Primary State Variables Research Articles

Heparosan biosynthesis in recombinant Bacillus megaterium: Influence of N-acetylglucosamine supplementation and kinetic modeling.

Heparosan, an unsulfated polysaccharide, plays a pivotal role as a primary precursor in the biosynthesis of heparin-an influential anticoagulant with diverse therapeutic applications. To enhance heparosan production, the utilization of metabolic engineering in nonpathogenic microbial strains is emerging as a secure and promising strategy. In the investigation of heparosan production by recombinant Bacillus megaterium, a kinetic modeling approach was employed to explore the impact of initial substrate concentration and the supplementation of precursor sugars. The adapted logistic model was utilized to thoroughly analyze three vital parameters: the B. megaterium growth dynamics, sucrose utilization, and heparosan formation. It was noted that at an initial sucrose concentration of 30gL-1 (S1), it caused an inhibitory effect on both cell growth and substrate utilization. Intriguingly, the inclusion of N-acetylglucosamine (S2) resulted in a significant 1.6-fold enhancement in heparosan concentration. In addressing the complexities of the dual substrate system involving S1 and S2, a multi-substrate kinetic models, specifically the double Andrew's model was employed. This approach not only delved into the intricacies of dual substrate kinetics but also effectively described the relationships among the primary state variables. Consequently, these models not only provide a nuanced understanding of the system's behavior but also serve as a roadmap for optimizing the design and management of the heparosan production method.

Online Prediction Method for Power System Frequency Response Analysis Based on Swarm Intelligence Fusion Model

Instability at transient frequency caused by faults in complex power systems is one of the greatest threats to operational safety. By analyzing the frequency response of power system in real-time and adopting control strategies promptly, power system accidents can be efficiently prevented. While existing online analysis methods integrate physical-driven and data-driven methodologies, they do not effectively utilize frequency timing characteristics. Consequently, a swarm intelligence fusion model, which integrates physical-driven and data-driven methods, is proposed as an improved frequency response analysis method. The transient frequency affecting components are separated into primary state variables and system time series data based on the properties of the time sequence. To preserve the actual relationship of the electrical mechanism model, the system frequency response (SFR) model is used as the physical-driven method for the primary state variables of the system. The Long Short Term Memory (LSTM) network was used as the data-driven method to extract timing features and correct the SFR model’s prediction using the system time series data as input. The two methods are combined using the bootstrap mode to form the fusion model, and the structure of the model is optimized using an improved sparrow search algorithm (ISSA), a swarm intelligence optimization algorithm. The model structure is adapted autonomously, implementing a method for online frequency response analysis. The simulation on the New England 39-bus system has verified that the method can quickly and accurately calculate the dynamic process of frequency response after a large-scale disturbance.

A Flexible Lattice Model for Pricing Contingent Claims under Multiple Risk Factors

The original binomial model is an easy-to-apply approximation procedure for valuing options under Black-Scholes assumptions. There is a single stochastic factor and the volatility, interest rate, and other parameters are known. However, weakening those assumptions typically produces a non-recombining lattice that blows up asymptotically when the number of time steps is increased for closer replication of the underlying continuous-time process. Various extensions of the basic lattice structure have been developed over the years. In this article, Russo and Staino provide a very general lattice model in the form of a “forward-shooting grid” that can handle three correlated risk factors: volatility, interest rate, and stock price. An innovation in the model is that volatility and the riskless interest rate are the primary state variables, while the asset price (whose returns process is a function of both volatility and the riskless rate) is treated as an auxiliary variable. The lattice determines the possible evolution of the volatility and interest rate, and the stock price is carried along as a set of possible values falling into discrete buckets at each node. The trivariate branching structure is represented in a lattice that allows eight branches from each node. This accommodates many of the standard continuous-time models, including non-zero correlation among the stochastic factors. A simulation exercise shows striking improvement in performance relative to earlier models in the literature.

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

The article proposes a method for nonlinear control of the dynamical system that is formed by a DC–DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system’s flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which enables to obtain estimates of the initial nonlinear state-space model. Moreover, to compensate for parametric uncertainties and external perturbations the filter is redesigned as a disturbance observer. By estimating the perturbation inputs that affect the joint model of the DC–DC converter and of the DC motor their compensation becomes possible. The efficiency of the proposed control scheme is further confirmed through simulation experiments.

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables. A very important key feature of the model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic evolution equation of the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the principles of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume and ADER discontinuous Galerkin finite element schemes in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier-Stokes equations. To show the universality of the model, the paper is rounded-off with an application to wave propagation in elastic solids.

A computational model for fluid leakage in heterogeneous layered porous media

This paper introduces a new and computationally efficient model for the simulation of non-wetting phase leakage in a rigid heterogeneous layered medium domain constituting layers of different physical properties. Such a leakage exhibits a discontinuity in the saturation field at the interface between layers. The governing field equations are derived based on the averaging theory and solved numerically using a mixed finite element discretization scheme. This scheme entails solving different balance equations using different discretization techniques, which are tailored to accurately simulate the physical behavior of the primary state variables. A discontinuous non-wetting phase saturation–continuous water pressure formulation is adopted. The standard Galerkin finite element method is utilized to discretize the water phase pressure field, and the partition of unity finite element method is utilized to discretize the non-wetting phase saturation field. This mixed discretization scheme leads to a locally conservative system, giving accurate simulation of the saturation jump. The boundary between layers is embedded within the finite elements, alleviating the need to use the typical interface elements, and allowing for the use of structured, geometry-independent and relatively coarse meshes. The accuracy and capability of the proposed model are evaluated by verification and numerical examples covering water, DNAPL and CO2 leakage through layers of different hydraulic properties.

A contact finite element algorithm for the multileaf spring of vehicle suspension systems

This paper presents an innovative finite element (FE) algorithm for the contact problem of the multileaf spring in vehicles. The well-established classic beam theory is adopted to construct the complementary strain energy variational. A piecewise contact stress pattern is approximated to the real contact state between two layered beams. The vector of nodal contact stresses is taken to represent primary state variables. To implement the principle of the least complementary energy, a quadratic programming (QP) problem with equality and unilateral constraints is formulated. The corresponding Kuhn-Tucker condition is equivalent to the linear complementary problem. In this study, Lemke's algorithm is applied to solve for the nodal stress vector and subsequently to determine the contact stress distribution over the contact surfaces between the layered beams. The algorithm is verified against experimental stress analysis, and it is found that the computation and test correlate well.

Implications of the glacial CO2 “iron hypothesis” for Quaternary climate change

The “iron hypothesis” posits a role for increased supply of mineral aerosol to the ocean surface during glacial periods in driving atmospheric CO2 lower; that changes in CO2 and climate strongly affect dust supply raises the possibility of feedback. Here I take a systems view in analyzing the properties and implications of such a feedback and consider three primary state variables that can be related empirically to each other: dust supply, atmospheric CO2, and “climate” (surface air temperature). The results of this analysis suggest that the dust‐CO2‐climate feedback is primarily an intraglacial phenomenon, when it can account for about a third of the temperature variability recorded in Antarctic ice cores. Since glacial‐interglacial cyclicity prior to ca. 800 kyr BP is characterized by the absence of a “full” glacial state (such as the Last Glacial Maximum), it is possible that destabilization of climate by the marine iron cycle is fundamental to the differences between “41 kyr” and “100 kyr” climatic regimes. The critical role played by the state of the land surface in this feedback also has implications for the longer‐term evolution of the Earth system during the Cenozoic.

Basal mechanics of Ice Stream B, west Antarctica: 1. Till mechanics

Data from laboratory geotechnical tests on till recovered from beneath Ice Stream B, West Antarctica, at the Upstream B camp (hereinafter the UpB till) show that failure strength of this till is strongly dependent on effective stress but is practically independent of strain and strain rate. These data support use of a Coulomb‐plastic rheology in modeling of ice stream behavior and subglacial till deformation. Our testing program combined triaxial, ring shear, and confined uniaxial tests to investigate till strength and compressibility. Results show that the UpB till follows closely Coulomb's equation in which shear strength is a linear function of normal effective stress (apparent cohesion near zero and internal friction angle ϕ equal to 24°). Till compressibility is best described by a logarithmic function that relates void ratio to normal effective stress. In general, the behavior of the UpB till is consistent with other experimental evidence regarding mechanical behavior of granular materials. Based on our laboratory results we formulate the Compressible‐Coulomb‐Plastic till model in which there are three interrelated, primary state variables: shear strength, void ratio, and normal effective stress. This model is used in the second part of our study to simulate response of subglacial till to realistic effective stress forcings. These simulations demonstrate that the model is capable of reproducing fundamental aspects of subglacial till kinematics: (1) occurrence of tilt rate oscillations and negative tilt rates in tiltmeter records, and (2) distributed till deformation to depths of 0.1–1.0 m beneath the ice base. Our laboratory and modeling results substantiate application of the Compressible‐Coulomb‐Plastic model in simulations of the motion of Ice Stream B over its weak till bed.

A process model for the microstructure evolution in ductile cast iron: Part I. the model

In the present investigation, the multiple phase changes occurring during solidification and subsequent cooling of near-eutectic ductile cast iron have been modeled using the internal state variable approach. According to this formalism, the microstructure evolution is captured mathematically in terms of differential variation of the primary state variables with time for each of the relevant mechanisms. Separate response equations have then been developed to convert the current values of the state variables into equivalent volume fractions of constituent phases utilizing the constraints provided by the phase diagram. The results may conveniently be represented in the form of C curves and process diagrams to illuminate how changes in alloy composition, graphite nucleation potential, and thermal program affect the microstructure evolution at various stages of the process. The model can readily be implemented in a dedicated numerical code for the thermal field in real castings and used as a guiding tool in design of new treatment alloys for ductile cast irons. An illustration of this is given in an accompanying article (Part II).

Analytical modelling of equiaxed solidification

A framework for modelling the overall microstructure evolution during equiaxed solidification is presented, based on the internal state variable approach. In its simplest form the microstructure evolution can be captured mathematically in terms of differential variation of two primary state variables with time. The model utilizes input data from thermal analysis as a means for calibrating unknown kinetic constants, and has proved useful to describe the solidification behaviour of hypoeutectic Al–Si alloys under different inoculation conditions. The results may conveniently be presented in the form of continuous cooling transformation (CCT) diagrams to show the competition between the different variables involved. Because of the analogy with solid state transformations, the proposed formalism is well suited for modelling of coupled microstructure problems in real castings or fusion welds.

Snowmelt modelling on signy island, South Orkney Islands

The ability of the Utah energy-balance and snowmelt model (UEB) to simulate decline in snow water equivalent (SWE) at an extreme location was assessed. Field data were collected at Paternoster Valley, Signy Island, South Orkney Islands (60°43′S) during the austral summer of 1996–97. This is the first application of UEB in a maritime Antarctic site. UEB is a physically based snow melt model using a lumped snow-pack representation with primary state variables SWE and snow pack-energy content (U). Meteorological inputs are air temperature, wind speed, humidity, precipitation and total incoming solar and longwave radiation. The Paternoster Valley catchment was subdivided into eight non-contiguous terrain classes for sampling and modelling using a geographical information system (GIS). Simulations of SWE in each of these classes were compared พ with field observations. It is shown that initial U and snow-surface thermal conductance (Ks) affect model simulations. Good approximations of SWE depletion are obtained using measured incoming solar radiation to drive the model but there are shortcomings in the characterization of long wave radiation and sensible-heat fluxes.

Snowmelt modelling on signy island, South Orkney Islands

The ability of the Utah energy-balance and snowmelt model (UEB) to simulate decline in snow water equivalent (SWE) at an extreme location was assessed. Field data were collected at Paternoster Valley, Signy Island, South Orkney Islands (60°43′S) during the austral summer of 1996–97. This is the first application of UEB in a maritime Antarctic site. UEB is a physically based snow melt model using a lumped snow-pack representation with primary state variables SWE and snow pack-energy content(U).Meteorological inputs are air temperature, wind speed, humidity, precipitation and total incoming solar and longwave radiation. The Paternoster Valley catchment was subdivided into eight non-contiguous terrain classes for sampling and modelling using a geographical information system (GIS). Simulations of SWE in each of these classes were compared พ with field observations. It is shown that initialUand snow-surface thermal conductance(Ks)affect model simulations. Good approximations of SWE depletion are obtained using measured incoming solar radiation to drive the model but there are shortcomings in the characterization of long wave radiation and sensible-heat fluxes.

The fully-coupled model for rock engineering systems

This paper introduces the fully-coupled model (FCM). The model is developed from rock engineering systems (RES) concepts and graph theory. The basic device used in the RES approach is the interaction matrix: for any rock mechanics or rock engineering problem, the relevant state variables of the system are listed along the leading diagonal of the matrix—and the relations between each pair of variables, i.e. the binary mechanisms, are identified in the off-diagonal boxes. The interaction matrix can contain any number of state variables, depending on the engineering objective and level of analysis required. The FCM considers the interaction matrix as a mechanism network. Graph theory is used to assess the contributions of all the mechanisms in all the pathways, a key feature being the identification of mechanism feedback loops and their stability. The (uncoupled) binary interaction matrix is thus transformed into a (fully-coupled) global interaction matrix. The system outputs for any problem being modelled are then obtained from the system inputs via the global interaction matrix. Advantages of the FCM in the context of rock engineering are that the primary state variables of the system, the binary interactions, all the mechanism pathways, each step in the coupling process, and the consequential evolution of the matrix values can be clearly identified. The FCM has been developed initially with linear mechanisms. Five numerical examples of the linear FCM are given: simultaneous equations, spring structures, a pressurized thick cylinder, a six-variable dam system and a nine-variable pressure tunnel system. Using these examples, we demonstrate that the output resulting from any input perturbations can be rapidly assessed with the FCM. We also indicate how the FCM can be extended to include non-linear mechanisms.

A two-fluid model for critical flashing flows in pipes

A one-dimensional two-fluid model is described for the analysis of critical flows in pipes of nondiverging cross-sectional area. The model accounts for thermal nonequilibrium between the liquid and vapor bubbles and for interphase relative motion. Closure of the set of governing equations is performed with constitutive relationships which determine the pressure drop along the flow channel as a function of the flow regime, and the number and rate of growth of vapor bubbles in a variable temperature field in terms of the problem's primary state variables and geometrical configuration. An empirical correlation is derived which fits the number density of bubble nuclei in the flow as a function of the flow channel length-to-diameter ratio. Model predictions compare favorably with experimental data in small- and large-scale systems over a wide range of pressures and pipe diameters and lengths.