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In this paper, we introduce SODES (Stepwise Ordinary Differential Equations Solver) a new solver for Ordinary Differential Equations (ODE). SODES can optionally provide the solution displaying all the steps needed to obtain it. This way, SODES is an important tool not only for researchers who need solving ODE but also constitutes an important tool for the teaching and learning process of ODE. SODES has been developed using programming with a Computer Algebra System (CAS). Specifically, we use the CAS Derive but it can be easily adapted to any other CAS supporting programming. SODES provides, step by step, the solution of the following types of ODE: separable, homogeneous, exact, integrating factors, linear, Bernoulli, Riccati, first order ODE of n th degree, Cauchy's problems of first order ODE, higher order linear homogeneous equations with constant coefficients, Lagrange's method for particular solutions of higher order linear equations with constant coefficients, higher order linear equations with constant coefficients and Cauchy's problems of higher order linear equations with constant coefficients. SODES also deals with two generic programs which determine the type or types of a given ODE and provides the solution. In this paper we will also introduce a draft of a Graphical User Interface (GUI) for SODES in a local web application using programming in Python (using its CAS module SymPy) which is a more portable and free CAS. This draft can be used in English, French and Spanish, and can be easily extended to other languages. The code of SODES and the GUI are freely available so that it can be used by users who also will be able to adapt it to their needs. [ABSTRACT FROM AUTHOR]

Compliant Mechanisms (CMs) have been a hot research spot in recent years due to their distinguished mechanism concept from conventional rigid-body mechanisms: CMs can transfer motion, force, and energy only through the deflection of flexible components. Therefore, the accurate and efficient kinetostatic modeling for these elementary flexible components plays a rather important role regarding conducting synthesis of a studied compliant mechanism. In this paper, we have reviewed the commonly-used beam modeling methods in CMs, most of which are essentially dedicated to handling geometrically nonlinear Euler–Bernoulli beam theory. Mathematically speaking, this beam model is essentially a boundary value problem (BVP) of an ordinary differential equation (ODE). We then introduced certain commonly used numerical methods for BVPs to solve the problem where straight beams and circular initially curved beams (ICBs) are studied as two example cases. We have also demonstrated the detailed derivation of these methods and the numerical results along with the corresponding insights on them as well. Besides, we have modeled 2 representative revolute mechanisms (straight-beam-based cross-axis compliant revolute joint and circular-beam-based compliant revolute joint) to prove the feasibility of synthesizing CMs using these numerical methods. Error analysis is presented thereafter, which also confirms the effectiveness of these numerical methods. • We formulated the large beam-deflection problem as a general nonlinear BVP. • We reviewed the commonly used methods for modeling beam deflection in CMs. • We introduced efficient numerical methods to solve beam deflection problems. • We provided comments and analysis about all the mentioned methods. [ABSTRACT FROM AUTHOR]

Abstract: Bioinformatics tools have facilitated the reconstruction and analysis of cellular metabolism of various organisms based on information encoded in their genomes. Characterization of cellular metabolism is useful to understand the phenotypic capabilities of these organisms. It has been done quantitatively through the analysis of pathway operations. There are several in silico approaches for analyzing metabolic networks, including structural and stoichiometric analysis, metabolic flux analysis, metabolic control analysis, and several kinetic modeling based analyses. They can serve as a virtual laboratory to give insights into basic principles of cellular functions. This article summarizes the progress and advances in software and algorithm development for metabolic network analysis, along with their applications relevant to cellular physiology, and metabolic engineering with an emphasis on microbial strain optimization. Moreover, it provides a detailed comparative analysis of existing approaches under different categories. [Copyright &y& Elsevier]

Abstract: In this paper, fluid flow and heat transfer of vertical full cone embedded in porous media have been studied. Similarity solution for full cone subjected to wall temperature boundary conditions gives us a nonlinear ordinary differential equation which the obtained nonlinear ODE has been solved through homotopy analysis method (HAM). The obtained analytical solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region. By the way we also calculate Nusselt number that is an important parameter in heat transfer by obtained analytical solution by HAM. [Copyright &y& Elsevier]

Abstract: Mixed time integration methods, also known as multiple time-step methods (MTS), have been proposed and implemented successfully to reduce the stiffness of problems in molecular dynamics and solid mechanics, where different time scales are used to integrate different motions or meshes. We apply the similar concept and develop an asynchronous time-stepping (ATS) integrator for atmospheric application. This paper first presents ATS as a generalized ordinary differential equation solver and describes its key components including: (1) global and local time management; (2) dynamic time-scale ordering; and (3) integration and iteration methods. Then we apply ATS to solve stiff problems in aerosol dynamics, where we further introduce several techniques such as grouping particulate species by particle sections to speed up computations. The comparisons between ATS and standard ODE solvers including LSODE, LSODES and VODE in aerosol dynamics simulation are presented, which show that ATS is robust and able to achieve a significant digit average (SDA) value of 2.0 to 3.0 while its speed is around 10 to 100 times faster than LSODE with equivalent accuracy. ATS has been implemented in CMAQ-UCD, a sectional, dynamic aerosol model built on USEPA''s CMAQ platform. [Copyright &y& Elsevier]

Fluorescence induction curves (F(t)) in low intensity 1s light pulses have been measured in leaf discs in the presence and absence of valinomycin (VMC). Addition of VMC causes: (i) no effect on the initial fluorescence level Fo and the initial (O–J) phase of F(t) in the 0.01–1 ms time range. (ii) An approximately 10% decrease in the maximal fluorescence Fm in the light reached at the P level in the O–J–I–P induction curve. (iii) Nearly twofold increase in the rate and extent of the F(t) rise in the J–I phase in the 1–50 ms time range. (iv) A 60–70% decrease in the rise (I–P phase) in the 50–1000 ms time range with no appreciable effect, if at all, on the rate. System analysis of F(t) in terms of rate constants of electron transfer at donor and acceptor sides have been done using the Three State Trapping Model (TSTM). This reveals that VMC causes: (i) no, or very little effect on rate constants of e-transfer reactions powered by PSII. (ii) A manifold lower rate constant of radical pair recombination (k−1) in the light as compared to that in the control. The low rate constant of radical pair recombination in the reaction center (RC) in the presence of VMC is reflected by a substantial increase in the nonzero trapping efficiency in RCs in which the primary quinone acceptor (QA) is reduced (semi-open centers). This causes an increase in their rate of closure and in the overall trapping efficiency. Data suggest evidence that membrane chaotropic agents like VMC abolish the stimulation of the rate constant of radical pair recombination by light. This light stimulation that becomes apparent as an increase in Fo has been documented before [Biophys. J. 79 (2000) 26]. It has been ascribed to effects of (changes in) local electric fields in the vicinity of the RC. The decrease of the I–P phase is attributed to a decrease in the photoelectric trans-thylakoid potential in the presence of VMC. Such effects have been hypothesized and illustrated [Bioelectrochemistry 57 (2002) 123]. [Copyright &y& Elsevier]

Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research. [ABSTRACT FROM AUTHOR]