Amplitude equations for Rayleigh-Benard convective rolls far from threshold

An extension of the amplitude method is proposed. An iterative algorithm is developed to build an amplitude equation model that is shown to provide precise quantitative results even far from the linear instability threshold. The method is applied to the study of stationary Rayleigh-Benard thermoconvective rolls in the nonlinear regime. In particular, the generation of second and third spatial harmonics is analyzed. Comparison with experimental results and direct numerical calculations is also made and a very good agreement is found.Peer reviewe

Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.Comment: 26 pages, 9 figure

A novel method for computing the derivatives of the mean and amplitude of physiological variables with respect to the parameters of a cardiovascular system model

While studying the cardiovascular system (CVS), it is frequent that only the mean and amplitude of physiological variables (pressures and volumes) are available. Computing the derivative of this discrete data with respect to the parameters of a CVS model is a necessary step to identify these parameters. Currently, such derivatives are computed through forward difference approximations, hence requiring two model simulations per derivative. In this work, we develop a method aiming to compute the derivatives along with the model simulation

Subject-specific cardiovascular system model-based identification and diagnosis of septic shock with a minimally invasive data set: Animal experiments and proof of concept

A cardiovascular system (CVS) model and parameter identification method have previously been validated for identifying different cardiac and circulatory dysfunctions in simulation and using porcine models of pulmonary embolism, hypovolemia with PEEP titrations, and induced endotoxic shock. However, these studies required both left and right heart catheters to collect the data required for subject-specific monitoring and diagnosis – a maximally invasive data set in a critical care setting although it does occur in practice. Hence, use of this model-based diagnostic would require significant additional invasive sensors for some subjects, which is unacceptable in some, if not all, cases. The main goal of this study is to prove the concept of using only measurements from one side of the heart (right) in a “minimal” data set to identify an effective patient-specific model that can capture key clinical trends in endotoxic shock. This research extends existing methods to a reduced and minimal data set requiring only a single catheter and reducing the risk of infection and other complications – a very common, typical situation in critical care patients, particularly after cardiac surgery. The extended methods and assumptions that found it are developed and presented in a case study for the patient-specific parameter identification of pig-specific parameters in an animal model of induced endotoxic shock. This case study is used to define the impact of this minimal data set on the quality and accuracy of the model-application for monitoring, detecting and diagnosing septic shock. Six anesthetized healthy pigs weighing 20-30 kg received a 0.5- mg/kg endotoxin infusion over a period of 30 mins from T0 to T30. For this research, only right heart measurements were obtained. Errors for the identified model are within 8% when the model is identified from data, re-simulated and then compared to the experimentally measured data, including measurements not used in the identification process for validation. Importantly, all identified parameter trends match physiologically and clinically and experimentally expected changes, indicating that no diagnostic power is lost. This work represents a further with human subjects validation for this model-based approach to cardiovascular diagnosis and therapy guidance in monitoring endotoxic disease states. The results and methods obtained can be readily extended from this case study to the other animal model results presented previously. Overall, these results provide further support for prospective, proof of concept clinical testing with humans

Structural model of the mitral valve included in a cardiovascular closed-loop model: Static and dynamic validation

invited, 6-pagesA minimal cardiovascular system (CVS) model including mitral valve dynamics has been previously validated in silico. It accounts for valve dynamics using a second order differential equation to simulate the physiological opening valve law. This second order equation is based on output heart signals and is very difficult to match its anatomical or physiological parameters, making this model difficult to interpret and to particularise to pathological situations. In contrast, a simple non-linear rotational spring model of the motion of the mitral valve, located between the left atrium and ventricle, has been validated. A measured pressure difference curve was the model input, which provides an applied torque to the valve chords. Various damping and hysteresis states were investigated to find a model that best matches reported animal data of chord movement during a heartbeat. This model is based on simple physiological behavior modeling, defining parameters that are directly linked with physiological or anatomical data, and is thus more physiologically relevant. This research describes a new closed-loop CVS model integrating the simple non-linear rotational spring model. This new model is shown to fit the static and dynamic heart behaviour observed, as an initial validation of its relevance in a larger CVS model

Patient-specific modelling of the cardiovascular system – application to septic shock with a minimal data set

We use a previously validated cardiovascular system (CVS) model and parameter identification method to identify the pig-specific parameters during induced endotoxic shock. Six anesthetized healthy pigs weighing 20-30 kg received a 0.5- mg/kg endotoxin infusion over a period of 30 mins from T0 to T30. Only right heart measurements were obtained and thus significantly less data was available for the model parameter identification compared to previous studies. Errors for the identified model are within 8% when the model is identified from data, re-simulated and then compared to the clinically measured data. All identified parameter trends match physiologically expected changes. This work represents a further clinical validation for this model-based approach to cardiovascular diagnosis and therapy guidance in monitoring endotoxic disease states

Influence of a nonlinear reference temperature profile on oscillatory Benard-Marangoni convection.

We analyze oscillatory instabilities in a fluid layer of infinite horizontal extent, heated from above or cooled from below, taking into account the nonlinearity of the reference temperature profile during the transient state of heat conduction. The linear stability analysis shows that a nonlinear reference temperature profile can have a strong effect on the system, either stabilizing or destabilizing, depending on the relative importance of buoyancy and surface tension forces. For the nonlinear analysis we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations. In the two-dimensional (2D) case, we show the solution of these amplitude equations are standing waves

Constitutive equations of rheological materials: towards a thermodynamic unified approach

AbstractExtended Irreversible Thermodynamics is shown to be a very appropriate theorotical frame for the discription of rheological materials. By splitting the total viscous pressure tensor into two independent contributions due to the solvent and the polymer and assuming that the polymer contribution is a function of the conformation tensor, one generates general non-linear constitutive equations. The Giesekus, Jeffreys and Oldroyd 8-constants models are recovered as particular cases. The results are also compared with another EIT derivation of Oldroyd's model

Microscopic rheological models and extended irreversible thermodynamics

AbstractThe expressions of the constitutive equations of dilute polymer solutions, as predicted by the main microscopic rheological models, are shown to be in agreement with these derived from extended irreversible thermodynamics. Accord between the thermodynamic and Boltzmann microscopic expressions of entropy is also completed for steady state flows