f Gravity and gravitational singularities

TRAUTMAN has postulated1 that the usual space−time singularity occurring in classical cosmological models and in the gravitational collapse of massive objects could be averted if intrinsic spin effects are incorporated into general relativity by adding torsion terms to the usual Einstein field equations, that is through the Einstein−Cartan theory. Invoking a primordial magnetic field for aligning all the individual nuclear spins he shows that his universe consisting of 1080 aligned neutrons collapses to a minimum radius of the order of 1 cm with a corresponding matter density of 1055 g cm-3.

f Gravity and gravitational singularities

TRAUTMAN has postulated1 that the usual space−time singularity occurring in classical cosmological models and in the gravitational collapse of massive objects could be averted if intrinsic spin effects are incorporated into general relativity by adding torsion terms to the usual Einstein field equations, that is through the Einstein−Cartan theory. Invoking a primordial magnetic field for aligning all the individual nuclear spins he shows that his universe consisting of 1080 aligned neutrons collapses to a minimum radius of the order of 1 cm with a corresponding matter density of 1055 g cm-3.

Non-diffusive classical transport in a medium with static randomness

The probability distribution for the displacement x of a particle moving in a one-dimensional continuum is derived exactly for the general case of combined static and dynamic gaussian randomness of the applied force. The dynamics of the particle is governed by the high-friction limit of Brownian motion discussed originally by Einstein and Smoluchowski. In particular, the mean square displacement of the particle varies as t2 for t to infinity . This ballistic motion induced by the disorder does not give rise to a 1/f power spectrum, contrary to recent suggestions based on the above dynamical model.

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (R-g) varies as N-1/3, the self-diffusion constant (D) scales, surprisingly, as N-alpha, with alpha=0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

Magneto-transport and optical properties of diluted magnetic semiconductor Ga1-xMnxSb

We have studied magneto-transport and optical properties of Ga1-xMnxSb crystals (x = 0.01, 0.02, 0.03 and 0.04) grown by horizontal Bridgman method. Negative magnetoresistance and anomalous Hall effect have been observed below 10K. Temperature dependence of magnetization measurement shows a magnetic ordering below 10K which could arise from Ga1-xMnxSb alloy formation. Also, saturation in magnetization observed even at room temperature suggests the existence of ferromagnetic MnSb clusters. Reduction in band gap is observed with increasing Mn concentration in the crystals. Temperature dependence of band gap follows Bose-Einstein's model.

Splitting Algorithms for Fast Relay Selection: Generalizations, Analysis, and a Unified View

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new contention load' parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q >= 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

Selection of intrusion detection system threshold bounds for effective sensor fusion

The motivation behind the fusion of Intrusion Detection Systems was the realization that with the increasing traffic and increasing complexity of attacks, none of the present day stand-alone Intrusion Detection Systems can meet the high demand for a very high detection rate and an extremely low false positive rate. Multi-sensor fusion can be used to meet these requirements by a refinement of the combined response of different Intrusion Detection Systems. In this paper, we show the design technique of sensor fusion to best utilize the useful response from multiple sensors by an appropriate adjustment of the fusion threshold. The threshold is generally chosen according to the past experiences or by an expert system. In this paper, we show that the choice of the threshold bounds according to the Chebyshev inequality principle performs better. This approach also helps to solve the problem of scalability and has the advantage of failsafe capability. This paper theoretically models the fusion of Intrusion Detection Systems for the purpose of proving the improvement in performance, supplemented with the empirical evaluation. The combination of complementary sensors is shown to detect more attacks than the individual components. Since the individual sensors chosen detect sufficiently different attacks, their result can be merged for improved performance. The combination is done in different ways like (i) taking all the alarms from each system and avoiding duplications, (ii) taking alarms from each system by fixing threshold bounds, and (iii) rule-based fusion with a priori knowledge of the individual sensor performance. A number of evaluation metrics are used, and the results indicate that there is an overall enhancement in the performance of the combined detector using sensor fusion incorporating the threshold bounds and significantly better performance using simple rule-based fusion.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

On the compactness of isometry groups in complex analysis

We prove that the group of continuous isometries for the Kobayashi or Caratheodory metrics of a strongly convex domain in C-n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuk's rescaling technique gives the main result.

Locant: A nature inspired location service for ad hoc networks

An efficient location service is a prerequisite to any robust, effective and precise location information aided Mobile Ad Hoc Network (MANET) routing protocol. Locant, presented in this paper is a nature inspired location service which derives inspiration from the insect colony framework, and it is designed to work with a host of location information aided MANET routing protocols. Using an extensive set of simulation experiments, we have compared the performance of Locant with RLS, SLS and DLS, and found that it has comparable or better performance compared to the above three location services on most metrics and has the least overhead in terms of number of bytes transmitted per location query answered.

Design and analysis of rate aware ad hoc 802.11 networks

802.11 WLANs are characterized by high bit error rate and frequent changes in network topology. The key feature that distinguishes WLANs from wired networks is the multi-rate transmission capability, which helps to accommodate a wide range of channel conditions. This has a significant impact on higher layers such as routing and transport levels. While many WLAN products provide rate control at the hardware level to adapt to the channel conditions, some chipsets like Atheros do not have support for automatic rate control. We first present a design and implementation of an FER-based automatic rate control state machine, which utilizes the statistics available at the device driver to find the optimal rate. The results show that the proposed rate switching mechanism adapts quite fast to the channel conditions. The hop count metric used by current routing protocols has proven itself for single rate networks. But it fails to take into account other important factors in a multi-rate network environment. We propose transmission time as a better path quality metric to guide routing decisions. It incorporates the effects of contention for the channel, the air time to send the data and the asymmetry of links. In this paper, we present a new design for a multi-rate mechanism as well as a new routing metric that is responsive to the rate. We address the issues involved in using transmission time as a metric and presents a comparison of the performance of different metrics for dynamic routing.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

A singularity-free cosmological model in ECSK theory

In the framework of the ECSK [Einstein-Cartan-Sciama-Kibble] theory of cosmology, a scalar field nonminimally coupled to the gravitational field is considered. For a Robertson-Walker open universe (k=0) in the radiation era, the field equations admit a singularity-free solution for the scale factor. In theory, the torsion is generated through nonminimal coupling of a scalar field to the gravitation field. The nonsingular nature of the cosmological model automatically solves the flatness problem. Further absence of event horizon and particle horizon explains the high degree of isotropy, especially of 2.7-K background radiation.