Internal State Variable
Internal State Variable - Related Videos
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Topology of cell adhesion on a substrate is measured with nanometre precision by variable-angle total internal reflection fluorescence microscopy (VA-TIRFM).
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Internal Standards
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Source: Laboratory of Dr. B. Jill Venton - University of Virginia The goal of many chemical analyses is a quantitative analysis, where the amount of a substance in a sample is determined. In order to accurately calculate the concentration of an unknown from a sample, careful sample preparation is key. Every time a sample is handled or transferred, some of the sample can be lost. There are strategies however, for minimizing sample loss. There are also strategies for coping with sample loss and...
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The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with initial internal energy, Uinitial, undergoes a change in energy (transfer of work or heat), and the final internal energy of the system is Ufinal. Change in internal energy equals the difference between Ufinal and Uinitial. Although the values for Ufinal and Uinitial cannot be determined for a system, the first law of thermodynamics only...
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The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...
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Functions of Three or More Variables
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A function of three variables assigns a single real number to each point in three-dimensional space. Every point is identified by its Cartesian coordinates, x, y, and z, and the function maps this ordered triple to a scalar value. Such functions are commonly used to describe physical quantities that vary throughout space.A representative example is the electric potential generated by a point charge. In this case, the potential at a given location depends only on the distance from the charge. If...
FAQs
The model uses the variable’s current value as a compact record of prior loading, transport, reaction, or biological regulation. An evolution law updates that value as conditions change, while the constitutive response depends on both present inputs and the stored state. This allows future behavior to be predicted without reconstructing the entire earlier sequence of events.
Its evolution law specifies how the hidden condition responds to relevant drivers, such as mechanical loading, transport, reaction, or biological regulation. The updated value can then alter the system’s subsequent response. Selecting drivers that represent the actual mechanism is important because an incomplete evolution law may fail to capture damage, adaptation, chemical change, or cellular activation.
An external input describes what is imposed on the system, whereas a directly measured response describes what the system produces or exhibits. An internal state variable occupies the modeling link between them by representing a changing condition that may not be directly captured by either quantity. This distinction helps explain why identical inputs can lead to different later responses.
A practical formulation identifies the hidden feature to represent, defines its initial value, specifies an evolution law, and determines how the variable influences the modeled response. The chosen structure should match the relevant driver, whether mechanical, transport-related, reactive, or biological. This workflow produces a model that can track changes such as degradation, remodeling, or adaptation.
The variable can track an evolving material or tissue condition while the constitutive model translates that condition into subsequent behavior. Under changing mechanical or biological influences, its value is updated rather than held fixed. This supports analysis of time-dependent responses, including damage progression and remodeling, and can improve interpretation of how biomaterials or tissues change during operation.
They help models account for evolving chemical composition, cellular activation, degradation, or adaptation that external conditions alone cannot describe. By allowing those hidden conditions to influence later predictions, the framework can support analysis of bioprocess behavior and evaluation of treatment or device performance. The resulting model is more informative when system behavior depends on prior history.