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The mathematical model of such a process can be thought of as an inverse percolation process. Percolation theory models the process of randomly placing pebbles on an n-dimensional lattice with probability p, and predicts the sudden formation of a single large cluster at a critical probability p c {\displaystyle p_{c}} . [ 5 ]
Resilience is an important concept in the study of complex systems, where there are many interacting components that can affect each other in unpredictable ways. [13] Mathematical models can be used to explore the resilience of such systems and to identify strategies for improving their resilience in the face of environmental or other changes.
Constant elasticity of substitution (CES) is a common specification of many production functions and utility functions in neoclassical economics. CES holds that the ability to substitute one input factor with another (for example labour with capital) to maintain the same level of production stays constant over different production levels.
The first type of resilience engineering work is determining how to best take advantage of the resilience that is already present in the system. Cook uses the example of setting a broken bone as this type of work: the resilience is already present in the physiology of bone, and setting the bone uses this resilience to achieving better healing ...
Flexibility is used as an attribute of various types of systems. In the field of engineering systems design, it refers to designs that can adapt when external changes occur. Flexibility has been defined differently in many fields of engineering, architecture , biology , economics , etc.
The tradeoff exists because accommodating flexibility requires satisfying a larger set of requirements, which results in complexity and usability compromises. [ 1 ] Design theory maintains that over their lifecycle, systems shift from supporting multiple uses inefficiently, towards efficiently supporting a single use as users' needs become more ...
In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion.
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the members' flexibility matrices also has the name the matrix force method due to its use of member forces ...