Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Phase relations between Al2O3---Cr2O3 and FeAl2O4---FeCr2O4 solid solutions at 1823 K

Tie-lines between the corundum and spinel solid solutions have been determined experimentally at 1823 K. Next, activities of FeCr2O4 and FeAl2O4 in the spinel solid solution were determined by combining the tie-line data with literature values for the activities of Cr2O3 and Al2O3 in the corundum phase. Activities and the Gibbs energy of mixing for the spinel solid solution were also obtained from a model based on cation distribution between nonequivalent crystallographic sites in the oxide lattice. The difference between the Gibbs energy of mixing obtained experimentally and from the model has been attributed to a strain enthalpy term which is relatively unchanged in magnitude from the reported at 1373 K. The integral enthalpy of mixing obtained from experimental data at 1373 and 1823 K using the second law is compared with the model result.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Effect of Crowding Agents, Signal Peptide, and Chaperone SecB on the Folding and Aggregation of E. coli Maltose Binding Protein

SecB, a soluble cytosolic chaperone component of the Secexport pathway, binds to newly synthesized precursor proteins and prevents their premature aggregation and folding and subsequently targets them to the translocation machinery on the membrane. PreMBP, the precursor form of maltose binding protein, has a 26-residue signal sequence attached to the N-terminus of MBP and is a physiological substrate of SecB. We examine the effect of macromolecular crowding and SecB on the stability and refolding of denatured preMBP and MBP. PreMBP was less stable than MBP (ΔTm =7( 0.5 K) in both crowded and uncrowded solutions. Crowding did not cause any substantial changes in the thermal stability ofMBP(ΔTm=1(0.4 K) or preMBP (ΔTm=0(0.6 K), as observed in spectroscopically monitored thermal unfolding experiments. However, both MBP and preMBP were prone to aggregation while refolding under crowded conditions. In contrast to MBP aggregates, which were amorphous, preMBP aggregates form amyloid fibrils.Under uncrowded conditions, a molar excess of SecB was able to completely prevent aggregation and promote disaggregation of preformed aggregates of MBP. When a complex of the denatured protein and SecB was preformed, SecB could completely prevent aggregation and promote folding of MBP and preMBP even in crowded solution. Thus, in addition to maintaining substrates in an unfolded, export-competent conformation, SecB also suppresses the aggregation of its substrates in the crowded intracellular environment. SecB is also able to promote passive disaggregation of macroscopic aggregates of MBP in the absence of an energy source such as ATP or additional cofactors. These experiments also demonstrate that signal peptide can reatly influence protein stability and aggregation propensity.

Dipole ordering in dilute solutions of ferroelectrics in antiferroelectric materials

The coefficients of thermal expansion reported by Worlton et al. [6] in the case of zircon are given in Table II along with the present data. Although Oql > or• in both cases, the anisotropy is more marked in the case of DyV04. From Table II, it is clear that the coefficient of volume expansion (,6) is almost the same for both compounds.

A combined XPS-UPS-EELS study of nitrogen adsorbed on clean and barium-promoted iron surfaces: The nature of the precursor to dissociation

For N2 on a clean Fe surface, the adsorbed precursor in a parallel orientation becomes predominant around 110 K, while at lower temperatures it coexists with a weakly adsorbed species. On a Ba-promoted Fe surface, however, N2 is present exclusively in the precursor state in the temperature range 80–150 K following moderate exposure. Besides exhibiting a low N-N stretching frequency of 1530 cm−1, the precursor shows a clear separation between the 5σ and 1π levels in the UPS; the precursor dissociates to give a nitridic species around 160 K.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.

Improving Flow-Insensitive Solutions for Non-Separable Dataflow Problems

Flow-insensitive solutions to dataflow problems have been known to be highly scalable; however also hugely imprecise. For non-separable dataflow problems this solution is further degraded due to spurious facts generated as a result of dependence among the dataflow facts. We propose an improvement to the standard flow-insensitive analysis by creating a generalized version of the dominator relation that reduces the number of spurious facts generated. In addition, the solution obtained contains extra information to facilitate the extraction of a better solution at any program point, very close to the flow-sensitive solution. To improve the solution further, we propose the use of an intra-block variable renaming scheme. We illustrate these concepts using two classic non-separable dataflow problems --- points-to analysis and constant propagation.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Stability criteria for single pulse solutions of cw passive mode-locked lasers

The stability of the steady-state solutions of mode-locking of cw lasers by a fast saturable absorber is imvestigated. It is shown that the solutions are stable if the condition (Ps/Pa) = (2/3) (P0Pa) is satisfied, where (Ps/Pa) is the steady-state la ser power, (P0/Pa) is the power at mode-locking threshold, and Pa is the saturated power of the absorber.

Low temperature ferrite formation using metal oxalate hydrazinate precursor

Magnesium ferrite, MgFe2O4 has been prepared at low temperatures by the thermal decomposition of a new precursor, MgFe2(C2O4)3. 5N2H4. The ferrite has been characterized by X-ray diffraction, infrared and Mössbauer spectra.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.