Phase turbulence in the Complex Ginzburg--Landau equation via Kuramoto--Sivashinsky phase dynamics

We study the Complex Ginzburg--Landau initial value problem $\partial_t u=(1+i\alpha) \partial_x^2 u + u - (1+i\beta) u |u|^2$, $u(x,0)=u_0(x)$ for a complex field $u\in{\bf C}$, with $\alpha,\beta\in{\bf R}$. We consider the Benjamin--Feir linear instability region $1+\alpha\beta=-\epsilon^2$ with $\epsilon\ll1$ and $\alpha^2<1/2$. We show that for all $\epsilon\leq{\cal O}(\sqrt{1-2\alpha^2} L_0^{-32/37})$, and for all initial data $u_0$ sufficiently close to 1 (up to a global phase factor \ed^{i \phi_0}, \phi_0\in{\bf R}) in the appropriate space, there exists a unique (spatially) periodic solution of space period $L_0$. These solutions are small {\em even} perturbations of the traveling wave solution, u=(1+\alpha^2 s) \ed^{i \phi_0-i\beta t} \ed^{i\alpha \eta}, and $s,\eta$ have bounded norms in various \L^p and Sobolev spaces. We prove that $s\approx-{1/2} \eta''$ apart from ${\cal O}(\epsilon^2)$ corrections whenever the initial data satisfy this condition, and that in the linear instability range $L_0^{-1}\leq\epsilon\leq{\cal O}(L_0^{-32/37})$, the dynamics is essentially determined by the motion of the phase alone, and so exhibits `phase turbulence'. Indeed, we prove that the phase $\eta$ satisfies the Kuramoto--Sivashinsky equation $\partial_t\eta= -\bigl({\textstyle\frac{1+\alpha^2}{2}}\bigr) \triangle^2\eta -\epsilon^2\triangle\eta -{(1+\alpha^2)} (\eta')^2$ for times $t_0\leq{\cal O}(\epsilon^{-52/5} L_0^{-32/5})$, while the amplitude $1+\alpha^2 s$ is essentially constant

Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies

I introduce an approximation scheme that allows to deduce differential equations for the renormalization group $\beta$-function from a Schwinger--Dyson equation for the propagator. This approximation is proven to give the dominant asymptotic behavior of the perturbative solution. In the supersymmetric Wess--Zumino model and a $\phi^3_6$ scalar model which do not have divergent vertex functions, this simple Schwinger--Dyson equation for the propagator captures the main quantum corrections.Comment: Clarification of the presentation of results. Equations and results unchanged. Match the published version. 12 page

Is Management Interdisciplinary? The Evolution of Management as an Interdisciplinary Field of Research and Education in the Netherlands

Management research and education are often characterized as being interdisciplinary. However, most discussions on what interdisciplinarity in management studies means have bogged down in ideological fixations. In this paper we alternatively take a historical perspective and analyze the evolution of the interdisciplinarity concept in management studies during the last decades in the Netherlands. We distinguish between two opposite versions of interdisciplinarity: a synoptic (conceptual) and an instrumental (pragmatic) one. Both versions resulted from different knowledge strategies (boundary-work) of competing and cooperating disciplines. We conclude that in the Netherlands instrumental versions of interdisciplinarity in management research and education prevailed.management science;Interdisciplinarity;disciplinarity;management education;history of management education

Social welfare effects of tax-benefit reform under endogenous participation and unemployment

This paper analyzes the effects of tax-benefit reforms in a framework integrating endogenous labor supply and unemployment. There is a discrete distribution of individuals’ productivities and labor supply decisions are limited to the participation decision. Unemployment is modeled in a search and matching framework with individual wage bargaining. We adopt an ordinal approach to social welfare comparisons and explore numerically various reform policies. For Switzerland, a participation income is shown to be an “uncontroversial” tax reform, improving social welfare according to any social welfare criterion displaying inequality aversion.

Asymptotics of solutions in nA+nB->C reaction Diffusion systems

We analyze the long time behavior of initial value problems that model a process where particles of type A and B diffuse in some substratum and react according to $nA+nB\to C$. The case n=1 has been studied before; it presents nontrivial behavior on the reactive scale only. In this paper we discuss in detail the cases $n>3$, and prove that they show nontrivial behavior on the reactive and the diffusive length scale.Comment: 22 pages, 1 figur

Effects of pharmaceutical wastes on growth of microalgae

The purpose of this work was to assay samples of waste material from Puerto Rican pharmaceutical industries for inhibition of growth of algae. Two samples (noted as I and II) supplied to us were tested for toxicity to six microalgae. The test organisms, two blue-green algae, two green algae, and two diatoms [r]epresent three major divisions of algae.University of Texas Marine Science InstituteMarine Scienc

Phase Turbulence in the Complex Ginzburg-Landau Equation via Kuramoto-Sivashinsky Phase Dynamics

Abstract:: We study the Complex Ginzburg-Landau initial value problem for a complex field u ∈ C, with α,β∈R. We consider the Benjamin-Feir linear instability region We show that for all and for all initial data u 0 sufficiently close to 1 (up to a global phase factor e iφ 0 ,φ0∈R) in the appropriate space, there exists a unique (spatially) periodic solution of space period L 0 . These solutions are small even perturbations of the traveling wave solution, and s,η have bounded norms in various L p and Sobolev spaces. We prove that apart from corrections whenever the initial data satisfy this condition, and that in the linear instability range the dynamics is essentially determined by the motion of the phase alone, and so exhibits ‘phase turbulence'. Indeed, we prove that the phase η satisfies the Kuramoto-Sivashinsky equation for times while the amplitude 1+α2 s is essentially constan

Associated factors of hope in cancer patients during treatment : a systematic literature review

Aim: To identify the associated factors of hope during treatment in cancer patients. Background: Hope is very important to cancer patients at all stages of the disease process. Hope is seen as an important coping mechanism. Most research about hope in cancer patients considered the end of life or in palliative care. Several and different factors are associated with hope. It is not yet sufficiently clear which factors are associated with hope during the treatment. Design: A systematic literature review of quantitative empirical studies on hope in cancer patients during treatment. Data Sources: Search in MEDLINE (PubMed interface), CINAHL (EBSCO interface), Psychinfo and Cochrane (January 2009-December 2018). Review Methods: Empirical quantitative studies were included regardless of the disease stage, written in English or Dutch, measuring hope from the perspective of cancer patients. Two authors independently screened all the studies and assessed their quality. Results: Thirty-three studies were included. Positive relationship has been established between hope and quality of life, social support, spiritual and existential well-being. Hope appears to be negatively associated with symptom burden, psychological distress and depression. There appears to be no relationship between hope and demographic and clinical variables. The relationship between anxiety and hope remains unclear. Conclusions: Hope primarily seems to be a process that takes place in a person's inner being rather than being determined from outside. Impact: Health professionals may want to focus on the meaning of hope for cancer patients in relation to the associated factors. A better understanding of the meaning of hope during treatment can be of great value in supporting cancer patients with regard to treatment decisions, psychosocial support, the experienced quality of life and symptom burden and any wishes they may have with regard to advanced care planning