Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Conflict or consensus : an investigation of stakeholder concerns during the participation process of major infrastructure and construction projects in Hong Kong

Public participate in the planning and design of major public infrastructure and construction (PIC) projects is crucial to their success, as the interests of different stakeholders can be systematically captured and built into the finalised scheme. However, public participation may not always yield a mutually acceptable solution, especially when the interests of stakeholders are diverse and conflicting. Confrontations and disputes can arise unless the concerns or needs of the community are carefully analysed and addressed. The aim of the paper is to propose a systematic method of analysing stakeholder concerns relating to PIC projects by examining the degree of consensus and/or conflict involved. The results of a questionnaire survey and a series of interviews with different entities are provided, which indicate the existence of a significant divergence of views among stakeholder groups and that conflicts arise when there is a mismatch between peoples’ perception concerning money and happiness on the one hand and development and damages on the other. Policy and decision-makers should strive to resolve at least the majority of conflicts that arise throughout the lifecycle of major PIC projects so as to maximise their chance of success.

Comparison of the binding stoichiometries of positively charged DNA-binding drugs using positive and negative ion electrospray ionization mass spectrometry

Positive and negative ion electrospray ionization (ESI) mass spectra of complexes of positively charged small molecules (distamycin, Hoechst 33258, [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2) have been compared. [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2 bind to DNA by intercalation. Negative ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA showed ions from DNA-ligand complexes consistent with solution studies. In contrast, only ions from freeDNAwere present in positive ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA, highlighting the need for obtaining ESI mass spectra of non-covalent complexes under a range of experimental conditions. Negative ion spectra of mixtures of the minor groove binder Hoechst 33258 with DNA containing a known minor groove binding sequence were dominated by ions from a 1:1 complex. In contrast, in positive ion spectra there were also ions present from a 2:1 (Hoechst 33258: DNA) complex, suggesting an alternative binding mode was possible either in solution or in the gas phase. When Hoechst 33258 was mixed with a DNA sequence lacking a high affinity minor groove binding site, the negative ion ESI mass spectra showed that 1:1 and 2:1 complexes were formed, consistent with existence of binding modes other than minor groove binding. The data presented suggest that comparison of positive and negative ion ESI-MS spectra might provide an insight into various binding modes in both solution and the gas phase.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Effective removal of zinc (II) from aqueous solutions by tricalcium aluminate (C3A)

Recently, studies have identified high zinc levels in various environmental resources, and excessive intake of zinc has long been considered to be harmful to human health. The aim of this research was to investigate the effectiveness of tricalcium aluminate (C3A) as a removal agent of zinc from aqueous solution. Inductively coupled plasma-atomic emission spectrometer (ICP-AES), X-ray diffraction (XRD) and scanning electron microscopy (SEM) have been used to characterize such removal behavior. The effects of various factors such as pH influence, temperature and contact time were investigated. The adsorption capacity of C3A for Zn2+ was computed to be up to 13.73 mmol g−1, and the highest zinc removal capacity was obtained when the initial pH of Zn(NO3)2 solution was between 6.0 and 7.0, with temperature around 308 K. The XRD analysis showed that the resultant products were ZnAl-LDHs. Combined with the analysis of solution component, it was proved the existence of both precipitation and cation exchange in the removal process. From the experimental results, it was clear that C3A could be potentially used as a cost-effective material for the removal of zinc in aqueous environment.

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cages are considered, in one of which the range of integration is a Single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Natural Frequencies And Transient Responses Of 3-Phase Rotating Machine Windings

The analysis of transient electrical stresses in the insulation of high voltage rotating machines is rendered difficult because of the existence of capacitive and inductive couplings between phases. The Published theories ignore many of the couplings between phases to obtain the solution. A new procedure is proposed here to determine the transient voltage distribution on rotating machine windings. All the significicant capacitive and inductive couplings between different sections in a phase and between different sections in different phases have been considered in this analysis. The experimental results show good correlation with those computed.

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.

Type II beta-turn conformation of pivaloyl-L-prolyl-alpha-aminoisobutyryl-N-methylamide: Theoretical, spectroscopic, and X-ray studies

Pivaloyl-L-Pro-Aib-N-methylamide has been shown to possess one intramolecular hydrogen bond in (CD3)2SO solution, by 1H-nmr methods, suggesting the existence of beta -turns, with Pro-Aib as the corner residues. Theoretical conformational analysis suggests that Type II beta-turn conformations are about 2 kcal mol-1 more stable than Type III structures. A crystallographic study has established the Type II beta-turn in the solid state. The molecule crystallizes in the space group P21 with a = 5.865 Å, b = 11.421 Å, c = 12.966 Å, beta = 97.55°, and Z = 2. The structure has been refined to a final R value of 0.061. The Type II -turn conformation is stabilized by an intramolecular 4 1 hydrogen bond between the methylamide NH and the pivaloyl CO group. The conformational angles are Pro = -57.8°, Pro = 139.3°, Aib = 61.4°, and Aib = 25.1°. The Type II beta-turn conformation for Pro-Aib in this peptide is compared with the Type III structures observed for the same segment in larger peptides.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Investigation of surface activity and photoinduced diffusion of metals in solution deposited amorphous films of As2S3

Surface activity of solution deposited (SD) amorphous films of As2S3 has been investigated. Silver and copper are readily deposited on such films from appropriate aqueous ionic solutions. The metals diffuse into the films upon irradiation with energetic photons. Structure and properties of SD films have been investigated using electron microscopy, optical spectroscopy and differential scanning calorimetry. The amorphous films tend to crystallize upon metal diffusion. The stability of amorphous films, the deposition of metals on their active surfaces and the photo-induced diffusion may all be attributed to the presence or production of charged defects in amorphous chalcogenide films.

Metal-Nucleotide Interactions: Crystal Structures of Alkali (Li+, Na+, K+) and Alkaline Earth (Ca2+, Mg2+) Metal Complexes of Adenosine 2'-Monophosphate

Crystal structures of lithium, sodium, potassium, calcium and magnesium salts of adenosine 2'-monophosphate (2'-AMP) have been obtained at atomic resolution by X-ray crystallographic methods. 2'-AMP.Li belongs to the monoclinic space group P21 with a = 7.472(3)Å, b = 26.853(6) Å, c = 9.184(1)Å, b = 113.36(1)Å and Z= 4. 2'-AMP.Na and 2'-AMP.K crystallize in the trigonal space groups P31 and P3121 with a = 8.762(1)Å, c = 34.630(5)Å, Z= 6 and a = 8.931(4), Åc = 34.852(9)Å and Z= 6 respectively while 2'-AMP.Ca and 2'-AMP.Mg belong to space groups P6522 and P21 with cell parameters a = 9.487(2), c = 74.622(13), Z = 12 and a = 4.973(1), b = 10.023(2), c = 16.506(2), beta = 91.1(0) and Z = 2 respectively. All the structures were solved by direct methods and refined by full matrix least-squares to final R factors of 0.033, 0.028, 0.075, 0.069 and 0.030 for 2'-AMP.Li, 2'-AMP.Na, 2'- AMP.K, 2'-AMP.Ca and 2'-AMP.Mg, respectively. The neutral adenine bases in all the structures are in syn conformation stabilized by the O5'-N3 intramolecular hydrogen bond as in free acid and ammonium complex reported earlier. In striking contrast, the adenine base is in the anti geometry (cCN = -156.4(2)°) in 2'-AMP.Mg. Ribose moieties adopt C2'-endo puckering in 2'-AMP.Li and 2'-AMP.Ca, C2'-endo-C3'-exo twist puckering in 2'-AMP.Na and 2'-AMP.K and a C3'-endo-C2'-exo twist puckering in 2'-AMP.Mg structure. The conformation about the exocyclic C4'-C5' bond is the commonly observed gauche-gauche (g+) in all the structures except the gauche- trans (g-) conformation observed in 2'-AMP.Mg structure. Lithium ions coordinate with water, ribose and phosphate oxygens at distances 1.88 to 1.99Å. Na+ ions and K+ ions interact with phosphate and ribose oxygens directly and with N7 indirectly through a water oxygen. A distinct feature of 2'-AMP.Na and 2'-AMP.K structures is the involvement of ribose O4' in metal coordination. The calcium ion situated on a two-fold axis coordinates directly with three oxygens OW1, OW2 and O2 and their symmetry mates at distances 2.18 to 2.42Å forming an octahedron. A classic example of an exception to the existence of the O5'-N3 intramolecular hydorgen bond is the 2'-AMP.Mg strucure. Magnesium ion forms an octahedral coordination with three water and three phosphate oxygens at distances ranging from 2.02 to 2.11Å. A noteworthy feature of its coordination is the indirect link with N3 through OW3 oxygen resulting in macrochelation between the base and the phosphate group. Greater affnity of metal clays towards 5' compared to 2' and 3' nucleotides (J. Lawless, E. Edelson, and L. Manring, Am. Chem. Soc. Northwest Region Meeting, Seattle. 1978) due to macrochelation infered from solution studies (S. S. Massoud, H. Sigel, Eur. J. Biochem. 179, 451-458 (1989)) and interligand hydrogen bonding induced by metals postulated from metal-nucleotide structures in solid state (V. Swaminathan and M. Sundaralingam, CRC. Crit. Rev. Biochem. 6, 245-336 (1979)) are borne out by our structures also. The stacking patterns of adenine bases of both 2'-AMP.Na and 2'-AMP.K structures resemble the 2'-AMP.NH4 structure reported in the previous article. 2'-AMP.Li, 2'-AMP.Ca and 2'-AMP.Mg structures display base-ribose O4' stacking. An overview of interaction of monovalent and divalent cations with 2' and 5'-nucleotides has been presented.