The intercalated CTA ions are organized with the cationic headgroups tethered to the inorganic sheet and the hydrocarbon tails arranged as bilayers. Simulations were performed at three temperatures, 65, 180, and 298 K, using an isothermal−isobaric ensemble that was subsequently switched once macroscopic parameters had converged to a canonical isothermal−isochoric ensemble. The simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and layer-to-layer separation distance. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained a planar all-trans conformation, and that gauche bonds occurred as part of a “kink” (gauche+−trans−gauche−) sequence and not as isolated gauche bonds. Trans−gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. A two-dimensional periodic Voronoi tessellation analysis was performed to obtain the single-molecular area of an alkyl chain in the bilayer. The single-molecular area relaxation times are an order of magnitude longer than the trans−gauche isomerization times. The results indicate that the trans−gauche isomerization is associated with the creation and annihilation of a kink defect sequence. The results of the present MD simulation explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C nuclear magnetic resonance measurements.

The influence of the motion of a rotor grid on a stator grid

In this paper we have used the method of characteristics developed for two dimensional unsteady flow problems to study a simplified axial turbine problem. The system consists of two sets of blades —the guiding vanes which are fixed and the rotor blades which move perpendicular to these vanes. The initial undisturbed constant flow in the system is perturbed by introducing a small velocity normal to the rotor blades to simulate a slight constant inclination. The resulting perturbed flow is periodic after the first three cycles. We have studied the perturbed density distribution throughout the system during a period.

Photodimerization of coumarin in aqueous and micellar media

The photochemical and photophysical processes of many organic compounds are a function of the environment in which they are present. In this connection we have chosen to investigate the environmental perturbations on the photodimerization of coumarin,l and the results of our study in aqueous and micellar media are presented in this paper. Coumarin has historically been the subject of intense photochemical and spectroscopic interest, mainly as a consequence of its importance in biological systems. Coumarin has been chosen for our investigation as its fascinating photochemical behavior has been fairly well explored,2 and therefore the environmental influence, which is the subject of our concern, would be easily understandable.

M. bovis BCG induced expression of COX-2 involves nitric oxide-dependent and -independent signaling pathways

In a multifaceted immunity to mycobacterial infection, induced expression of cyclooxygenase-2 (COX-2) by Mycobacterium bovis bacillus Calmette-Guerin (BCG) may act as an important influencing factor for the effective host immunity. We here demonstrate that M. bovis BCG-triggered TLR2-dependent signaling leads to COX-2 and PGE2 expression in vitro in macrophages and in vivo in mice. Further, the presence of PGE2 could be demonstrated in sera or cerebrospinal fluid of tuberculosis patients. The induced COX-2 expression in macrophages is dependent on NF-kappa B activation, which is mediated by inducible NO synthase (iNOS)/NO-dependent participation of the members of Notch1-PI-3K signaling cascades as well as iNOS-independent activation of ERK1/2 and p38 MAPKs. Inhibition of iNOS activity abrogated the M. bovis BCG ability to trigger the generation of Notch1 intracellular domain (NICD), a marker for Notch1 signaling activation, as well as activation of the PI-3K signaling cascade. On the contrary, treatment of macrophages with 3-morpholinosydnonimine, a NO donor, resulted in a rapid increase in generation of NICD, activation of PI-3K pathway, as well as the expression of COX-2. Stable expression of NICD in RAW 264.7 macrophages resulted in augmented expression of COX-2. Further, signaling perturbations suggested the involvement of the cross-talk of Notch1 with members with the PI-3K signaling cascade. These results implicate the dichotomous nature of TLR2 signaling during M. bovis BCG-triggered expression of COX-2. In this perspective, we propose the involvement of iNOS/NO as one of the obligatory, early, proximal signaling events during M. bovis BCG-induced COX-2 expression in macrophages.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.

Vacancy ordered phases and one-dimensional quasiperiodicity

The metastable vacancy ordered phases observed in aluminium transition metal alloys on rapid solidification or vapour deposition can be considered as a periodic arrangement of a truncated quasiperiodic string based on the Fibonacci sequence along the left angle bracket111right-pointing angle bracket stacking direction of the original CsCl cell. Using the projection formalism developed in the context of quasicrystals, the diffraction patterns of the vacancy ordered phases are calculated for both commensurate and incommensurate projection from a periodic cubic cell in four dimensions. These are compared with experimentally observed patterns. It is shown that at increasingly longer periodicity the patterns from commensurate crystals become indistinguishable from the truly quasiperiodic one. It is suggested that there is a strong link between vacancy ordered phases and quasicrystals.

The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

Some mechanisms of excitation of a railway wheel

Railway wheel vibrations are caused by a number of mechanisms. Two of these are considered: (a) gravitational load reaction acting on different points of the wheel rim, as the wheel rolls on, and (b) random fluctuating forces generated at the contact patch by roughness on the mating surfaces of the wheel and rail. The wheel is idealized as a thin ring, and the analysis is limited to a single wheel rolling on a rail. It is shown that the first mechanism results in a stationary pattern of vibration, which would not radiate any sound. The acceleration caused by roughness-excited forces is much higher at higher frequencies, but is of the same order as that caused by load reaction at lower frequencies. The computed acceleration level (and hence the radiated SPL) caused by roughness is comparable with the observed values, and is seen to increase by about 10 dB for a doubling of the wagon speed. The driving point impedance of the periodic rail-sleeper system at the contact patch, which is used in the analysis, is derived in a companion paper.

Flow over a cylinder with a hinged-splitter plate

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a hinged-splitter plate in the wake of a circular cylinder. The splitter plate can rotate about the hinge at the base of the cylinder due to the unsteady fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted as in the rigid splitter plate case. In our study, we investigate this problem in the limit where the stiffness and internal damping associated with the hinge are negligible, and the mass ratio of the splitter plate is small. The experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re, Re>4000. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force, and has been observed previously for transversely oscillating cylinders with no restorin force. In the present case, the saturation tip amplitude level can be tip to 0.45D, where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter ratio (L/D) is crucial in determining the character and magnitude of the oscillations. For small splitter plate length (L/D <= 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The nondiinensional oscillation frequencies (fD/U) on the other hand are found to continuously vary with L/D from fD/U approximate to 0.2 at L/D = 1 to fD/U approximate to 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D >= 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D >= 5.0. In the present case of the hinged-splitter plate, the sudden transition seen as the splitter plate length (L/D) is increased from 3 to 4 may be attributed to the fact that the wake vortices are no longer able to synchronize with the plate motions for larger splitter plate lengths. Hence, as observed in other vortex-induced vibration problems, the oscillations becomeaperiodic and the amplitude reduces dramatically.

Wall Shear Fluctuations in a Turbulent Boundary Layer

IN the last two decades, the instantaneous structure of a turbulent boundary layer has been examined by many in an effort to understand the dynamics of the flow. Distinct and well-defined flow patterns that seem to have great relevance to the turbulence production mechanism have been observed in the wall region.1'2 The flow near the wall is intermittent with periodic eruptions of the fluid, a phenomenon generally termed "bursting process." Earlier investigations in this field were limited to liquid flows at low speeds and the entire flowpattern was observed using flow visualization techniques.Study was later extended to boundary-layer flows in windtunnels at higher speeds and Reynolds numbers using hot-wiresignals for the analysis of the bursting phenomenon.

On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < Uc, where Uc is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, Uc is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U* > Uc is introduced due to the finiteness of the system. When Uc < U < U*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.