Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results

Management: thesis, antithesis, synthesis

Increasingly, managers live in a world of paradox. For instance, they are told that they must manage by surrendering control and that they must stay on top by continuing to learn, thus admitting that they do not fully know what they do. Paradox is becoming increasingly pervasive in and around organizations, increasing the need for an approach to management that allows both researchers and practitioners to address these paradoxes. A synthesis is required between such contradictory forces as efficiency and effectiveness, planning and action, and structure and freedom. A dialectical view of strategy and organizations, built from four identifiable principles of simultaneity, locality, minimality and generality, enables us to build the tools to achieve such synthesis. Put together, these principles offer new perspectives for researchers to look at management phenomena and provide practitioners with a means of addressing the increasingly paradoxical world that they confront.dialectics, improvisation, paradox, synthesis

STRUCTURING FOR GLOCALIZATION: THE MINIMAL NETWORK

Globalization and localization seem to be opposite concepts – a thesis and its antithesis. Nonetheless, managers seem to be able to handle the paradox posed by these two contradicting tensions by enacting, via action, a synthesis that allows for the co-presence of a high level of global integration and local adaptation (instead of a compromise between both), which has been labeled glocalization. We discuss how the concept of improvisation allows this synthesis by developing the two poles that ground it, namely ‘glocal’ strategy and ‘glocal’ organization. Global advantage requires a dialectical capability that organizations rarely achieve, and the importance of which orthodox management theory rarely recognizes. JEL codes:

Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\upsilon l^{-\eta}. In addition to the well-known universal (disorder-independent) power-law exponent \eta=2, we find interesting universal features displayed by the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3, otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and statistics, references added, published versio

FLOW AROUND MODIFIED CIRCULAR CILYNDERS

The flow around a circular cylinder has awaken the attention of different researchers since the historic Strouhal's work of 1878. Ever since, many experimental and numeric works have been carried out in order to determine the relationship between the vortex shedding frequency and the flow regime. Recently, a number of studies have been developed using several small modifications in circular cylinder. In this work a circular cylinder modified with a longitudinal concave notch, has been tested in order to determine the relationship between the non-dimensional vortex shedding frequency (Strouhal number) and the Reynolds number has been determined to Reynolds up to 600. Additionally a modified circular cylinder with a longitudinal slit also has been tested in order to determine the Strouhal-Reynolds relationship in several attack angle configurations. The experiments have been carried out in a vertical low turbulence hydrodynamic tunnel with 146x146x500 mm of test section operating in continuous mode. Flow visualization by direct liquid dye injection has been utilized in order to produce vortex images. These images have been captured in still chemical photography for different Reynolds numbers. A hot-film probe has been adequately positioned in the vortex wake to determine the vortex shedding frequency and consequently the Strouhal number

Another analytic view about quantifying social forces

Montroll had considered a Verhulst evolution approach for introducing a notion he called "social force", to describe a jump in some economic output when a new technology or product outcompetes a previous one. In fact, Montroll's adaptation of Verhulst equation is more like an economic field description than a "social force". The empirical Verhulst logistic function and the Gompertz double exponential law are used here in order to present an alternative view, within a similar mechanistic physics framework. As an example, a "social force" modifying the rate in the number of temples constructed by a religious movement, the Antoinist community, between 1910 and 1940 in Belgium is found and quantified. Practically, two temple inauguration regimes are seen to exist over different time spans, separated by a gap attributed to a specific "constraint", a taxation system, but allowing for a different, smooth, evolution rather than a jump. The impulse force duration is also emphasized as being better taken into account within the Gompertz framework. Moreover, a "social force" can be as here, attributed to a change in the limited need/capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already existing but competing goods as imagined by Montroll.Comment: 4 figures, 29 refs., 15 pages; prepared for Advances in Complex System

On the extra phase correction to the semiclassical spin coherent-state propagator

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.Comment: 19 pages, no figures; a more general treatment is presented, some references are added, title is slightly changed; submitted to JM