Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Physics interplay of the LHC and the ILC

Physics at the Large Hadron Collider (LHC) and the International e(+)e(-) Linear Collider (ILC) will be complementary in many respects, as has been demonstrated at previous generations of hadron and lepton colliders. This report addresses the possible interplay between the LHC and ILC in testing the Standard Model and in discovering and determining the origin of new physics. Mutual benefits for the physics programme at both machines can occur both at the level of a combined interpretation of Hadron Collider and Linear Collider data and at the level of combined analyses of the data, where results obtained at one machine can directly influence the way analyses are carried out at the other machine. Topics under study comprise the physics of weak and strong electroweak symmetry breaking, supersymmetric models, new gauge theories, models with extra dimensions, and electroweak and QCD precision physics. The status of the work that has been carried out within the LHC/ILC Study Group so far is summarized in this report. Possible topics for future studies are outlined.

Witten index of supersymmetric chiral theories

The Witten index can be defined in many supersymmetric theories by formulating them in the space-time R×S3. If the index is nonzero for any value of the radius of S3, it can be shown that the theory does not break supersymmetry in Minkowski space. This approach rules out supersymmetry breaking in a large class of models, chiral and otherwise. The index arguments are consistent with previous instanton calculations which indicate supersymmetry breaking in certain theories.

High-Temperature (1023 K to 1273 K 750 degrees C to 1000 degrees C]) Plastic Deformation Behavior of B-Modified Ti-6Al-4V Alloys: Temperature and Strain Rate Effects

A minor addition of B to the Ti-6Al-4V alloy, by similar to 0.1 wt pct, reduces its as-cast prior beta grain size by an order of magnitude, whereas higher B content leads to the presence of in situ formed TiB needles in significant amounts. An experimental investigation into the role played by these microstructural modifications on the high-temperature deformation behavior of Ti-6Al-4V-xB alloys, with x varying between 0 wt pct and 0.55 wt pct, was conducted. Uniaxial compression tests were performed in the temperature range of 1023 K to 1273 K (750 degrees C to 1000 degrees C) and in the strain rate range of 10(-3) to 10(+1) s(-1). True stress-true strain responses of all alloys exhibit flow softening at lower strain rates and oscillations at higher strain rates. The flow softening is aided by the occurrence of dynamic recrystallization through lath globularization in high temperature (1173 K to 1273 K 900 degrees C to 1000 degrees C]) and a lower strain rate (10(-2) to 10(-3) s(-1)) regime. The grain size refinement with the B addition to Ti64, despite being marked, had no significant effect on this. Oscillations in the flow curve at a higher strain rate (10(0) to 10(+1) s(-1)), however, are associated with microstructural instabilities such as bending of laths, breaking of lath boundaries, generation of cavities, and breakage of TiB needles. The presence of TiB needles affected the instability regime. Microstructural evidence suggests that the matrix cavitation is aided by the easy fracture of TiB needles.

Berry phenolics: isolation, analysis, identification, and antioxidant properties

The main objectives in this thesis were to isolate and identify the phenolic compounds in wild (Sorbus aucuparia) and cultivated rowanberries, European cranberries (Vaccinium microcarpon), lingonberries (Vaccinium vitis-idaea), and cloudberries (Rubus chamaemorus), as well as to investigate the antioxidant activity of phenolics occurring in berries in food oxidation models. In addition, the storage stability of cloudberry ellagitannin isolate was studied. In wild and cultivated rowanberries, the main phenolic compounds were chlorogenic acids and neochlorogenic acids with increasing anthocyanin content depending on the crossing partners. The proanthocyanidin contents of cranberries and lingonberries were investigated, revealing that the lingonberry contained more rare A-type dimers than the European cranberry. The liquid chromatography mass spectrometry (LC-MS) analysis of cloudberry ellagitannins showed that trimeric lambertianin C and sanguiin H-10 were the main ellagitannins. The berries, rich in different types of phenolic compounds including hydroxycinnamic acids, proanthocyanidins, and ellagitannins, showed antioxidant activity toward lipid oxidation in liposome and emulsion oxidation models. All the different rowanberry cultivars prevented lipid oxidation in the same way, in spite of the differences in their phenolic composition. In terms of liposomes, rowanberries were slightly more effective antioxidants than cranberry and lingonberry phenolics. Greater differences were found when comparing proanthocyanidin fractions. Proanthocyanidin dimers and trimers of both cranberries and lingonberries were most potent in inhibiting lipid oxidation. Antioxidant activities and antiradical capacities were also studied with hydroxycinnamic acid glycosides. The sinapic acid derivatives of the hydroxycinnamic acid glycosides were the most effective at preventing lipid oxidation in emulsions and liposomes and scavenging radicals in DPPH assay. In liposomes and emulsions, the formation of the secondary oxidation product, hexanal, was inhibited more than that of the primary oxidation product, conjugated diene hydroperoxides, by hydroxycinnamic acid derivatives. This indicates that they are principally chain-breaking antioxidants rather than metal chelators, although they possess chelating activity as well. The storage stability test of cloudberry ellagitannins was performed by storing ellagitannin isolate and ellagitannins encapsulated with maltodextrin at different relative vapor pressures. The storage stability was enhanced by the encapsulation when higher molecular weight maltodextrin was used. The best preservation was achieved when the capsules were stored at 0 or 33% relative vapor pressures. In addition, the antioxidant activities of encapsulated cloudberry extracts were followed during the storage period. Different storage conditions did not alter the antioxidant activity, even though changes in the ellagitannin contents were seen. The current results may be of use in improving the oxidative stability of food products by using berries as natural antioxidants.

Patents, Ethics and Stem Cell Research : The Case of hESC Innovation in Australia, Europe and the United States

Embryonic stem cells offer potentially a ground-breaking insight into health and diseases and are said to offer hope in discovering cures for many ailments unimaginable few years ago. Human embryonic stem cells are undifferentiated, immature cells that possess an amazing ability to develop into almost any body cell such as heart muscle, bone, nerve and blood cells and possibly even organs in due course. This remarkable feature, enabling embryonic stem cells to proliferate indefinitely in vitro (in a test tube), has branded them as a so-called miracle cure . Their potential use in clinical applications provides hope to many sufferers of debilitating and fatal medical conditions. However, the emergence of stem cell research has resulted in intense debates about its promises and dangers. On the one hand, advocates hail its potential, ranging from alleviating and even curing fatal and debilitating diseases such as Parkinson s, diabetes, heart ailments and so forth. On the other hand, opponents decry its dangers, drawing attention to the inherent risks of human embryo destruction, cloning for research purposes and reproductive cloning eventually. Lately, however, the policy battles surrounding human embryonic stem cell innovation have shifted from being a controversial research to scuffles within intellectual property rights. In fact, the ability to obtain patents represents a pivotal factor in the economic success or failure of this new biotechnology. Although, stem cell patents tend to more or less satisfy the standard patentability requirements, they also raise serious ethical and moral questions about the meaning of the exclusions on ethical or moral grounds as found in European and to an extent American and Australian patent laws. At present there is a sort of a calamity over human embryonic stem cell patents in Europe and to an extent in Australia and the United States. This in turn has created a sense of urgency to engage all relevant parties in the discourse on how best to approach patenting of this new form of scientific innovation. In essence, this should become a highly favoured patenting priority. To the contrary, stem cell innovation and its reliance on patent protection risk turmoil, uncertainty, confusion and even a halt on not only stem cell research but also further emerging biotechnology research and development. The patent system is premised upon the fundamental principle of balance which ought to ensure that the temporary monopoly awarded to the inventor equals that of the social benefit provided by the disclosure of the invention. Ensuring and maintaining this balance within the patent system when patenting human embryonic stem cells is of crucial contemporary relevance. Yet, the patenting of human embryonic stem cells raises some fundamental moral, social and legal questions. Overall, the present approach of patenting human embryonic stem cell related inventions is unsatisfactory and ineffective. This draws attention to a specific question which provides for a conceptual framework for this work. That question is the following: how can the investigated patent offices successfully deal with patentability of human embryonic stem cells? This in turn points at the thorny issue of application of the morality clause in this field. In particular, the interpretation of the exclusions on ethical or moral grounds as found in Australian, American and European legislative and judicial precedents. The Thesis seeks to compare laws and legal practices surrounding patentability of human embryonic stem cells in Australia and the United States with that of Europe. By using Europe as the primary case study for lessons and guidance, the central goal of the Thesis then becomes the determination of the type of solutions available to Europe with prospects to apply such to Australia and the United States. The Dissertation purports to define the ethical implications that arise with patenting human embryonic stem cells and intends to offer resolutions to the key ethical dilemmas surrounding patentability of human embryonic stem cells and other morally controversial biotechnology inventions. In particular, the Thesis goal is to propose a functional framework that may be used as a benchmark for an informed discussion on the solution to resolving ethical and legal tensions that come with patentability of human embryonic stem cells in Australian, American and European patent worlds. Key research questions that arise from these objectives and which continuously thread throughout the monograph are: 1. How do common law countries such as Australia and the United States approach and deal with patentability of human embryonic stem cells in their jurisdictions? These practices are then compared to the situation in Europe as represented by the United Kingdom (first two chapters), the Court of Justice of the European Union and the European Patent Office decisions (Chapter 3 onwards) in order to obtain a full picture of the present patenting procedures on the European soil. 2. How are ethical and moral considerations taken into account at patent offices investigated when assessing patentability of human embryonic stem cell related inventions? In order to assess this part, the Thesis evaluates how ethical issues that arise with patent applications are dealt with by: a) Legislative history of the modern patent system from its inception in 15th Century England to present day patent laws. b) Australian, American and European patent offices presently and in the past, including other relevant legal precedents on the subject matter. c) Normative ethical theories. d) The notion of human dignity used as the lowest common denominator for the interpretation of the European morality clause. 3. Given the existence of the morality clause in form of Article 6(1) of the Directive 98/44/EC of the European Parliament and of the Council of 6 July 1998 on the legal protection of biotechnological inventions which corresponds to Article 53(a) European Patent Convention, a special emphasis is put on Europe as a guiding principle for Australia and the United States. Any room for improvement of the European morality clause and Europe s current manner of evaluating ethical tensions surrounding human embryonic stem cell inventions is examined. 4. A summary of options (as represented by Australia, the United States and Europe) available as a basis for the optimal examination procedure of human embryonic stem cell inventions is depicted, whereas the best of such alternatives is deduced in order to create a benchmark framework. This framework is then utilised on and promoted as a tool to assist Europe (as represented by the European Patent Office) in examining human embryonic stem cell patent applications. This method suggests a possibility of implementing an institution solution. 5. Ultimately, a question of whether such reformed European patent system can be used as a founding stone for a potential patent reform in Australia and the United States when examining human embryonic stem cells or other morally controversial inventions is surveyed. The author wishes to emphasise that the guiding thought while carrying out this work is to convey the significance of identifying, analysing and clarifying the ethical tensions surrounding patenting human embryonic stem cells and ultimately present a solution that adequately assesses patentability of human embryonic stem cell inventions and related biotechnologies. In answering the key questions above, the Thesis strives to contribute to the broader stem cell debate about how and to which extent ethical and social positions should be integrated into the patenting procedure in pluralistic and morally divided democracies of Europe and subsequently Australia and the United States.

Optical and magnetic properties of the exact PPP states of biphenyl

The low-lying singlets and triplets of biphenyl are obtained exactly within the PPP model using the diagrammatic valence bond method. The energy gaps within the singlet manifold as well as the lowest singlet-triplet gap are found to be in good agreement with experimental results. The two weak absorptions between 4·1 and 4·2 eV reported experimentally are attributed to the two states lying below the optical gap that become weakly allowed on breaking electron-hole and inversion symmetries. The observed blue shift of the spectral lines, attributed to a change in dihedral angle, on going from crystalline to solution to vapour phase is also well reproduced within the PPP model. The bond orders show that the ground singlet state is benzenoidal while the dipole excited state as well as the lowest triplet state are quinonoidal and planar. Comparison with the experimental spin densities and the fine structure constants D and E in the triplet state point to slightly weaker correlations than assumed by the PPP model. The introduction of a 1-8 bond to mimic poly(paraphenylene)s gives an optical gap that is in good agreement with experiment.

Towards Understanding Powder Behavior Via Simulation

The aim of this study was to investigate powder and tablet behavior at the level of mechanical interactions between single particles. Various aspects of powder packing, mixing, compression, and bond formation were examined with the aid of computer simulations. The packing and mixing simulations were based on spring forces interacting between particles. Packing and breakage simulations included systems in which permanent bonds were formed and broken between particles, based on their interaction strengths. During the process, a new simulation environment based on Newtonian mechanics and elementary interactions between the particles was created, and a new method for evaluating mixing was developed. Powder behavior is a complicated process, and many of its aspects are still unclear. Powders as a whole exhibit some aspects of solids and others of liquids. Therefore, their physics is far from clear. However, using relatively simple models based on particle-particle interaction, many powder properties could be replicated during this work. Simulated packing densities were similar to values reported in the literature. The method developed for describing powder mixing correlated well with previous methods. The new method can be applied to determine mixing in completely homogeneous materials, without dividing them into different components. As such, it can describe the efficiency of the mixing method, regardless of the powder's initial setup. The mixing efficiency at different vibrations was examined, and we found that certain combinations of amplitude, direction, and frequencies resulted in better mixing while using less energy. Simulations using exponential force potentials between particles were able to explain the elementary compression behavior of tablets, and create force distributions that were similar to the pressure distributions reported in the literature. Tablet-breaking simulations resulted in breaking strengths that were similar to measured tablet breaking strengths. In general, many aspects of powder behavior can be explained with mechanical interactions at the particle level, and single particle properties can be reliably linked to powder behavior with accurate simulations.

Bridging East and West : The Establishment of the International Institute for Applied Systems Analysis (IIASA) in the United States Foreign Policy of Bridge Building, 1964-1972.

The dissertation examines the foreign policies of the United States through the prism of science and technology. In the focal point of scrutiny is the policy establishing the International Institute for Applied Systems Analysis (IIASA) and the development of the multilateral part of bridge building in American foreign policy during the 1960s and early 1970s. After a long and arduous negotiation process, the institute was finally established by twelve national member organizations from the following countries: Bulgaria, Canada, Czechoslovakia, Federal Republic of Germany (FRG), France, German Democratic Republic (GDR), Great Britain, Italy, Japan, Poland, Soviet Union and United States; a few years later Sweden, Finland and the Netherlands also joined. It is said that the goal of the institute was to bring together researchers from East and West to solve pertinent problems caused by the modernization process experienced in industrialized world. It originates from President Lyndon B. Johnson s bridge building policies that were launched in 1964, and was set in a well-contested and crowded domain of other international organizations of environmental and social planning. Since the distinct need for yet another organization was not evident, the process of negotiations in this multinational environment enlightens the foreign policy ambitions of the United States on the road to the Cold War détente. The study places this project within its political era, and juxtaposes it with other international organizations, especially that of the OECD, ECE and NATO. Conventionally, Lyndon Johnson s bridge building policies have been seen as a means to normalize its international relations bilaterally with different East European countries, and the multilateral dimension of the policy has been ignored. This is why IIASA s establishment process in this multilateral environment brings forth new information on US foreign policy goals, the means to achieve these goals, as well as its relations to other advanced industrialized societies before the time of détente, during the 1960s and early 1970s. Furthermore, the substance of the institute applied systems analysis illuminates the differences between European and American methodological thinking in social planning. Systems analysis is closely associated with (American) science and technology policies of the 1960s, especially in its military administrative applications, thus analysis within the foreign policy environment of the United States proved particularly fruitful. In the 1960s the institutional structures of European continent with faltering, and the growing tendencies of integration were in flux. One example of this was the long, drawn-out process of British membership in the EEC, another is de Gaulle s withdrawal from NATO s military-political cooperation. On the other hand, however, economic cooperation in Europe between East and West, and especially with the Soviet Union was expanding rapidly. This American initiative to form a new institutional actor has to be seen in that structural context, showing that bridge building was needed not only to the East, but also to the West. The narrative amounts to an analysis of how the United States managed both cooperation and conflict in its hegemonic aspirations in the emerging modern world, and how it used its special relationship with the United Kingdom to achieve its goals. The research is based on the archives of the United States, Great Britain, Sweden, Finland, and IIASA. The primary sources have been complemented with both contemporary and present day research literature, periodicals, and interviews.

Structure, dielectric, and magnetic properties of Sr2TiMnO6 ceramics

Sr2TiMnO6, a double perovskite associated with high degree of B-site cation disorder was investigated in detail for its structural, magnetic, and dielectric properties. Though x-ray powder diffraction analysis confirms its cubic structure, first order Raman scattering and infrared reflectivity spectra indicate a breaking of the local cubic symmetry. The magnetization study reveals an anomaly at 14 K owing to a ferrimagnetic/canted antiferromagneticlike ordering arising from local Mn-O-Mn clusters. Saturated M-H hysteresis loops obtained at 5 K also reflect the weak ferromagnetic exchange interactions present in the system and an approximate estimation of Mn3+/Mn4+ was done using the magnetization data for the samples sintered at different temperatures. The conductivity and dielectric behavior of this system has been investigated in a broad temperature range of 10 to 300 K. Intrinsic permittivity was obtained only below 100 K whereas giant permittivity due to conductivity and Maxwell-Wagner polarization was observed at higher temperatures. X-ray photoemission studies further confirmed the presence of mixed oxidation states of Mn and the valence band spectra analysis was carried out in detail. (C) 2010 American Institute of Physics. doi: 10.1063/1.3500369]

Yhteisestä toiminnasta yhteiseen kieleen : keskustelunanalyyttinen tutkimus toisen kielen oppimisesta kielikylpypäiväkodin arkitilanteissa

This dissertation examines how Finnish-speaking children learn Swedish in an immersion kindergarten where the method of Canadian immersion is used. Within the framework of conversation analysis, this study explores how second language learning is situated in interaction and evidenced in the participants´ verbal and non-verbal behavior. The database consists of 40 hours of videotaped data collected in naturally occurring situations in a group of 15 four-year-old children during the first two years of their immersion. Due to the immersion method, all the children share the same L1, in this case Finnish, and the teachers understand Finnish. However, they speak only Swedish to the children in all situations and Swedish is learned in interaction without formal teaching. The aim of the study is to discover how the children´s second language competence gradually increases when they participate in interaction with the Swedish-speaking teachers. The study also sheds light on the methodological question of how second language learning can be analyzed with the method of conversation analysis. The focus is on showing how the second language is learned in interaction, especially on how learning is achieved collaboratively. In this study, the emerging second language competence is explored by investigating how the children show understanding of the teachers´ non-verbal and verbal actions during the first and the second semester of the immersion. The children´s use of Swedish is analyzed by investigating how they recycle lexical items and later even syntactic structures from the teachers´ Swedish turns. The results show that the teachers´ actions are largely understood by the children even at the beginning of the immersion. The analyzes of the children´s responsive turns reveal that they interpret the teachers´ turns on the basis of non-verbal cues at first. Especially at the beginning of the immersion, the participants orient to the progress of interaction and not to problems in understanding. Even in situations where the next actions show that the children do not understand what is said, they tend to display understanding rather than non-understanding. This behavior changes, however, when the children´s competence in their second language increases. At the second semester, the children both show understanding of the teachers´ verbal turns and also display their non-understanding by initiating repair when they do not understand. Understanding of the teachers´ verbal turns, including their syntactic structure, is manifested in the ways the children tie their turns to the teachers´ turns. Recycling, on the other hand, proves to be the way by which the children start to speak the second language. In this study, the children´s common L1 is evidenced to be an important resource in interaction. It allows the children to participate in their individual ways and to share their experiences both with each other and with the teachers. It also enables them to co-construct conversations that lead to collaborative learning. Moreover, the uninhibited use of L1 proves to be an important analytic tool that makes the immersion data especially fruitful for conversation analytic research on second language learning, since the children´s interpretations of the second language are in evidence even when they do not speak the second language.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A nanosecond molecular dynamics study of antiparallel d(G)(7) quadruplex structures: Effect of the coordinated cations

Nanosecond scale molecular dynamics simulations have been performed on antiparallel Greek key type d(G(7)) quadruplex structures with different coordinated ions, namely Na+ and K+ ion, water and Na+ counter ions, using the AMBER force field and Particle Mesh Ewald technique for electrostatic interactions. Antiparallel structures are stable during the simulation, with root mean square deviation values of similar to1.5 Angstrom from the initial structures. Hydrogen bonding patterns within the G-tetrads depend on the nature of the coordinated ion, with the G-tetrad undergoing local structural variation to accommodate different cations. However, alternating syn-anti arrangement of bases along a chain as well as in a quartet is maintained through out the MD simulation. Coordinated Na+ ions, within the quadruplex cavity are quite mobile within the central channel and can even enter or exit from the quadruplex core, whereas coordinated K+ ions are quite immobile. MD studies at 400 K indicate that K+ ion cannot come out from the quadruplex core without breaking the terminal G-tetrads. Smaller grooves in antiparallel structures are better binding sites for hydrated counter ions, while a string of hydrogen bonded water molecules are observed within both the small and large grooves. The hydration free energy for the K+ ion coordinated structure is more favourable than that for the Na+ ion coordinated antiparallel quadruplex structure.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.