We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered. Examples include, but are not limited to the Fokker-Planck equation in physics, the Black-Scholes equation and the Hull-White model in finance.

Working towards sustainable solutions requires involving professionals and stakeholders from all sectors of society into research and teaching. This often presents a challenge to scholars at universities, as they lack capacity and time needed for negotiating different agendas, languages, competencies, and cultures among faculty, students, and stakeholders. Management approaches and quality criteria have been developed to cope with this challenge, including concepts of boundary organizations, transdisciplinary research, transition management, and interface management. However, few of these concepts present comprehensive proposals how to facilitate research with stakeholder participation while creating educational opportunities along the lifecycle of a project. The article focuses on the position of a transacademic interface manager (TIM) supporting participatory sustainability research and education efforts. We conceptualize the task portfolio of a TIM; outline the capacities a TIM needs to possess in order to successfully operate; and propose an educational approach for how to train students in becoming a TIM. For this, we review the existing literature on TIMs and present insights from empirical sustainability research and educational projects that involved TIMs in different functions. The article provides practical guidance to universities on how to organize these critical endeavors more effectively and to offer students an additional career perspective.

Jewish observance of shmita (alternatively spelled shemitah)—the sabbatical year, or seventh (sheviit) year—is changing. Historically rooted in agriculture, modern Jewish environmentalists are seizing upon the long-ignored environmental and social justice (tikkun olam) aspects of shmita as originally described in the five books of Moses, the Torah in the Hebrew Bible, the basis of Jewish law. Primary research was conducted through key-stakeholder interviews with leading American and Israeli Jewish environmentalists and thought leaders. They see shmita as a core Jewish value—one that, like Shabbat, the Jewish sabbath, has the power to transform society. Their work has brought shmita from an obscure law dealt with mainly by Israel’s Orthodox to a new Jewish ethos being discussed across the United States, Europe, Israel, and even on the floor of Knesset, Israel’s parliament. This article also describes shmita as delineated in the Torah and through the rabbinic canon of halacha (Jewish law), and explains shmita practice from biblical times to the present day.

International trade networks are manifestations of a complex combination of diverse underlying factors, both natural and social. Here we apply social network analytics to the international trade network of agricultural products to better understand the nature of this network and its relation to patterns of international development. Using a network tool known as triadic analysis we develop triad significance profiles for a series of agricultural commodities traded among countries. Results reveal a novel network “superfamily” combining properties of biological information processing networks and human social networks. To better understand this unique network signature, we examine in more detail the degree and triadic distributions within the trade network by country and commodity. Our results show that countries fall into two very distinct classes based on their triadic frequencies. Roughly 165 countries fall into one class while 18, all highly isolated with respect to international agricultural trade, fall into the other. Only Vietnam stands out as a unique case. Finally, we show that as a country becomes less isolated with respect to number of trading partners, the country's triadic signature follows a predictable trajectory that may correspond to a trajectory of development.

Complexities and uncertainties surrounding urbanization and climate change complicate water resource sustainability. Although research has examined various aspects of complex water systems, including uncertainties, relatively few attempts have been made to synthesize research findings in particular contexts. We fill this gap by examining the complexities, uncertainties, and decision processes for water sustainability and urban adaptation to climate change in the case study region of Phoenix, Arizona. In doing so, we integrate over a decade of research conducted by Arizona State University’s Decision Center for a Desert City (DCDC). DCDC is a boundary organization that conducts research in collaboration with policy makers, with the goal of informing decision-making under uncertainty. Our results highlight: the counterintuitive, non-linear, and competing relationships in human–environment dynamics; the myriad uncertainties in climatic, scientific, political, and other domains of knowledge and practice; and, the social learning that has occurred across science and policy spheres. Finally, we reflect on how our interdisciplinary research and boundary organization has evolved over time to enhance adaptive and sustainable governance in the face of complex system dynamics.

Problem- and project-based learning (PPBL) courses in sustainability address real-world sustainability problems. They are considered powerful educational settings for building students’ sustainability expertise. In practice, however, these courses often fail to fully incorporate sustainability competencies, participatory research education, and experiential learning. Only few studies exist that compare and appraise PPBL courses internationally against a synthesized body of the literature to create an evidence base for designing PPBL courses. This article introduces a framework for PPBL courses in sustainability and reviews PPBL practice in six programs around the world (Europe, North America, Australia). Data was collected through semi-structured qualitative interviews with course instructors and program officers, as well as document analysis. Findings indicate that the reviewed PPBL courses are of high quality and carefully designed. Each PPBL course features innovative approaches to partnerships between the university and private organizations, extended peer-review, and the role of knowledge brokers. Yet, the findings also indicate weaknesses including paucity of critical learning objectives, solution-oriented research methodology, and follow-up research on implementation. Through the comparative design, the study reveals improvement strategies for the identified challenges and provides guidance for design and redesign of PPBL courses.

If sustainability is to be an integral part of rethinking education organization, it is necessary to redesign mental models that shape present curricular structures. Assumptions underlying the design of most schools and curricula are based on linear industrial models, which raises an essential question: How can we use opposite concepts of systems dynamics and living structures to create a shift in our present thinking about curriculum and learning for sustainability? From this, we can begin a dramatic design shift toward innovative curriculum to prepare future students and teachers. This article begins with a critique of modern industrial education, then moves into an overview of sustainability concepts and structure through systems thinking. The article then presents the research of an original sustainability curriculum that structures assessment to measure systems thinking. From the results, the article then explores a conceptual design framework for a 21st century curriculum that bio-mimics living systems and organic molecular structure, based on systems thinking and mechanistic principles. By placing assessment on competency relationships and not solely assignment completion, this new framework encourages students and educators to develop emerging 21st century skills in the age of digital technology and communication. This essay and framework, which emerged from the author’s dissertation research and findings, offers a new conceptual tool to the field of sustainability education while challenging educators to adopt living systems into their own instructional designs.

Educational interventions are a promising way to shift individual behaviors towards Sustainability. Yet, as this research confirms, the standard fare of education, declarative knowledge, does not work. This study statistically analyzes the impact of an intervention designed and implemented in Mexico using the Educating for Sustainability (EfS) framework which focuses on imparting procedural and subjective knowledge about waste through innovative pedagogy. Using data from three different rounds of surveys we were able to confirm (1) the importance of subjective and procedural knowledge for Sustainable behavior in a new context; (2) the effectiveness of the EfS framework and (3) the importance of changing subjective knowledge for changing behavior. While the impact was significant in the short term, one year later most if not all of those gains had evaporated. Interventions targeted at subjective knowledge will work, but more research is needed on how to make behavior change for Sustainability durable.

Human vulnerability to heat varies at a range of spatial scales, especially within cities where there can be noticeable intra-urban differences in heat risk factors. Mapping and visualizing intra-urban heat vulnerability offers opportunities for presenting information to support decision-making. For example the visualization of the spatial variation of heat vulnerability has the potential to enable local governments to identify hot spots of vulnerability and allocate resources and increase assistance to people in areas of greatest need. Recently there has been a proliferation of heat vulnerability mapping studies, all of which, to varying degrees, justify the process of vulnerability mapping in a policy context. However, to date, there has not been a systematic review of the extent to which the results of vulnerability mapping studies have been applied in decision-making. Accordingly we undertook a comprehensive review of 37 recently published papers that use geospatial techniques for assessing human vulnerability to heat. In addition, we conducted an anonymous survey of the lead authors of the 37 papers in order to establish the level of interaction between the researchers as science information producers and local authorities as information users. Both paper review and author survey results show that heat vulnerability mapping has been used in an attempt to communicate policy recommendations, raise awareness and induce institutional networking and learning, but has not as yet had a substantive influence on policymaking or preventive action.

The purpose of the United Nations-guided process to establish Sustainable Development Goals is to galvanize governments and civil society to rise to the interlinked environmental, societal, and economic challenges we face in the Anthropocene. We argue that the process of setting Sustainable Development Goals should take three key aspects into consideration. First, it should embrace an integrated social-ecological system perspective and acknowledge the key dynamics that such systems entail, including the role of ecosystems in sustaining human wellbeing, multiple cross-scale interactions, and uncertain thresholds. Second, the process needs to address trade-offs between the ambition of goals and the feasibility in reaching them, recognizing biophysical, social, and political constraints. Third, the goal-setting exercise and the management of goal implementation need to be guided by existing knowledge about the principles, dynamics, and constraints of social change processes at all scales, from the individual to the global. Combining these three aspects will increase the chances of establishing and achieving effective Sustainable Development Goals.