Narrow Results

In this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equation and the associated linearized Cahn–Hilliard (C-H) model (also Kuramoto–Sivashinsky equation), formulated in the spatiotemporal quarter-plane. Such models are of relevance to heat-mass transfer phenomena, solid-fluid dynamics and the applied sciences. In particular, we derive formally effective solution representations, justifying a posteriori their validity. This includes the reconstruction of the prescribed initial and boundary data, which requires careful analysis of the various integral terms appearing in the formulae, proving that they converge in a strictly defined sense. In each IBVP, the novel formula is utilized to rigorously deduce the solution’s regularity and asymptotic properties near the boundaries of the domain, including uniform convergence, eventual (long-time) periodicity under (eventually) periodic boundary conditions, and null noncontrollability. Importantly, this analysis is indispensable for exploring the (non)uniqueness of the problem’s solution and a new counter-example is constructed. Our work is based on the synergy between: (i) the well-known Fokas unified transform method and (ii) a new approach recently introduced for the rigorous analysis of the Fokas method and for investigating qualitative properties of linear evolution partial differential equations (PDE) on semi-infinite strips. Since only up to third-order evolution PDE have been investigated within this novel framework to date, we present our analysis and results in an illustrative manner and in order of progressively greater complexity, for the convenience of readers. The solution formulae established herein are expected to find utility in well-posedness and asymptotics studies for nonlinear counterparts too.

The nonlinear coupled Schrödinger equation in fiber Bragg gratings is studied in this paper. The existence of soliton solutions and periodic solutions are proved by qualitative analysis, and exact solutions are given, as well as the parameter condition of each solution is described. Then the modulation instability (MI) analysis is carried out and the linear stability criterion is given. In particular, external perturbation terms are introduced to prove that the equation exists chaotic behaviors.

This paper deals with the identification and the qualitative analysis of a dynamic model of a shallow lagoon. The model describes the relations between biotic (phytoplankton, zooplankton) and abiotic (oxygen, nutrients) components of a lagoon. The first step of the paper is to derive estimates for the model parameters through an identification procedure using real data. The second step is to perform a qualitative analysis of the model dynamics, via the introduction of a parameterized reduced order model. The main contribution of the paper is to make an effort in the direction of synergyzing the identification stage with the qualitative analysis of the model dynamics, in order to gain a better understanding of the system behavior and obtain more reliable estimates for the model parameters and exogenous inputs.

A coupled model for axial/torsional/lateral vibrations of the drill string is presented, in which the nonlinear dynamics and qualitative analysis method are employed to find out the key factors and sensitive zone for coupled vibration. The drill string is simplified as an equivalent shell under axial rotation. After dimensionless processing, the mathematical model for coupled axial/torsional/lateral vibrations of the drill string is obtained. The Runge–Kutta–Fehlberg method is employed for the numerical simulation, and the rules that govern the changing of the torsional and axial excitation are revealed. And the stability domains of the explicit Runge–Kutta method are analyzed. Furthermore, the suggestions for field applications are also presented. It is demonstrated by simulation results that the lateral/axial/torsional vibrations exist simultaneously and couple with each other. The system will obtain a stable period motion with an axial excitation zone before the coupled vibration in the three directions, and continue to increase the axial excitation to cause the coupled vibration easily. The torsional excitation of the drill string mainly contributes to the coupled vibration in the three directions when in a specific rotation speed zone. The system is more likely to obtain a periodic motion through adjusting the torsional excitation out of this zone.

In this paper, we address the free (uncontrolled) dynamics of a snakeboard consisting of two wheel pairs fastened to a platform. The snakeboard is one of the well-known sports vehicles on which the sportsman executes necessary body movements. From the theoretical point of view, this system is a direct generalization of the classical nonholonomic system of the Chaplygin sleigh. We carry out a topological and qualitative analysis of trajectories of this dynamical system. An important feature of the problem is that the common level set of first integrals is a compact two-dimensional surface of genus 5. We specify conditions under which the reaction forces infinitely increase during motion and the so-called phenomenon of nonholonomic jamming is observed. In this case, the nonholonomic model ceases to work and it is necessary to use more complex mechanical models incorporating sliding, elasticity, etc.

This paper, that deals with the modelling of crowd dynamics, is the first one of a project finalized to develop a mathematical theory refereing to the modelling of the complex systems constituted by several interacting individuals in bounded and unbounded domains. The first part of the paper is devoted to scaling and related representation problems, then the macroscopic scale is selected and a variety of models are proposed according to different approximations of the pedestrian strategies and interactions. The second part of the paper deals with a qualitative analysis of the models with the aim of analyzing their properties. Finally, a critical analysis is proposed in view of further development of the modelling approach. Additional reasonings are devoted to understanding the conceptual differences between crowd and swarm modelling.

In this paper, the dynamical behavior of Middle East respiration syndrome coronavirus (MERS-CoV) via a sense of Caputo fractal-fractional order system of differential equation is established. A novel approach of fractional operator known as fractal-fractional Riemann–Liouville derivative is applied to the model considered. Moreover, fractal-fractional derivative is applied to the said problem. Furthermore, the existence and uniqueness of the solution of the considered model are verified by the fixed-point theory approach. The local and global stability of developed system are investigated with the help of the Ulam–Hyers stability technique from nonlinear functional analysis. The fractal-fractional type Adams–Bashforth iterative method is used to establish the numerical solution of said problem. The proposed model is simulated by considering different fractal dimensions $(𝜃)$ and fractional order $(\delta )$, converging to the integer order. Hence, it is evident that all the compartmental quantities possess convergence and stability in fractal-fractional form. Moreover, the Fractal-fractional techniques may also be used as a powerful technique/tool to investigate the global dynamics of the disease. However, it can be concluded from the results that quick recovery is possible for human population in the pandemic if there is no animal interaction with humans. In future, we are planning to extend the reported analysis to other fractional (fractal-fractional) operators. Furthermore, the behavior of different infectious models can also be analyzed with the help of newly developed scheme at different fractional orders lying between 0 and 1.

In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system’s boundedness and positivity are checked. According to the Arzela Ascoli theorem, the model is completely continuous. As a result of the discovery of Schauder’s fixed point, it has at least one solution. The existence and uniqueness of the concerned solution have been examined using the fixed point theory technique. Numerical simulations are used to demonstrate the accuracy of the proposed techniques using a generalized form of Mittag-Leffler kernel with a fractal fractional operator. Finally, simulations are utilized to represent the spread of group emotional contagion (spontaneous spread of emotions and related behaviors) dynamically.

An aneurysm is a local enlargement of the vessel lumen due to the weakening of the wall material. We propose a mathematical model of the pulsatile blood flow through the system consisting of the cerebral artery and an aneurysm. The mathematical model is based on mass and energy conservation laws. It comprises non-linear rheological properties of the aneurysm and artery, and inertial and resistant properties of the blood flow. The model equations are analyzed by the methods of non-linear dynamics and they are solved numerically. Special attention is paid to the flow stability as a function of the aneurysmal and arterial material properties, the mean and oscillating arterial pressure, and the frequency of heart pulsations. The results of the work can be summarized as follows: (i) the model equations are stable at normal physiological conditions and developed aneurysms, (ii) with decreasing of the aneurysmal compliance, the aneurysmal volume pulsations increase and a limit point of flow stability is approached, (iii) the increased amplitude of the pulsatile pressure and the heart frequency cannot lead to flow instabilities.

This paper investigates the impact of blogging on knowledge processes and proposes a way to manage collective knowledge. Qualitative methods are used to collect data through individual semi-structured interviews, think-aloud protocols, focus groups, and document analysis. Data analysis is pursued with the use of the qualitative software package Atlas.ti^®. This qualitative research contributes to our understanding of how a self-organised group of individuals involved in a temporary joint project in the Kingdom of Bahrain creates, transfers, retains and shares knowledge in a blog and provides insights into the knowledge management processes. It reveals the impact of blogging on knowledge management and examines issues concerned with the individual, the groups, and the organisation. It also suggests strategies on how to improve the management of an effective blog. Findings contribute to the debate on knowledge management processes and provide insights for academics and practitioners who are interested in a new theoretical approach connecting individual knowledge to collective knowledge, as well as to those studying online repositories and new information technology tools for the management of organisational knowledge. Future research should be conducted on how blogs may impact the effectiveness of organisational communication. Empirical research should also be conducted to explain how internal and external bloggers contribute to the development of organisational expertise.

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.

In this paper, we argue that ambiguity is an essential component of "fuzziness" in the Fuzzy Front End of New Product Development (NPD), and that a better understanding of how ambiguity emerges and is reduced, is called for. We explore the process by which ambiguity was reduced in four NPD projects, and propose a model that enhances our understanding of this process. Ambiguity arises as multiple interpretations, and interpretations can be understood as hypotheses, hence these can be tested by using the hypothetical-deductive method (HDM). We present a model showing that ambiguity in NPD projects is efficiently reduced by applying the HDM to test the multiple interpretations that give rise to ambiguity and the assumptions underlying these interpretations. We discuss theoretical implications and the usefulness of the model for practitioners of NPD.

This paper takes one step towards addressing the question of how activity mediated by shared representations — notations that are manipulated by more than one person — might constitute knowledge construction activity, and how the shared representations are appropriated for this purpose. The primary contribution of this paper is a methodology for qualitative analysis of activity in a workspace built on the concept of "uptake": how participants take up and build on prior contributions. By examining patterns of uptake we can see ways in which participants' activities constitute an intersubjective cognitive activity distributed across persons and the representations they are manipulating. The analysis is conducted in three phases: identification of acts of media manipulation, identification of information uptake relations between these acts, and application of theoretical perspectives to identify evidence of knowledge construction via the representational media. The uptake graph is intended to minimize theoretical commitments in order to support eclectic analysis. The methodology is applied to data from a prior study in which participants collaborated via an evidence map and a chat tool. These case examples illustrate how the methodology uncovered argumentation and knowledge construction conducted solely through the graph workspace.

A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population, infected with Ebola virus, on human-to-human transmission of Ebola Virus Disease (EVD) in a disease-free area. In view of the dynamics of Ebola virus disease, here, the infected class is supposed to be divided into subclasses, viz. primary and secondary infected. The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation. The obtained results, qualitatively and quantitatively, suggest that migration and contact rates play an important role in controlling the spreading of disease. Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values, it leads to delay in the stabilization of the system. It is also found that primary reproductive number increases with increase in migration rate. Besides this, the approximate time required to attain stability of the disease model system is also determined. The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.

For surpassing this hyper-competitive recruiting situation of the most strict mutual pressures and influences on the lowest birth-rate fertility trend and the highest development of higher education institutions, the more of Taiwanese higher education institutions have commenced to offer the most critical Massive Open Online Courses (MOOCs) to definitely add complete institutions revenues with the lowest online courses costs for formulating the most effective sustainability in institutional operation through the diversified utilization of multiple social media technology. In statistic, the Factor Analysis (FA) approach of quantitative analysis as well as the Analytical Network Process (ANP) avenue of quantitative analysis were also hierarchically appraised the questionnaire of large-scale random interviewees and 20 professional experts in order to conduce the best principle of Higher-education Sustainability under the influence of declining birth-rate.

This chapter explores the perceptions held about “good” corporate governance (GCG) in three different transforming economies of Central and Eastern Europe [CEE] (East Germany, Estonia, and Hungary). Forty-nine interviews were conducted with corporate governance experts from various institutions in the three countries between 2003 and 2004. They were analyzed with the help of several qualitative techniques, resulting in a typology of GCG perceptions. Our findings show that these perceptions are strongly influenced by the institutional and historical background of the countries. However, they are far from being uniform or shaped along the lines of well-known Western models but take, rather, some hybrid forms. This chapter also highlights the crucial role (native) professionals and experts play in the development process of GCG.

It is tested by qualitative and quantitative analysis to Bu-gong tea saponin that the oxidative substance contained in Bu-gong tea saponin is sodium percarbonate with content of 45%. There are two kinds of alkalis in Bu-gong tea saponin by qualitative analysis: sodium hydroxide and sodium carbonate, and the content of them is respectively 29% and 4.5%.