Comparison of Pore-Level and Volume-Averaged Computations in Highly Conductive Spherical-Void-Phase Porous Materials

A study has been carried out to compare results obtained from pore-level simulations conducted on three-dimensional idealized spherical-void-phase geometric models to similar results obtained from a solver based on volume-averaging and local thermal non-equilibrium. The purpose of the comparison is to establish closure coefficients for the viscous and form drag terms in the volume-averaged momentum equations and the interstitial convective exchange coefficient required to couple the volume-averaged energy equations for the solid and fluid constituents. A method is also described for determining the solid-phase conduction shape factor, which is shown to be important for accurate volume-average simulation of highly conductive porous materials. The shape factor has been addressed in previous literature (using various terminology) and accounts in a bulk manner for resistance due to the elongated conduction path and for changes in the effective heat flow area along the conduction path. The conduction shape factor is a function of the geometry only and is found herein from a detailed comparison between pore-level and volume-averaged simulations of conjugate heat transfer. The conduction shape factor vastly improves volume-averaged predictions of the overall heat transfer and the temperature distributions in the porous material.     

Progress in numerical simulation of yield stress fluid flows

Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant to natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, and combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.     

Hydrology of the North Klondike River: carbon export,water balance and inter-annual climate influences within a sub-alpine permafrost catchment

Arctic and sub-arctic watersheds are undergoing significant changes due to recent climate warming and degrading permafrost, engendering enhanced monitoring of arctic rivers. Smaller catchments provide understanding of discharge, solute flux and groundwater recharge at the process level that contributes to an understanding of how larger arctic watersheds are responding to climate change. The North Klondike River, located in west central Yukon, is a sub-alpine permafrost catchment, which maintains an active hydrological monitoring station with a record of >40 years. In addition to being able to monitor intra-annual variability, this data set allows for more complex analysis of streamflow records. Streamflow data, geochemistry and stable isotope data for 2014 show a groundwater-dominated system, predominantly recharged during periods of snowmelt. Radiocarbon is shown to be a valuable tracer of soil zone recharge processes and carbon sources. Winter groundwater baseflow contributes 20?% of total annual discharge, and accounts for up to 50?% of total river discharge during the spring and summer months. Although total stream discharge remains unchanged, mean annual groundwater baseflow has increased over the 40-year monitoring period. Wavelet analysis reveals a catchment that responds to El Niño and longer solar cycles, as well as climatic shifts such as the Pacific Decadal Oscillation.

Dedicated to Professor Peter Fritz on the occasion of his 80th birthday     

The Principal Element of a Frobenius Lie Algebra

We introduce the notion of the principal element of a Frobenius Lie algebra ${\frak{f}}$ . The principal element corresponds to a choice of ${F \in \frak{f}^{*}}$ such that F[–, –] non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to sl _n , its eigenvalues are integers and are independent of F. For certain “small” functionals F, a simple construction is given which readily yields the principal element. When applied to the first maximal parabolic subalgebra of sl _n , the principal element coincides with semisimple element of the principal three-dimensional subalgebra. We also show that Frobenius algebras are stable under deformation.     

A Class of Integrable Flows on the Space of Symmetric Matrices

For a given skew symmetric real n × n matrix N, the bracket [X, Y] _N = XNY − YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n × n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to investigate the geometry, integrability, and linearizability of the Hamiltonian system , or equivalently in Lax form, the equation on this space along with a detailed study of the Poisson geometry itself. If N has distinct eigenvalues, it is proved that this system is integrable on a generic symplectic leaf of the Lie-Poisson structure of Sym(n, N). This is established by finding another compatible Poisson structure. If N is invertible, several remarkable identifications can be implemented. First, (Sym(n, N), [·, ·]) is Lie algebra isomorphic with the symplectic Lie algebra associated to the symplectic form on given by N ⁻¹. In this case, the system is the reduction of the geodesic flow of the left invariant Frobenius metric on the underlying symplectic group Sp(n, N ⁻¹). Second, the trace of the product of matrices defines a non-invariant non-degenerate inner product on Sym(n, N) which identifies it with its dual. Therefore Sym(n, N) carries a natural Lie-Poisson structure as well as a compatible “frozen bracket” structure. The Poisson diffeomorphism from Sym(n, N) to maps our system to a Mischenko-Fomenko system, thereby providing another proof of its integrability if N is invertible with distinct eigenvalues. Third, there is a second ad-invariant inner product on Sym(n, N); using it to identify Sym(n, N) with itself and composing it with the dual of the Lie algebra isomorphism with , our system becomes a Mischenko- Fomenko system directly on Sym(n, N). If N is invertible and has distinct eigenvalues, it is shown that this geodesic flow on Sym(n, N) is linearized on the Prym subvariety of the Jacobian of the spectral curve associated to a Lax pair formulation with parameter of the system. If, on the other hand, N has nullity one and distinct eigenvalues, in spite of the fact that the system is completely integrable, it is shown that the flow does not linearize on the Jacobian of the spectral curve. Research partially supported by NSF grants CMS-0408542 and DMS-0604307. Research partially supported by the Swiss SCOPES grant IB7320-110721/1, 2005-2008, and MEdC Contract 2-CEx 06-11-22/25.07.2006. Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. Research partially supported by the Swiss NSF and the Swiss SCOPES grant IB7320-110721/1.     

Stretch-bend combination polyads in the ÃAu state of acetylene, C2H2

Rotational analyses are reported for a number of newly-discovered vibrational levels of the S₁-trans (ùA_u) state of C₂H₂. These levels are combinations where the Franck-Condon active and vibrational modes are excited together with the low-lying bending vibrations, and . The structures of the bands are complicated by strong a- and b-axis Coriolis coupling, as well as Darling-Dennison resonance for those bands that involve overtones of the bending vibrations. The most interesting result is the strong anharmonicity in the combinations of (trans bend, a_g) and (in-plane cis bend, b_u). This anharmonicity presumably represents the approach of the molecule to the trans-cis isomerization barrier, where ab initio results have predicted the transition state to be half-linear, corresponding to simultaneous excitation of and . The anharmonicity also causes difficulty in the least squares fitting of some of the polyads, because the simple model of Coriolis coupling and Darling-Dennison resonance starts to break down. The effective Darling-Dennison parameter, K₄₄₆₆, is found to increase rapidly with excitation of , while many small centrifugal distortion terms have had to be included in the least squares fits in order to reproduce the rotational structure correctly. Fermi resonances become important where the K-structures of different polyads overlap, as happens with the 2¹3¹B¹ and 3¹B³ polyads (B = 4 or 6). The aim of this work is to establish the detailed vibrational level structure of the S₁-trans state in order to search for possible S₁-cis (¹A₂) levels. This work, along with results from other workers, identifies at least one K sub-level of every single vibrational level expected up to a vibrational energy of 3500 cm⁻¹.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Synthesis and Reactions of a New Cyclobutanethione Derivative

The 3,3‐dichloro‐2,2,4,4‐tetramethylcyclobutanethione ( 4b ) was prepared from the parent diketone by successive reaction with PCl₅ and Lawesson reagent in pyridine. This new thioketone 4b was transformed into 1‐chlorocyclobutanesulfanyl chloride 5 and chloro 1‐chlorocyclobutyl disulfide 9 by treatment with PCl₅ and SCl₂, respectively, in chlorinated solvents (Schemes 1 and 2). These products reacted with S‐ and P‐nucleophiles by substitution of Cl⁻ at the S‐atom; e.g., the reaction with 4b yielded the di‐ and trisulfides 6b and 11 , respectively. Surprisingly, only pentasulfide 12 was formed in the reaction of 9 with thiobenzophenone (Scheme 3). In contrast to 5 and 9 , the corresponding chloro 1‐chlorocyclobutyl trisulfide 13 could not be detected, but reacted immediately with the starting thioketone 4b to give the tetrasulfide 14 (Scheme 4). Oxidation of 4b with 3‐chloroperbenzoic acid (mCPBA) yielded the corresponding thione oxides (= sulfine) 15 , which underwent 1,3‐dipolar cycloadditions with thioketones 3a and 4b (Scheme 5). Furthermore, 4b was shown to be a good dipolarophile in reactions with thiocarbonylium methanides (Scheme 6) and iminium ylides (= azomethine ylides; Scheme 7). In the case of phenyl azide, the reaction with 4b gave the symmetrical trithiolane 25 (Scheme 8).     

Modeling force-induced bio-polymer unfolding

We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N = 55 using exact enumeration techniques. We analyze in detail the differences between the constant force and constant distance ensembles for large but finite N. At low temperatures, and in the constant force ensemble, the force–extension curve shows multiple plateaus (intermediate states), in contrast with the abrupt transition to an extended state prevailing in the N → ∞ limit. In the constant distance ensemble, the same curve provides a unified response to pulling and compressing forces, and agrees qualitatively with recent experimental results. We identify a cross-over length, proportional to N, below which the critical force of unfolding decreases with temperature, while above, it increases with temperature. Finally, the force–extension curve for stiff chains exhibits “saw-tooth” like behavior, as observed in protein unfolding experiments.