The hard-particle model for a dense granular flow down an inclined plane

Perfectly hard particles are those which experience an infinite repulsive force when they overlap, and no force when they do not overlap. In the hard-particle model, the only static state is the isostatic state where the forces between particles are statically determinate. In the flowing state, the interactions between particles are instantaneous because the time of contact approaches zero in the limit of infinite particle stiffness. Here, we discuss the development of a hard particle model for a realistic granular flow down an inclined plane, and examine its utility for predicting the salient features both qualitatively and quantitatively. We first discuss Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.58 are in the rapid flow regime, due to the very high particle stiffness. An important length scale in the shear flow of inelastic particles is the `conduction length' delta = (d/(1 - e(2))(1/2)), where d is the particle diameter and e is the coefficient of restitution. When the macroscopic scale h (height of the flowing layer) is larger than the conduction length, the rates of shear production and inelastic dissipation are nearly equal in the bulk of the flow, while the rate of conduction of energy is O((delta/h)(2)) smaller than the rate of dissipation of energy. Energy conduction is important in boundary layers of thickness delta at the top and bottom. The flow in the boundary layer at the top and bottom is examined using asymptotic analysis. We derive an exact relationship showing that the a boundary layer solution exists only if the volume fraction in the bulk decreases as the angle of inclination is increased. In the opposite case, where the volume fraction increases as the angle of inclination is increased, there is no boundary layer solution. The boundary layer theory also provides us with a way of understanding the cessation of flow when at a given angle of inclination when the height of the layer is decreased below a value h(stop), which is a function of the angle of inclination. There is dissipation of energy due to particle collisions in the flow as well as due to particle collisions with the base, and the fraction of energy dissipation in the base increases as the thickness decreases. When the shear production in the flow cannot compensate for the additional energy drawn out of the flow due to the wall collisions, the temperature decreases to zero and the flow stops. Scaling relations can be derived for h(stop) as a function of angle of inclination.

The stress in a slowly sheared granular column

We report measurements of the wall stress in a granular material sheared in a cylindrical Couette cell, as a function of the distance from the free surface. Our results shows that when the material is static, all components of the stress saturate to constant values within a short distance from the free surface, in conformity with earlier experiments and theoretical predictions. When the material is sheared by rotating the inner cylinder at a constant rate, the stresses are remarkably altered. The radial normal stress does not saturate, and increases even more rapidly with depth than the linear hydrostatic pressure profile. The axial shear stress changes sign on shearing, and its magnitude increases with depth. These results are discussed in the context of the predictions of the classical and Cosserat plasticity theories.

Neel order, quantum spin liquids, and quantum criticality in two dimensions

This paper is concerned with the possibility of a direct second-order transition out of a collinear Neel phase to a paramagnetic spin liquid in two-dimensional quantum antiferromagnets. Contrary to conventional wisdom, we show that such second-order quantum transitions can potentially occur to certain spin liquid states popular in theories of the cuprates. We provide a theory of this transition and study its universal properties in an epsilon expansion. The existence of such a transition has a number of interesting implications for spin-liquid-based approaches to the underdoped cuprates. In particular it considerably clarifies existing ideas for incorporating antiferromagnetic long range order into such a spin-liquid-based approach.

Kinetic theory for the density plateau in the granular flow down an inclined plane

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is O(delta(2)) smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter delta = (d/(1 - e(n))H-1/2), d is the particle diameter, en is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small delta. Numerical estimates of both the parameter delta and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.

The dimensions of the ester unit

The dimensions of the ester unit, which is a component of the depsipeptide unit has been obtained by analysing the data on crystal structures of compounds having the ester unit. The dimensions indicate that this unit is slightly different from the peptide unit both as far as the bond length and bond angles are concerned.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Dimensions of University Student Learning in Medicine and Pharmacy

Study orientations in higher education consist of various dimensions, such as approaches to learning, conceptions of learning and knowledge (i.e. epistemologies), self-regulation, and motivation. They have also been measured in different ways. The main orientations typically reported are reproducing and meaning orientations. The present study explored dimensions of study orientations, focusing in particular on pharmacy and medicine. New versions of self-report instruments were developed and tested in various contexts and in two countries. Furthermore, the linkages between study orientations and students epistemological development were explored. The context of problem-based (PBL) small groups was investigated in order to better understand how collaboration contributes to the quality of learning. The participants of Study I (n=66) were pharmacy students, who were followed during a three-year professionally oriented program in terms of their study orientations and epistemologies. A reproducing orientation to studying diminished during studying, whereas only a few students maintained their original level of meaning orientation. Dualism was found to be associated with a reproducing orientation. In Study II practices associated with deep and surface approaches to learning were measured in two differing ways, in order to better distinguish between what students believed to be useful in studying, and the extent to which they applied their beliefs to practice when preparing for examinations. Differences between domains were investigated by including a sample of Finnish and Swedish medical students (n=956) and a Finnish non-medical sample of university students (n=865). Memorizing and rote learning appeared as differing components of a surface approach to learning, while understanding, relating, and critical evaluation of knowledge emerged as aspects of a deep approach to learning. A structural model confirmed these results in both student samples. Study III explored a wide variety of dimensions of learning in medical education. Swedish medical students (n=280) answered the questionnaire. The deep approach to learning was strongly related to collaboration and reflective learning, whereas the surface approach was associated with novice-like views of knowledge and the valuing of certain and directly applicable knowledge. PBL students aimed at understanding, but also valued the role of memorization. Study IV investigated 12 PBL tutorial groups of students (n=116) studying microbiology and pharmacology in a medical school. The educational application was expected to support a deep approach to learning: Group members course grades in a final examination were related to the perceived functioning of the PBL tutorial groups. Further, the quality of cases that had been used as triggers for learning, was associated with the quality of small group functioning. New dimensions of study orientations were discovered. In particular, novel, finer distinctions were found within the deep approach component. In medicine, critical evaluation of knowledge appeared to be less valued than understanding and relating. Further, collaboration appeared to be closely related to the deep approach, and it was also important in terms of successful PBL studying. The results of the studies confirmed the previously found associations between approaches to learning and study success, but showed interesting context- and subgroup-related differences in this respect. Students ideas about the nature of knowledge and their approaches to learning were shown to be closely related. The present study expanded our understanding of the dimensions of study orientations, of their development, and their contextual variability in pharmacy and medicine.

Non-periodic tilings in 2-dimensions: 4- and 7-fold symmetries

By inflating basic rhombuses, with a self-similarity principle, non-periodic tiling of 2-d planes is possible with 4, 5, 6, 7, 8, … -fold symmetries. As examples, non-periodic tilings with crystallographically allowed 4-fold symmetry and crystallographically forbidden 7-fold symmetry are presented in detail. The computed diffraction patterns of these tilings are also discussed.

Dynamics of sheared inelastic dumbbells

We study the dynamical properties of the homogeneous shear flow of inelastic dumbbells in two dimensions as a first step towards examining the effect of shape on the properties of flowing granular materials. The dumbbells are modelled as smooth fused disks characterized by the ratio of the distance between centres (L) and the disk diameter (D), with an aspect ratio (L/D) varying between 0 and 1 in our simulations. Area fractions studied are in the range 0.1-0.7, while coefficients of normal restitution (e(n)) from 0.99 to 0.7 are considered. The simulations use a modified form of the event-driven methodology for circular disks. The average orientation is characterized by an order parameter S, which varies between 0 (for a perfectly disordered fluid) and 1 (for a fluid with the axes of all dumbbells in the same direction). We investigate power-law fits of S as a function of (L D) and (1 - e(n)(2)) There is a gradual increase in ordering as the area fraction is increased, as the aspect ratio is increased or as the coefficient of restitution is decreased. The order parameter has a maximum value of about 0.5 for the highest area fraction and lowest coefficient of restitution considered here. The mean energy of the velocity fluctuations in the flow direction is higher than that in the gradient direction and the rotational energy, though the difference decreases as the area fraction increases, due to the efficient collisional transfer of energy between the three directions. The distributions of the translational and rotational velocities are Gaussian to a very good approximation. The pressure is found to be remarkably independent of the coefficient of restitution. The pressure and dissipation rate show relatively little variation when scaled by the collision frequency for all the area fractions studied here, indicating that the collision frequency determines the momentum transport and energy dissipation, even at the lowest area fractions studied here. The mean angular velocity of the particles is equal to half the vorticity at low area fractions, but the magnitude systematically decreases to less than half the vorticity as the area fraction is increased, even though the stress tensor is symmetric.

Studies in biogas technology. Part II. Optimisation of plant dimensions

In this paper, the design basis of the conventional Khadi and Village Industries Commission biogas plants has been elucidated. It has been shown that minimisation of the cost of the gas holder alone leads to the narrow and deep digesters of conventional plants. If instead, the total capital cost of the gas holder plus digester is minimised, the optimisation leads to wide and shallow digesters, which are less expensive. To test this alternative, two prototype plants have been designed, constructed and operated. These plants are not only 25–40% cheaper, but their performance is actually slightly better than the conventional plants.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Chinese immigrants to Finland: A qualitative study of housing, employment, access to health care and child care as sociological dimensions in their settlement process

The Master’s thesis is qualitative research based on interviews of 15 Chinese immigrants to Finland in order to provide a sociological perspective of the migration experience through the eyes of Chinese immigrants in the Finnish social welfare context. This research is mainly focused upon four crucial aspects of life in the settlement process: housing, employment, access to health care and child care. Inspired by Allardt’s theoretical framework ‘Having, Loving and Being’, social relationships and individual satisfaction are examined in the case of Chinese interviewees dealing with the four life aspects. Finland was not perceived as an attractive migration destination for most Chinese interviewees in the beginning. However, with longer residence in Finland, the Finnish social welfare system gradually became a crucial appealing factor in their permanent settlement in Finland. And meanwhile, social responsibility of attending their old parents in China, strong feelings of being isolated in Finland, and insufficient integration into the Finnish society were influential factors for their decision of returning to China. Social relationships with personal friends, migration brokers, schools, employers and family relatives had great influences in the four life aspects of Chinese immigrants in Finland. The social relationship with the Finnish social welfare sector is supportive to Chinese immigrants, but Chinese immigrants do not heavily rely on Finnish social protection. The housing conditions were greatly improved over time while the upward mobility in the Finnish labour market was not significant among Chinese immigrants. All Chinese immigrants were satisfied with their current housing by the time I interviewed them while most of them had subjective feelings of being alienated in the Finnish labour market, which seriously prevented them from integrating into the Finnish society. In general, Chinese immigrants were satisfied with the low cost of accessing the Finnish public health care services and affordable Finnish child day care services and financial subsidies for children from the Finnish social welfare sector. This research also suggests that employment is the central basis in well-being. Support from the Finnish social welfare sector can improve the satisfaction levels among immigrants, especially when it mitigates the effects of low-paid employment. As well, my empirical study of Chinese immigrants in Finland shows that Having (needs for materials), Loving (needs for social relations) and Being (needs for social integration) are all involved in the four concrete aspects (housing, employment, access to health care and child care).

Solitons of Coupled Scalar Field Theories in Two Dimensions

This work offers a method for finding some exact soliton solutions to coupled relativistic scalar field theories in 1+1 dimensions. The method can yield static solutions as well as quasistatic "charged" solutions for a variety of Lagrangians. Explicit solutions are derived as examples. A particularly interesting class of solutions is nontopological without being either charged or time dependent.