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The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
Parallel power can be simplified, by recalling the relationship between effort and flow for 0 and 1-junctions. To solve parallel power you will first want to write down all of the equations for the junctions. For the example provided, the equations can be seen below. (Please make note of the number bond the effort/flow variable represents).
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the phase space usually consists of all possible values of the position and momentum parameters.
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r corresponds to spatial position or external coordinates) dispersed in a continuous phase defined by a phase vector Y(r,t) (which again is a function of all such vectors which ...
Thus the set of all states of M with the weak-* topology forms a compact Hausdorff space, known as the state space of M. In the C*-algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i.e. mappings from physical observables (self-adjoint elements of the C*-algebra) to their expected ...
A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example ...
The Rabi problem concerns the response of an atom to an applied harmonic electric field, with an applied frequency very close to the atom's natural frequency. It provides a simple and generally solvable example of light–atom interactions and is named after Isidor Isaac Rabi.