Differential equation

In this work a general multibody system theory is implemented within a bond graph modeling framework. In classical mechanics several procedures exist by which differential equations can be derived of a system of rigid bodies. In the case of large systems these procedures are labor-intensive and consequently error-prone, unless they are computerized. The bond graphs formalism allows for a unified modeling of multidisciplinary physical systems. It is well-suited for a modular modeling approach based on physical principles. The theory of multibody system dynamics in terms of bond graphs modeling is revisited with the purpose of designing a multibond graph library for such systems. Several mechanical systems undergoing large 3-dimensional rotations are numerically solved in order to validate this software library written in 20-sim software.   J z J y J x t z y x z y x J z J y J x

RIASSUNTO L'eccessivo sfruttamento degli acquiferi carsici del Salento ha prodotto, da tempo, l'insorgere del fenomeno della salsificazione delle acque di falda. L'uso di acque salmastre per l'irriga-zione delle colture può determinare, nel lungo termine, la perdita del ...

By using an approach based on the full nonlinear Barkhausen criterion, it is possible to describe oscillator behavior under the form of a nonlinear characteristic polynomial whose coefficients are functions of the circuit components and of the oscillation amplitude. Solving the polynomial in the frequency domain leads to the steady state oscillation amplitude and frequency. In the time domain, the characteristic polynomial represents a nonlinear differential equation whose solution gives the oscillator signal transient. It is shown how symbolic manipulation capabilities of commercially available softwares can be used to automatically generate the coding of the oscillator characteristic polynomial from the SPICE description netlist. The numerical processing of such an equation in the time domain leads to unacceptable computer time because of the high quality factor of the oscillator circuits involved. Nevertheless, by using the slowly varying amplitude and phase method, it is possible to transform the initial nonlinear differential equation into a nonlinear first order differential equation system in the amplitude and phase variables. The solution of this system directly gives the designer the most relevant features of the oscillation; that is, the amplitude, phase, or frequency transients which can be accurately obtained within a short computer time by using classical numerical algorithms.

In this paper we derive some a priori estimates on the resolvent of one dimensional Schrodinger operators from the solutions of the associated differential equation with real energy. In particular this implies the existence of an absolutely continuous spectrum in some situations.

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

Thermal oxidation of sulfur vulcanized polyisoprene samples was studied by gravimetry and IR mapping of carbonyl groups (to determine the oxidized layer thickness (TOL)) at temperatures ranging from 60 to 150 C in air. Oxidation appears noticeably lower than that for the starting non-vulcanized polyisoprene, revealing a stabilizing effect of sulfur-containing species. After a short period where mass loss presumably due to water evaporation predominates, the sample mass increases until a plateau corresponding to 6.3% (at 60 C) to 0.5% (at 140 C) mass gain. Practically no weight gain (w0.1%) was observed at 150 C. The mass uptake is due to oxygen grafting to the chains. TOL varies from about 4.6 mm (70 C) to about 1 mm (150 C). A kinetic model, derived from a mechanistic scheme of radical chain oxidation including stabilizing events due to hydroperoxide reduction by sulfur-containing groups and taking into account the diffusionereaction coupling, was established and numerically resolved. The model predictions for mass changes and TOL values are in good agreement with experimental data.

Using the ladder operator technique, a construction of the supersymmetric Hamiltonian is proposed. We show that the accidental degeneracies associated with the Coulomb and isotropic oscillator problems may be attributed to the existence of a supersymmetry of the Hamiltonians.

There are two common types of solution methods for solving simple integrals: using integration constants or using limits of integration. We use the resources framework to model student solution methods. Preliminary results indicate both problematic and meaningful intersections of physical meaning and mathematical formalism when solving linked integrals.

Gene regulatory network is a collection of DNA which interact with each other and with other matter in the cell. The lac operon is an example of a relatively simple genetic network and is one of the best-studied structures in the Escherichia coli bacteria. In this work we consider a deterministic model of the lac operon with a noise term, representing the stochastic nature of the regulation. The model is written in terms of a system of simultaneous first order differential equations with delays. We investigate an analytical and numerical solution and analyse the range of values for the parameters corresponding to a stable solution.

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie group G. In particular, it is shown that if a 'strongly invariant' equation exists, then all 'weakly invariant' equations differ from it only by an arbitrary multiplicative factor. If no 'strongly invariant' equation exists, then cohomology theory can be used to simplify the search for 'weakly invariant' equations. (1991). 17B56, 57T10, 22Exx.

We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions

The homogeneous precipitation kinetics of the ordered phases Al 3 Zr and Al 3 Sc in Al solid solutions has been simulated at the mesoscopic scale by the cluster dynamics method. The polyatomic clusters, embedded in the solid solution, have an L1 2 structure and exchange solute atoms via absorption and emission reactions controlled by interfacial and long range diffusion. The time evolution of the cluster distribution is determined numerically, solving a set of master differential equations coupled through monomer exchanges. Results are presented for different temperatures and solute supersaturations and are discussed in terms of the classical schemes of precipitation and of recent atomistic Monte-Carlo simulations.

The properties of 20 wt % CeO 2 and 21 wt % Ce 0.5 Zr 0.5 O 2 films, deposited onto a γ-Al 2 O 3 by Atomic Layer Deposition (ALD), were compared to bulk Ce 0.5 Zr 0.5 O 2 and γ-Al 2 O 3-supported samples on which 20 wt % CeO 2 or 21 wt % CeO 2-ZrO 2 were deposited by impregnation. Following calcination to 1073 K, the ALD-prepared catalysts showed much lower XRD peak intensities, implying that these samples existed as thin films, rather than larger crystallites. Following the addition of 1 wt % Pd to each of the supports, the ALD-prepared samples exhibited much higher rates for CO oxidation due to better interfacial contact between the Pd and ceria-containing phases. The redox properties of the ALD samples and bulk Ce 0.5 Zr 0.5 O 2 were measured by determining the oxidation state of the ceria as a function of the H 2 :H 2 O ratio using flow titration and coulometric titration. The 20 wt % CeO 2 ALD film exhibited similar thermodynamics to that measured previously for a sample prepared by impregnation. However, the sample with 21 wt % Ce 0.5 Zr 0.5 O 2 on γ-Al 2 O 3 reduced at a much higher P O 2 and showed evidence for transition between the Ce 0.5 Zr 0.5 O 2 and Ce 0.5 Zr 0.5 O 1.75 phases.

We consider the questions of existence and uniqueness of solutions of equation (0.1) below. Under natural assumptions on Ω, µ and f , we show that the solutions u of (0.1) are in one-to-one correspondence with the set of nonnegative harmonic functions h in Ω. The correspondence is given by M : u h, where h is the largest harmonic minorant of u in Ω.

A new formulation is presented for the perturbed Lambert problem. The formulation employs the variation-of-parameters method in the KS transformed state space to determine perturbations of a Keplerian Lambert solution. The approach is universal (in that its validity is not restricted to a particular energy domain). For the case of the second zonal harmonic (oblateness) perturbation, first order perturbations are carried out entirely analytically; non-iterative corrections are determined through solution of a pair of algebraic equations. For more general perturbations, numerical quadratures are required.

Solution algebras can be associated to any connection over a smooth affine variety. It turns out that he spectrum of a solution algebra is an algebraic fiber space over the base variety, with quasi-homogeneous fiber. We discuss the relevance of this result to Transcendental Number Theory.

The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semiinfinite flat plate. The Blasius function is the solution to 2fxxx + ffxx = 0 on x ∈ [0, ∞] subject to f (0) = fx(0) = 0, fx(∞) = 1. We use this famous problem to illustrate several themes. First, although the flow solves a nonlinear partial differential equation (PDE), Toepfer successfully computed highly accurate numerical solutions in 1912. His secret was to combine a Runge-Kutta method for integrating an ordinary differential equation (ODE) initial value problem with some symmetry principles and similarity reductions, which collapse the PDE system to the ODE shown above. This shows that PDE numerical studies were possible even in the precomputer age. The truth, both a hundred years ago and now, is that mathematical theorems and insights are an arithmurgist's best friend, and they can vastly reduce the computational burden. Second, we show that special tricks, applicable only to a given problem, can be as useful as the broad, general methods that are the fabric of most applied mathematics courses: the importance of "particularity." In spite of these triumphs, many properties of the Blasius function f (x) are unknown. We give a list of interesting projects for undergraduates and another list of challenging issues for the research mathematician.

A novel method, based on genetic algorithms, has been developed and applied to the solution of di erential equations. The new approach is based on the use of real numbers to form the candidate solutions which are improved iteratively by a suitable breeding process. The algorithm was tested in the calculation of the bound states of a double well potential and in the nonlinear density functional calculation. Comparison of the results with those obtained using the direct relaxation method shows excellent agreement.

This report was prepared as an a w u n t of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof. nor any of their employes, makes any warranty. express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus. product, or process disclosed. or represents that its usc would not infringe privately owned rights. Reference herein to any sptcific commercial product, process, or scrvicc by trade name, trademark. manufacturer. or otherwise does not necessarily constitute or imply its endorsement, m mmendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not nccessarily state or reflect thost of the United States Government or any agency thereof.

This paper is concerned with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation methods to obtain our results.

A methodology to efficiently design products based on magneto-dielectric (ferrite) materials with desirable frequency responses that satisfy electromagnetic compatibility and signal integrity requirements over RF and microwave bands is presented here. This methodology is based on an analytical model of a composite magneto-dielectric material with both frequency-dispersive permittivity and permeability. A procedure for extracting complex permittivity and permeability of materials from experimental data is based on transmission line measurements. The genetic algorithm is applied for approximating both permittivity and permeability of materials by series of Debye frequency dependencies, so that they are represented as "double-Debye materials" (DDM). The DDM is incorporated in the finite-difference time-domain numerical codes by the auxiliary differential equation approach.

This work presents a procedure to solve nonlinear dynamic data reconciliation (NDDR) problems with simultaneous parameter estimation based on particle swarm optimization (PSO). The performance of the proposed procedure is compared to the performance of a standard Gauss-Newton (GN) scheme in a real industrial problem, as presented previously by Simultaneous data reconciliation and parameter estimation in bulk polypropylene polymerizations in real time. Macromolecular Symposia 243, 91-103; 2008. In-line monitoring of bulk polypropylene reactors based on data reconciliation procedures. Macromolecular Symposia 271, 26-37]. Both methods are used to solve the NDDR problem in an industrial bulk propylene polymerization process, using real data in real time for the simultaneous estimation of model parameters and process states. A phenomenological model of the real process, based on the detailed mass and energy balances and constituted by a set of algebraic-differential equations, was implemented and used for interpretation of the actual plant behavior in real time. The resulting nonlinear dynamic optimization problem was solved iteratively on a moving time window, in order to capture the current process behavior and allow for dynamic adaptation of model parameters. Obtained results indicate that the proposed PSO procedure can be implemented in real time, allowing for estimation of more reliable process states and model parameters and leading to much more robust and reproducible numerical performance.

0 Previous studies showed that the in situ absorption of baclofen in rat jejunum was inhibited by -alanine, a nonessential amino acid, and therefore mediated, at least in part, by some -amino acid carrier. In this paper a similar study was undertaken using taurine, a sulfonic -amino acid, in order to evaluate its effect and to establish a general inhibition model. To achieve this goal, remaining concentrations of inhibitor were also measured and incorporated into the model. Previously, kinetic absorption in situ parameters for taurine in free solution were obtained: V m ) 27.73 ± 9.99 mM h -1 , K m ) 8.06 ± 2.82 mM, k a (passive difussion component) ) 0.40 ± 0.28 h -1 . Isotonic solutions containing 0.5 mM baclofen with starting taurine concentrations ranging from 0 to 100 mM were perfused in rat jejunum, and the remaining concentrations of both compounds were measured. The apparent rate pseudoconstant of the drug clearly decreased as the remaining taurine concentration increased. The interaction can be described as a complete competitive inhibition plus a second component, K, noninhibited, K ) 0.58 (±0.03) h -1 , K i ) 20.62 (±4.04) mM, V mi ) 28.12 (±6.12) mM h -1 , K mi ) 11.71 (±2.53) mM, k ai ) 0.47 (±0.10) h -1 . A residual absorption of baclofen in the presence of high taurine concentrations was observed, which should be attributed to another transport system not associated with the taurine carrier. In order to elucidate whether or not taurine and -alanine carriers are two separate entities that baclofen can use for absorption, further experiments using -alanine and taurine together as inhibitors (baclofen, 0.5 mM; -alanine, 50 mM, and taurine, 50 mM) were developed. Results indicated that baclofen and both amino acids share the same carrier in the intestinal absorption process. We have completed studies using leucine, taurine, and GABA together as inhibitors of drug absorption. An isotonic perfusion solution of 0.5 mM baclofen in the presence of 50 mM leucine, 25 mM taurine, and 25 mM GABA was perfused. Under these conditions the absorption rate pseudoconstant of baclofen decreases until 0.080 h -1 (±0.069). Practical implications of these phenomena are briefly discussed.

Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronise with one another, while the remaining oscillators are incoherent. Several groups have studied chimerae in networks of identical oscillators, but here we study these states in heterogeneous models for which the natural frequencies of the oscillators are chosen from a distribution. For a model consisting of two subnetworks we obtain exact results by reduction to a finite set of differential equations, and for a network of oscillators in a ring we generalise known results. We find that heterogeneity can destroy chimerae, destroy all states except chimerae, or destabilise chimerae in Hopf bifurcations, depending on the form of the heterogeneity. * c.r.laing@massey.ac.nz

Elephant seals migrate over vast areas of the eastern Nonh Pacific Ocean between rookeries in southern California and distant northern foraging areas. Several models of particle movement were evaluated and a model for great-circle motion found to give reasonable results for the movement of an adult female. This model takes specific account of the fact that the movement is on the surface of a sphere and that the animal is apparently heading toward a particular destination. The parameters of the motion were estimated. Such a great-circle path of migration may imply that these seals have the ability to assess their position with respect to some global or celestial cues, allowing them to continually adjust their course and achieve the most direct geodesic route between origin and destination of migration. But the navigational mechanism actually used by these seals to accomplish such feats is as yet unknown. Deux fois par annee. les elephants de mer entreprennent de longues migrations au nord de I'ocCan Pacifique. Plusieurs sont poneurs d'instruments qui enregistrent la profondeur et I'intensitt lumineuse h intervalles rtguliers. Ces instruments sont ensuite recupirts et permettent de faire plusieurs estimations. par exemple les positions i mi-journte. Dans cet expose on s'interessera h la modelisation des itineraires de surface des animaux i I'aide d'equations differentielles stochastiqeus. Les distances sont suffisament importantes pour ftre incluses dans le modele la nature sphtrique de la surface terrestre. Une question intiressante est de determiner si les itineraires sont des grands cercles de la sphere terrestre.

We consider optimal estimation problems characterized by a state vector with i) dynamics described via a differential equation with Lipschitz nonlinearities, ii) partial information provided via a Lipschitz nonlinear mapping, and iii) an Lp norm measure of the estimation error to be minimized. An approximate solution of such optimal estimation problem is searched for by restricting the optimization to parameterized nonlinear approximators such as feedforward neural networks. The parameters of a feedforward neural network are the neural weights. This approach entails a constrained nonlinear programming problem, whose constraints are given by the dynamic and measurement equations, and the conditions guaranteeing the stability of the estimation error. To optimize the parameters values of neural networks an algorithm is developed that is based on appropriate sampling of the state and error spaces. Choices of the sample points are devised based on the notion of dispersion, which allow one to obtain an approximate solution of the optimal estimation problem by a small sample complexity.

In this paper, a new computer software package, Yalzer, is introduced for simulating single-compartmental model of neurons. Passive or excitable membranes with voltage-gated ion channels can be modeled, and current clamp and voltage clamp experiments can be simulated. In the Yalzer, first-order differential equations used to define the dynamics of the gate variables and the membrane potential are solved by two separate integration methods with variable time steps: forward Euler and exponential Euler methods. Outputs of the simulation are shown on a spreadsheet template for allowing flexible data manipulation and can be graphically displayed. The user can define the model in detail, and examine the excitability of the model and the dynamics of voltage-gated ion channels. The software package addresses to ones who want to run simple simulations of neurons without need to any programming language skills or expensive software. It can also be used for educational purposes.

The use of dynamical system techniques, optimization methods and statistical algorithms to estimate the characteristics of brain electrical activity are explored. A system approach for characterizing EEG (electroencephalogram) signals, based on nonlinear estimation of dynamical characteristics and modeling the evolution of dynamical processes over time is applied. The dynamical characteristics can be used to better visualize the “state vector” of epileptic EEG signals and for the purpose of pattern recognition. An optimization method for reconstructing parameter spaces of dynamical systems is applied to systems with one or more hidden variables, and can be used to reconstruct maps or differential equations of the brain dynamics. The methods are illustrated by using numerically generated data and EEG data from epileptic patients.

In this paper we use symmetry methods to study networks of coupled cells, which are models for central pattern generators (CPGs). In these models the cells obey identical systems of differential equations and the network specifies how cells are coupled. Previously, Collins and Stewart showed that the phase relations of many of the standard gaits of quadrupeds and hexapods can be obtained naturally via Hopf bifurcation in small networks. For example, the networks they used to study quadrupeds all had four cells, with the understanding that each cell determined the phase of the motion of one leg. However, in their work it seemed necessary to employ several different four-oscillator networks to obtain all of the standard quadrupedal gaits.

In this paper infinite-dimensional dynamical systems described by nonlinear abstract differential equations are considered. Using the generalized open mapping theorem sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. As an illustrative example a constrained exact local controllability problem for a nonlinear delayed dynamical system is solved in detail. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented. ᮊ

The Pom-Pom model, recently introduced by McLeish and Larson ͓J. Rheol. 42, 81-110 ͑1998͔͒, is a breakthrough in the field of viscoelastic constitutive equations. With this model, a correct nonlinear behavior in both elongation and shear is accomplished. The original differential equations, improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified extended Pom-Pom model does not show the three problems and is easy for implementation in finite element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxial, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial low density polyethylene ͑LDPE͒ melts and one high density polyethylene ͑HDPE͒ melt. Such a good agreement over a full range of well defined rheometric experiments, i.e., shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi. bility for the accuracy, completeness, or uselulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Timber-concrete structures can be applied to bridge superstructures of vicinal roads with innumerable advantages in relation to the usual structures made of timber or reinforced concrete. This paper presents both an experimental analysis and a theoretical study on models of bridges with timber and concrete composite structures whose systems of connections composed by nails or screws are semi-rigid. The experimental procedure consisted basically of bending tests in three panels, representing a bridge prototype to evaluate the performance structural. Besides this, in order to define the slip modulus shear tests in small specimens were performed. The theoretical study was based on differential equations developed from the equilibrium of forces and the compatibility of displacements and these results were compared to the Finite Element Method. From this analysis, it can be concluded that the timber-concrete composite structures have favorable perspective of application in this type of civil construction.

Due to its heat integration utility, heat exchange reformer (HER) is suitable to use for PEMFC-based residential power generation system. Since dynamics response of reformer affects overall dynamics of fuel processing system, response of HER with step change in various input parameters also needs to be studied. In this study, we present an improved distributed dynamic model for HER which is capable of computing load following characteristics. The dynamic model consists of 20 partial differential equations which are discritized using spline collocation on finite elements. Resulting differential equations along with boundary conditions are solved by stiff solver which utilizes variable order method based on numerical differentiation formulae. Step variations in various input parameters are considered and dynamic response of HER is simulated at those variations. The results provide valuable information about dynamic nature of HER which can be used to frame suitable control strategy.

It is shown that in the hyperspherical representation terms of the three-and fourbody scattering functions corresponding to elastic 3-f 3 and 4-> 4 scattering have g~5/ 2 and g~4 asymptotic behavior in the 6-and 9-dimensional configuration space, respectively. Nonlinear first-order system of differential equations and the optical theorem for such processes are given.

We study spatially periodic patterns for 1-D nonlocal reactiondiffusion equations that arise from various biological models. The problem reduces to study periodic and homoclinic solutions of differential equations with perturbations containing convolution terms. We consider the case that the system is time-reversible. Assuming the unperturbed system has a family of periodic orbits surrounded by a homoclinic orbit, we establish the persistence of these solutions for the perturbed equations. We apply this result to the important Gray-Scott autocatalytic model.

Multi-proxy approach was used to reconstruct the environmental conditions of remote lakes in the High Tatra Mountains (Slovakia) over the past few centuries (approximately 500-1000 years). Short sediment cores (*30 cm) taken from three morphologically similar glacial lakes distributed along altitudinal gradient (subalpine to alpine conditions) were analysed for organic matter content (LOI), diatoms and chironomids. Both descriptive and correlative approaches were used for analysing stratigraphical data. Predictive canonical correspondence analysis and co-correspondence analysis were applied to directly relate physical and biological proxies to each other. The relationship between LOI and biotic proxies was inconsistent across groups and lakes. Concordant patterns in diatom and chironomid composition were found in two non-acidified lakes. Common trends in those assemblages indicated major past environmental events such as the Little Ice Age, air pollution and lake acidification. In contrast, no relationship between the composition of diatom and chironomid assemblages was found in the formerly acidified lake, suggesting different responses of assemblages to acidification. While chironomids showed shifts that are attributable to recovery, diatoms assemblage remained relatively stable throughout the uppermost layers of the sediment record. On the other hand, climatic-driven changes in assemblages detected in the deeper layers were more pronounced in diatoms than in chironomids.

The paper presents a dynamic model considering the human upper limb as a mechanic system with 6 degrees of freedom where the segments are moved by their own weight forces. The bones were modeled in Solid Works, the model of the upper limb obtained being very close as form to the real one. Based on this model, the calculus of

We investigate the stability of barium sulphate precipitation in an ideally mixed reactor under stoichiometric conditions. The process is modelled by a population balance equation describing the crystal size distribution coupled with a system of integro-differential equations for the substances in solution. A reduction to a closed moment model is used to analyse the stability of equilibrium solutions. In a certain range of parameters an unstable equilibrium is detected by a numerical calculation of the eigenvalues of the moment system. In this case sustained oscillations of the crystal size distribution are observed in numerical simulations. The numerical results are compared to data obtained from chemical experiments.

sail:lab, as an interdisciplinary project of mathematicians and sport scientists, uses the physical description of sailing to develop an E-Learning component, which can be integrated in Blended Learning scenarios in both departments. By calculating the forces and moments due to wind and current which take effect at sail, hull, rudder, and fin, the movement of a jolly-boat is visualized. An