The Boltzmann collision integrals for a combination of Maxwellians

The gain and loss integrals in the Boltzmann equation for a rigid sphere gas are evaluated in closed form for a distribution which can be expressed as a linear combination of Maxwellians. Application to the Mott-Smith bimodal distribution shows that the gain is also bimodal, but the two modes in the gain are less pronounced than in the distribution. Implications of these results for simple collision models in non-equilibrium flow are discussed.

The collective dynamics of self-propelled particles

We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p, whose locomotion is driven by the action of a force dipole Sp of constant magnitude S0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force Fp to effect propulsion. The magnitude F0 of this force is proportional to S0. The directions of Sp and Fp are determined by p. In isolation, a self-propelled particle moves at a constant velocity u0 p, with the speed u0 determined by S0. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φa. We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φa are qualitatively different; it is close to the normal distribution at high φa, in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φa. The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

Environment Education for Ecosystem Conservation

Conservation of natural resources through sustainable ecosystem management and development is the key to our secured future. The management of ecosystem involves inventorying and monitoring, and applying integrated technologies, methodologies and interdisciplinary approaches for its conservation. Hence, now it is even more critical than ever before for the humans to be environmentally literate. To realise this vision, both ecological and environmental education must become a fundamental part of the education system at all levels of education. Currently, it is even more critical than ever before for the humankind as a whole to have a clear understanding of environmental concerns and to follow sustainable development practices. The degradation of our environment is linked to continuing problems of pollution, loss of forest, solid waste disposal, and issues related to economic productivity and national as well as ecological security. Environmental management has gained momentum in the recent years with the initiatives focussing on managing environmental hazards and preventing possible disasters. Environmental issues make better sense, when one can understand them in the context of one’s own cognitive sphere. Environmental education focusing on real-world contexts and issues often begins close to home, encouraging learners to understand and forge connections with their immediate surroundings. The awareness, knowledge, and skills needed for these local connections and understandings provide a base for moving out into larger systems, broader issues, and a more sophisticated comprehension of causes, connections, and consequences. Environmental Education Programme at CES in collaboration with Karnataka Environment Research Foundation (KERF) referred as ‘Know your Ecosystem’ focuses on the importance of investigating the ecosystems within the context of human influences, incorporating an examination of ecology, economics, culture, political structure, and social equity as well as natural processes and systems. The ultimate goal of environment education is to develop an environmentally literate public. It needs to address the connection between our conception and practice of education and our relationship as human cultures to life-sustaining ecological systems. For each environmental issue there are many perspectives and much uncertainty. Environmental education cultivates the ability to recognise uncertainty, envision alternative scenarios, and adapt to changing conditions and information. These knowledge, skills, and mindset translate into a citizenry who is better equipped to address its common problems and take advantage of opportunities, whether environmental concerns are involved or not.

Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

On a Novel Geometric Representation of Rotation

This paper presents a novel method of representing rotation and its application to representing the ranges of motion of coupled joints in the human body, using planar maps. The present work focuses on the viability of this representation for situations that relied on maps on a unit sphere. Maps on a unit sphere have been used in diverse applications such as Gauss map, visibility maps, axis-angle and Euler-angle representations of rotation etc. Computations on a spherical surface are difficult and computationally expensive; all the above applications suffer from problems associated with singularities at the poles. There are methods to represent the ranges of motion of such joints using two-dimensional spherical polygons. The present work proposes to use multiple planar domain “cube” instead of a single spherical domain, to achieve the above objective. The parameterization on the planar domains is easy to obtain and convert to spherical coordinates. Further, there is no localized and extreme distortion of the parameter space and it gives robustness to the computations. The representation has been compared with the spherical representation in terms of computational ease and issues related to singularities. Methods have been proposed to represent joint range of motion and coupled degrees of freedom for various joints in digital human models (such as shoulder, wrist and fingers). A novel method has been proposed to represent twist in addition to the existing swing-swivel representation.

Environment Education for Ecosystem Conservation

Conservation of natural resources through sustainable ecosystem management and development is the key to our secured future. The management of ecosystem involves inventorying and monitoring, and applying integrated technologies, methodologies and interdisciplinary approaches for its conservation. Hence, now it is even more critical than ever before for the humans to be environmentally literate. To realise this vision, both ecological and environmental education must become a fundamental part of the education system at all levels of education. Currently, it is even more critical than ever before for the humankind as a whole to have a clear understanding of environmental concerns and to follow sustainable development practices. The degradation of our environment is linked to continuing problems of pollution, loss of forest, solid waste disposal, and issues related to economic productivity and national as well as ecological security. Environmental management has gained momentum in the recent years with the initiatives focussing on managing environmental hazards and preventing possible disasters. Environmental issues make better sense, when one can understand them in the context of one’s own cognitive sphere. Environmental education focusing on real-world contexts and issues often begins close to home, encouraging learners to understand and forge connections with their immediate surroundings. The awareness, knowledge, and skills needed for these local connections and understandings provide a base for moving out into larger systems, broader issues, and a more sophisticated comprehension of causes, connections, and consequences. Environmental Education Programme at CES in collaboration with Karnataka Environment Research Foundation (KERF) referred as ‘Know your Ecosystem’ focuses on the importance of investigating the ecosystems within the context of human influences, incorporating an examination of ecology, economics, culture, political structure, and social equity as well as natural processes and systems. The ultimate goal of environment education is to develop an environmentally literate public. It needs to address the connection between our conception and practice of education and our relationship as human cultures to life-sustaining ecological systems. For each environmental issue there are many perspectives and much uncertainty. Environmental education cultivates the ability to recognise uncertainty, envision alternative scenarios, and adapt to changing conditions and information. These knowledge, skills, and mindset translate into a citizenry who is better equipped to address its common problems and take advantage of opportunities, whether environmental concerns are involved or not.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), non-orthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the OAF and NAF protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. In the two-relay case, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known static protocol for higher values of multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays.

Possible Neutrino-Antineutrino Oscillation Under Gravity and its Consequences

We show that under gravity the effective masses for neutrino and antineutrino are different which opens a possible window of neutrino-antineutrino oscillation even if the rest masses of the corresponding eigenstates are same. This is due to CPT violation and possible to demonstrate if the neutrino mass eigenstates are expressed as a combination of neutrino and antineutrino eigenstates, as of the neutral kaon system, with the plausible breaking of lepton number conservation. In early universe, in presence of various lepton number violating processes, this oscillation might lead to neutrino-antineutrino asymmetry which resulted baryogenesis from the B-L symmetry by electro-weak sphaleron processes. On the other hand, for Majorana neutrinos, this oscillation is expected to affect the inner edge of neutrino dominated accretion disks around a compact object by influencing the neutrino sphere which controls the accretion dynamics, and then the related type-II supernova evolution and the r-process nucleosynthesis.

A family of Runge-Kutta based explicit methods for rotational dynamics

The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.

Environment Education for Ecosystem Conservation

Conservation of natural resources through sustainable ecosystem management and development is the key to our secured future. The management of ecosystem involves inventorying and monitoring, and applying integrated technologies, methodologies and interdisciplinary approaches for its conservation. Hence, now it is even more critical than ever before for the humans to be environmentally literate. To realise this vision, both ecological and environmental education must become a fundamental part of the education system at all levels of education. Currently, it is even more critical than ever before for the humankind as a whole to have a clear understanding of environmental concerns and to follow sustainable development practices. The degradation of our environment is linked to continuing problems of pollution, loss of forest, solid waste disposal, and issues related to economic productivity and national as well as ecological security. Environmental management has gained momentum in the recent years with the initiatives focussing on managing environmental hazards and preventing possible disasters. Environmental issues make better sense, when one can understand them in the context of one’s own cognitive sphere. Environmental education focusing on real-world contexts and issues often begins close to home, encouraging learners to understand and forge connections with their immediate surroundings. The awareness, knowledge, and skills needed for these local connections and understandings provide a base for moving out into larger systems, broader issues, and a more sophisticated comprehension of causes, connections, and consequences. Environmental Education Programme at CES in collaboration with Karnataka Environment Research Foundation (KERF) referred as ‘Know your Ecosystem’ focuses on the importance of investigating the ecosystems within the context of human influences, incorporating an examination of ecology, economics, culture, political structure, and social equity as well as natural processes and systems. The ultimate goal of environment education is to develop an environmentally literate public. It needs to address the connection between our conception and practice of education and our relationship as human cultures to life-sustaining ecological systems. For each environmental issue there are many perspectives and much uncertainty. Environmental education cultivates the ability to recognise uncertainty, envision alternative scenarios, and adapt to changing conditions and information. These knowledge, skills, and mindset translate into a citizenry who is better equipped to address its common problems and take advantage of opportunities, whether environmental concerns are involved or not.

A Low ML-Decoding Complexity, Full-Diversity, Full-Rate MIMO Precoder

Precoding for multiple-input multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For two transmit antennas and QAM constellations, a real-valued precoder which is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for two transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E - d(min) precoder for 4-QAM by Vrigneau et al. which is an extension of the complex-valued optimal precoder for 4-QAM. The proposed precoder's ML-decoding complexity as a function of the constellation size M is only O(root M)while that of the E - d(min) precoder is O(M root M)(M = 4). Compared to the recently proposed X- and Y-precoders, the error performance of the proposed precoder is significantly better while being only marginally worse than that of the E - d(min) precoder for 4-QAM. It is argued that the proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 x 2, 4 x 4 and 8 x 8 systems.

3D Acoustic Analysis Of Spherical Chamber Having Single Inlet And Multiple Outlet: An Impedance Matrix Approach

The transmission loss (TL) performance of spherical chambers having single inlet and multiple outlet is obtained analytically through modal expansion of acoustic field inside the spherical cavity in terms of the spherical Bessel functions and Legendre polynomials. The uniform piston driven model based upon the impedance [Z] matrix is used to characterize the multi-port spherical chamber. It is shown analytically that the [Z] parameters are independent of the azimuthal angle (phi) due to the axisymmetric shape of the sphere; rather, they depend only upon the polar angle (theta) and radius of the chamber R(0). Thus, the effects of relative polar angular location of the ports and number of outlet ports are investigated. The analytical results are shown to be in good agreement with the 3D FEA results, thereby validating the procedure suggested in this work.

Structure of DNA-functionalized dendrimer nanoparticles

Atomistic molecular dynamics simulations have been carried out to reveal the characteristic features of ethylenediamine (EDA) cored protonated (corresponding to neutral pH) poly amido amine (PAMAM) dendrimers of generation 3 (G3) and 4 (G4) that are functionalized with single strand DNAs (ssDNAs). The four ssDNA strands that are attached via an alkythiolate [-S(CH(2))(6)-] linker molecule to the free amine groups on the surface of the PAMAM dendrimers are observed to undergo a rapid conformational change during the 25 ns long simulation period. From the RMSD values of ssDNAs, we find relative stability in the case of purine rich (having more adenine and guanine) ssDNA strands than pyrimidine rich (thymine and cytosine) ssDNA strands. The degree of wrapping of ssDNA strands on the dendrimer molecule was found to be influenced by the charge ratio of DNA and the dendrimer. As the G4 dendrimer contains relatively more positive charge than G3 dendrimer, we observe extensive wrapping of ssDNAs on the G4 dendrimer than G3 dendrimer. This might indicate that DNA functionalized G3 dendrimer is more suitable to construct higher order nanostructures. The linker molecule was also found to undergo drastic conformational change during the simulation. During nanosecond long simulation some portion of the linker molecule was found to be lying nearly flat on the surface of the dendrimer molecule. The ssDNA strands along with the linkers are seen to penetrate the surface of the dendrimer molecule and approach closer to the center of the dendrimer indicating the soft sphere nature of the dendrimer molecule. The effective radius of DNA-functionalized dendrimer nanoparticles was found to be independent of base composition of ssDNAs and was observed to be around 19.5 angstrom and 22.4 angstrom when we used G3 and G4 PAMAM dendrimers as the core of the nanoparticle respectively. The observed effective radius of DNA-functionalized dendrimer molecules apparently indicates the significant shrinkage in the structure that has taken place in dendrimer, linker and DNA strands. As a whole our results describe the characteristic features of DNA-functionalized dendrimer nanoparticles and can be used as strong inputs to design effectively the DNA-dendrimer nanoparticle self-assembly for their active biological applications.

A Monoclonal Antibody against Human Notch1 Ligand-Binding Domain Depletes Subpopulation of Putative Breast Cancer Stem-like Cells

Overexpression of Notch receptors and ligands has been associated with various cancers and developmental disorders, making Notch a potential therapeutic target. Here, we report characterization of Notch1 monoclonal antibodies (mAb) with therapeutic potential. The mAbs generated against epidermal growth factor (EGF) repeats 11 to 15 inhibited binding of Jagged1 and Delta-like4 and consequently, signaling in a dose-dependent manner, the antibodies against EGF repeats 11 to 12 being more effective than those against repeats 13 to 15. These data emphasize the role of EGF repeats 11 to 12 in ligand binding. One of the mAbs, 602.101, which specifically recognizes Notch1, inhibited ligand-dependent expression of downstream target genes of Notch such as HES-1, HES-5, and HEY-L in the breast cancer cell line MDA-MB-231. The mAb also decreased cell proliferation and induced apoptotic cell death. Furthermore, exposure to this antibody reduced CD44(Hi)/CD24(Low) subpopulation in MDA-MB-231 cells, suggesting a decrease in the cancer stem-like cell subpopulation. This was confirmed by showing that exposure to the antibody decreased the primary, secondary, and tertiary mammosphere formation efficiency of the cells. Interestingly, effect of the antibody on the putative stem-like cells appeared to be irreversible, because the mammosphere-forming efficiency could not be salvaged even after antibody removal during the secondary sphere formation. The antibody also modulated expression of genes associated with stemness and epithelial-mesenchymal transition. Thus, targeting individual Notch receptors by specific mAbs is a potential therapeutic strategy to reduce the potential breast cancer stem-like cell subpopulation. Mol Cancer Ther; 11(1); 77-86. (C) 2011 AACR.