Interacting partially directed self avoiding walk. From phase transition to the geometry of the collapsed phase

In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by $\beta$ and $f$, respectively. The IPDSAW is known to undergo a collapse transition at $\beta_c$. We provide the precise asymptotic of the free energy close to criticality, that is we show that $f(\beta_c-\epsilon)\sim \gamma \epsilon^{3/2}$ where $\gamma$ is computed explicitly and interpreted in terms of an associated continuous model. We also establish some path properties of the random walk inside the collapsed phase $(\beta>\beta_c)$. We prove that the geometric conformation adopted by the polymer is made of a succession of long vertical stretches that attract each other to form a unique macroscopic bead, we identify the horizontal extension of the random walk inside the collapsed phase and we establish the convergence of the rescaled envelope of the macroscopic bead towards a deterministic Wulff shape.Comment: Accepted for publication in the Annals of Probabilit

Research on the Application of E-commerce to Small and Medium Enterprises (SMEs): the Case of India

SMEs account for a large proportion and play an important role in the development of each country in the world, including India. The globalization will bring many advantages for enterprises however SMEs will face fierce competition at the local, national and International level. In order to maintain and promote the important role of SMEs in the context of increased competition, SMEs have to change and adopt new technologies. E-commerce and digital technologies are bringing opportunities to help SMEs improve their competitiveness, narrow the gap with big enterprises thanks to their fairness and flexibility of the digital business environment.       According to UNIDO (2017), India is one of the countries successfully applying e-commerce to SMEs. Contributing to this success is the important role of the Indian government. Therefore, this paper focuses on researching the application of e-commerce to SMEs in terms of the role of government in promoting and creating an ecosystem for SMEs and e-commerce development

Internal branding in universities and the lessons learnt from the past: the significance of employee brand support and transformational leadership

The paper reviews the literature on the concept of internal branding and its effects in the service sector in general, as well as in UK universities. In addition, the concept of employee brand support is reviewed, discussing the influence of leadership characteristics on internal branding in universities. Employee brand support is a crucial element to successful internal branding activities. A great concern is that the knowledge of internal branding and employee brand support in higher education institutions is based on knowledge imported from the business sector, and more practices should thus be adapted and implemented. It is found that transformation leadership, despite being little researched in the internal branding context, remains the pivotal element to the successful implementation of internal branding, as transformational leadership provides space for intellectual stimulation and consideration of individuals that are present at universities. Potential future research areas for internal branding studies are identified and discussed

Towards a branding oriented higher education sector: an overview of the four perspectives on university marketing studies

The paper provides a background to the discussion of the evolution and influence of marketing and brand management within UK universities. Four perspectives are considered, namely, marketing management in universities, branding in universities, corporate branding in universities and internal branding. The discussion suggests that higher education institutions are encouraged on all sides to become more market oriented. Private universities, which may be more dependent upon tuition fees (since they receive less funding from the government), appear to be ahead of public universities in using the initiatives in internal brand communication. Employees need to understand the brand values, in order to align their attitudes and behaviour in support of the corporate brand. Although internal branding has become important for universities in increasingly competitive markets, it is still recognised as a new phenomenon and therefore more research is encouraged in this area

Origin of conductivity cross over in entangled multi-walled carbon nanotube network filled by iron

A realistic transport model showing the interplay of the hopping transport between the outer shells of iron filled entangled multi-walled carbon nanotubes (MWNT) and the diffusive transport through the inner part of the tubes, as a function of the filling percentage, is developed. This model is based on low-temperature electrical resistivity and magneto-resistance (MR) measurements. The conductivity at low temperatures showed a crossover from Efros-Shklovski (E-S) variable range hopping (VRH) to Mott VRH in 3 dimensions (3D) between the neighboring tubes as the iron weight percentage is increased from 11% to 19% in the MWNTs. The MR in the hopping regime is strongly dependent on temperature as well as magnetic field and shows both positive and negative signs, which are discussed in terms of wave function shrinkage and quantum interference effects, respectively. A further increase of the iron percentage from 19% to 31% gives a conductivity crossover from Mott VRH to 3D weak localization (WL). This change is ascribed to the formation of long iron nanowires at the core of the nanotubes, which yields a long dephasing length (e.g. 30 nm) at the lowest measured temperature. Although the overall transport in this network is described by a 3D WL model, the weak temperature dependence of inelastic scattering length expressed as L_phi ~T^-0.3 suggests the possibility for the presence of one-dimensional channels in the network due to the formation of long Fe nanowires inside the tubes, which might introduce an alignment in the random structure.Comment: 29 pages,10 figures, 2 tables, submitted to Phys. Rev.

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.Comment: 5 pages, 4 figure

Magnetoresistance in semiconductor structures with hopping conductivity: effects of random potential and generalization for the case of acceptor states

We reconsider the theory of magnetoresistance in hopping semiconductors. First, we have shown that the random potential of the background impurities affects significantly preexponential factor of the tunneling amplitude which becomes to be a short-range one in contrast to the long-range one for purely Coulomb hopping centers. This factor to some extent suppresses the negative interference magnetoresistance and can lead to its decrease with temperature decrease which is in agreement with earlier experimental observations. We have also extended the theoretical models of positive spin magnetoresistance, in particular, related to a presence of doubly occupied states (corresponding to the upper Hubbard band) to the case of acceptor states in 2D structures. We have shown that this mechanism can dominate over classical wave-shrinkage magnetoresistance at low temperatures. Our results are in semi-quantitative agreement with experimental data.Comment: 19 pages, 3 figure

SLE_k: correlation functions in the coefficient problem

We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for special values of kappa in the whole-plane Schramm-Loewner evolution (SLE_kappa). We propose to use multi-point correlation functions for the study of higher moments in coefficient problem. Generalizations related to the Levy-type processes are also considered. The exact multifractal spectrum of considered version of the whole-plane SLE_kappa is discussed

Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex

This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We show that the faces of $Ax$ are contained in the set of all weak$^*$ convergent limits of bounded nets of the operator at nearby points of $x$, then we obtain a representation for $Ax$ by use of this set. In addition, representations for the support function of $Ax$ based on the minimal-norm selection of the operator in certain Banach spaces are given.Comment: Comments are welcome