]> composedOf componentIn hasPropertyAttribute isPropertyPlayerIn isPropertyOf hasPortionOfEnergy hasThermodynamicEntity isConstitutivePlayerIn hasProcessProperty hasPositivePlayer isProcessPropertyOf hasPortionOfEntropy hasProperty hasNegativePlayer hasPhysicsDomain has Constitutive Player hasPropertyScope isShapeOf isBoundedBy isReciprocalOf isNegativePlayerIn isConverseOf isPositivePlayerIn isBoundaryOf hasPlayerProperty hasShape isThermodynamicEntityOf has Example has Synonym discussion Calculus dependency ...are dependencies that encode theorems of calculus Differential dependency Integral dependency Compositional dependency ...by which physical properties of wholes, parts, parts of parts, and the boundaries between parts depend upon one another Dynamical dependency Mass action rate dependency Portion of pure liquid ...that is composed of a single molecular species Set of physical entities Partial gas pressure Portion of energy Portion of entropy Portion of potential energy Portion of kinetic energy Portion of thermodynamic entropy Portion of information entropy Magnetic field Electromagnetic field Origin of temporal coordinate system Set of quantal charges ...that is a countable set of quantal charges Portion of fluid kinetic energy Portion of solid kinetic energy Portion of fluid potential energy Portion of strain potential energy Portion of chemical potential energy Portion of thermal potential energy Portion of diffusion potential energy Portion of electrical potential energy Portion of magnetic potential energy Portion of magnetic inductive energy Multimolecular structure ...that is composed of more than one molecule Element that is a single atom Portion of liquid solution ...that is mixture of solute molecules of one or more species dissolved in a liquid Portion of monomolecular gas Portion of gas mixture Portion of gas-particulate mixture Portion of liquid-particulate mixture Discrete scope A physical property has discrete scope if its value applies to the entire spatial region of a physical entity. Conservation of mass Continuum scope A physical property has continuum scope if it's values vary smoothly throughout a spatial region occupied by the physical entity that has the physical property. Property spatial coordinate ...that is the form of the spatial coordinate system to which a physical property is referred OneD coordinate TwoD coordinate TwoD radial coordinate TwoD cartesian coordinate ThreeD coordinate ThreeD cartesian coordinate ThreeD spherical coordinate ThreeD cylindrical coordinate Constitutive property ...whose value is a parameter that characterizes a constitutive dependency. Locus of point region Entropy dimension Homologous set Scalar matrix form Geometric form Heterologous set Thermodynamic property ...that is a property of an energy-bearing physical entity whose value is the amount or rate of change of the amount of thermodynamic energy inhering in an entity. Spatial differential dependency Fluid-Solid transducer Kinetic energy amount Potential energy amount Chemical-solid transducer Real scalar form Magnetic flux linkage Imaginary scalar form Complex scalar form Dynamical rate property ...that is the temporal differential of a state property Information entropy amount Thermodynamic entropy amount Total energy amount Electrical resistive dependency Fluid resistive dependency Solid resistive dependency Diffusive resistive dependency Heat resistive dependency Electrical inductive dependency Solid inductive dependency Fluid inductive dependency Fluid capacitive dependency Solid capacitive dependency Electrical capacitive dependency Diffusive capacitive dependency Heat capacitive dependency Chemical capacitive dependency Particle concentration Particle count Physical process Conservation of space Conservation of amount Chemical flow transactor ...that is the dependence of a chemical flow on one or more chemical amounts; all chemical mass-action laws are Chemical flow transactors. Thermodynamic dependency Kinetic energy definition Potential energy definition Energy flow rate definition Energy state definition Dynamical boundary Chemical kinetic boundary Fluid kinetic boundary Dynamical entity Process property Energy property Energy definition Entropy definition Existential process Conservative dynamical process ZeroD-discrete Thermodynamic definition Subatomic particle Discrete portion of energy Thermodynamic law First law of thermodynamics Second law of thermodynamics Solid potential energy amount Fluid potential energy amount Chemical potential energy amount Fluid kinetic energy amount Solid kinetic energy amount Physical state trajectory Property state trajectory Structural event Existential event Physical change event Threshold-crossing event Minimal value event Maximal value event Structural state trajectory Existential state trajectory Entity appears Entity disappears Entity transforms Property value event Composite dynamical process Event interval Physical property trajectory Ion exchange pump dependency Ion exchange pump Chemical conductance 1 Solid conductance 1 Capacitance dependency Fluid conductance 1 Heat conductance 1 Bounded surface 1 Electrical conductance 1 Boltzmann constant ...that is the proportionality of the energy of a particle per rise in absolute temperature; equal to the Gas constant divided by Avogadro's number. Boltzmann constant Diffusion kinetic domain Discrete electrical conductance Electromagnetic constant NIST>Electromagnetic constant Intensive electrical conductance Spatial amount property ...that is the spatial extent of a spatial region Chemical kinetic rate control Intensive electrical conductance field Discrete heat conductance Intensive heat conductance Intensive heat conductance field Discrete fluid conductance Temporal domain ...in which temporal properties are related by temporal dependencies. Translational momentum Translational momentum Solid force Solid force Portion of liquid Portion of liquid ...and is a liquid Chemical capacitance 1 Intensive fluid conductance Intensive fluid conductance field Temporal differential of work Temporal differential of Work Conductance parameter ...is the derivative of flow versus force in a resistive dependency; the reciprocal of kinetic resistance property Discrete solid conductance Intensive solid conductance Event rate ...is an Event summation divided by the Duration of the Temporal interval over which the Event summation occurs Intensive solid conductance field Electrical resistivity 1 Amount of material dimension ...that is proportional to Amount of material dimension Property of event trajectory Discrete chemical conductance Bending displacement Torsional mechanics domain Quantal electrical charge ...that is the quantum of electrical charge Chemical amount ...is the temporal integral of a Chemical flow Chemical amount Intensive chemical conductance Polar coordinate system 2D 2D-Polar coordinate system Length dependency Length dependency Intensive chemical conductance field Transducer modulus ...is the nondimensional derivative of the magnitudes of kinetic property that are players in a transducer dependency Cardinality dimension ...is the count of the members of a set of physical entities; e.g., molecules, particles, cells... Discrete fluid inductance Intensive fluid inductance Unitary dimension ...that is a unit-less dimension Intensive fluid inductance field Intensive solid mass equal to mass density Pressure momentum 1 ...is the temporal integral of a Fluid pressure; also the Fluid flow times the mass density of a Portion of fluid Pressure momentum Spatial locus ...that is the set of all spatial points within a spatial region Intensive solid mass field Fluid volumetric elastance 1 Chemical elastance 1 Solid velocity ...is the temporal derivative of a Solid displacement Solid velocity Discrete chemical resistance Solid elastance 1 Shear capacitance Fluid flow transactor ...is the dependence of a fluid flow rate on a kinetic displacement. Constitutive dynamical process ...is the transformation of Energy within or between participating Energetic physical entities according to a constitutive dependency. Electrical elastance 1 Particle diffusive elastance Faraday constant ...is the amount of electric charge per mole of electrons; Faraday constant Chemical resistive dependency ...that is the dependence of a chemical flow rate on the amount or chemical potential of reactants (e.g., substrates, products) in a chemical reaction. Heat elastance Gravitational field ...by which material entities exert an attractive force on each other that is proportional to the product of their masses Gravitational field Spatial coordinate system ...is a spatial entity that is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. Spatial coordinate stystem Discrete heat elastance Intensive heat elastance Intensive heat elastance field Temporal integral dependency ...that is the temporal integral of a Physical property Temporal integral dependency Discrete particle elastance Transformer ratio ...is the nondimensional derivative of the magnitudes of kinetic property that are players in a transformer dependency Mass volumetric density Intensive particle elastance Sum of displacements Sum of displacements Fluid inductance 1 ...for the fluid domain Intensive particle elastance field Intensive electrical elastance Dynamical dimension ...is a dimension to which units of spatial extent apply Discrete electrical elastance Fluid viscosity 1 Intensive electrical elastance field One dimensional spatial region ..is a mathematical function that, given one value, returns a spatial point Time dimension ...is the temporal dimension to which units of units of time duration apply Conservation of momentum Conservation of momentum Sum of momenta ... Sum of momenta Rotational solid elastance Shear force Shear force Force dimension Force dimension Bounded volume shape Tensile force Tensile force Acceleration dimension Acceleration dimension http://physics.nist.gov/cuu/Units/units.html Discrete rotational inertia Dependency of constitutive property ...is the dependence of a constitutive property on intensive constitutive and spatial properties of a kinetic entity Inductance parameter ...is the derivative momentum versus force in an inductive dependency Spatial coordinate location ...that is a point in a spatial coordinate system Amount property ...is the temporal integral of a flow rate Solid bending velocity Intensive solid elastance Standard gravity constant ... is the nominal acceleration due to gravity at the Earth's surface at sea level; http://en.wikipedia.org/wiki/Standard gravity Spatial dimension ...is the dimension to which units of spatial extent apply Intensive solid elastance field Cartesian coordinate system 2D 2D-Cartesian coordinate system Physical property ...is a dependent continuant that encodes a quantitative attribute of a physical entity, property, or process whose value is measureable by a physical device. Discrete solid elastance Electrical resistance 1 Jerk dimension Jerk dimension Quantal electrical charge ...is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. Fluid volume 1 Fluid volume ...is the temporal integral of a Fluid flow Intensive electrical resistance Intensive electrical resistance field Temporal instant ...is a point in time Temporal moment Fluid resistance 1 Intensive fluid resistance Intensive fluid resistance field Angular momentum Angular momentum Transformer process Transformer process Temperature dimension Temperature dimension Area dimension Area dimension Property dimension ...is a fundamental coordinate of a physical property upon which its units of measure are based ---need to outsource this class to existing unit ontology Chemical resistance 1 Sum of flows Sum of flows Solid capacitance 1 Sum of rate property Sum of rate property Transducer dependency Transformer dependency ...in which energy is transferred and conserved between physics entities of different kinetic domains; constrained by the quantitative relationships: E1 = nF2, and nF1 = E2 where E and F are force and flow properties, respectively, of entities 1 and 2 , and n is a positive scalar transducer ratio. Solid momentum 1 Solid momentum ...is the temporal integral of a Solid force; also the Solid-velocity times the mass of a solid Material physical entity Cardinality of set ...that is the number of individuals in a set Cardinality of set Intensive chemical resistance Closed line 0 Intensive chemical resistance field Solid resistance 1 Intensive solid resistance Bending capacitance Locus of points in surface region Mass dimension ...that is proportional to the Mass of an entity Mass dimension Mass lineal density Length of line region Tensile capacitance Solid mechanics domain ...in which the entities are solid structures Solid domain Intensive solid resistance field Heat resistance 1 Heat flow rate ......is the temporal derivative of a Heat amount Heat flow Intensive heat resistance Motion dimension Motion dimension Intensive heat resistance field Charge dimension Charge dimension Statistical property of value distribution ...that is a Electrochemical domain ...in which the entities are portions of ions Newtonian gravitational constant ...that is the constant of proportionality that relates the gravitational force between two Material physical entities as the product of the masses of the entities divided by the distance between the entities; <http://en.wikipedia.org/wiki/Gravitational constant> Newtonian gravitational constant Sum of forces Sum of forces Ligand-gated ion current control Ligand-gated ion current control Electric constant formerly "dielectric constant" Energy dimension Energy dimension Elastance parameter ...is the derivative of force versus displacement in a capacitive dependency; reciprocal of capacitance property Locus of points in volume region Resistance parameter ...is the derivative of force versus flow in a resistive dependency; reciprocal of kinetic conductance property Variance of property magnitude Diffusion resistance 1 Discrete diffusion resistance Torsional capacitance Chemical flow maximum Angle dimension Angle dimension Angle dimension; UCUM ref: http://aurora.regenstrief.org/UCUM/ucum.html#section-Base-Units Constitutive coupling process ...that is the flow of energy or the modulation of an energy flow according to a entity-coupling dependency Intensive diffusion resistance Chemical flow rate Chemical flow ...is the temporal derivative of a Chemical amount Momentum dimension Volume dimension Volume dimension Constitutive path process ...that is the tranformation of energy according to a constitutive kinetic dependency Intensive diffusion resistance field Capacitive dependency 1 1 Capacitive dependency ...in which a displacement depends on a force differential applied to the entity. Ionic current transactor Ionic current control dependency Discrete chemical capacitance Dynamical domain Kinetic domain ...in which kinetic properties are related by kinetic physical dependencies. Chemical bond A Bond is an abstraction that represents ONLY the energetics of an attractive interaction between entities; i.e., the bond is manifested as a minimum energy state (usually as a function of entity-entity distance). Thus, a bond can be defined irrespective of the physical mechanism that mediates the bond such as electron-sharing or the extracellular matrix between cells. ...that is an attractive interaction between physical entities that requires force to be displaced or disrupted Discrete solid resistance Solid translational velocity Solid translational velocity Intensive chemical capacitance Temporal integral of flow rate 1 ...in which a change of Displacement is the temporal integral of Flow rate Temporal integral of Flow Intensive chemical capacitance field Spatial entity 1 Spatial entity ..that is a spatial region that has neither mass, charge, or energy but has spatial properties Mass areal density Discrete shear capacitance Intensive shear capacitance Intensive shear capacitance field Physical event trajectory ...that is a time-series of Moments of Process events during a Physical process Process event record Material entity ...that consists of matter Discrete bending capacitance Shear mechanics domain Capacitive process ...that is a Capacitive dependency Capacitive process Temporal duration ...is the amount of time between two temporal instants Translational displacement Translational displacement Constitutive path dependency ...is a constitutive dependency whose players are the kinetic properties of a single physical entity Intensive bending capacitance Thermodynamic domain Thermodynamic domain ...in which thermodynamic properties are related by thermodynamic dependencies. Temporal differential dependency Temporal differential dependency Potential energy field Force field ...is an immaterial spatial distribution of potential energy by which physical entities exert force upon each other. Transactor parameter Intensive bending capacitance field Discrete tensile capacitance Intensive tensile capacitance Positive quantal charge Temperature Area of surface region Intensive tensile capacitance field Fluid flow rate Fluid flow ...is the temporal derivative of a Fluid volume Discrete torsional capacitance One dimensional spatial coordinate system 1D-coordinate system Intensive torsional capacitance Closed surface 0 Physical entity ...that is a continuant that is a bearer of physical properties Intensive torsional capacitance field Negative quantal charge. Statistical property of value correlation Discrete fluid volumetric capacitance Conservation dependency Intensive fluid volumetric capacitance Intensive fluid volumetric capacitance field Electric current ...is the temporal derivative of an Ion amount Electrical current Luminosity dimension Solid displacement 1 Solid displacement ...is the temporal integral of a Solid velocity Portion of particulate ...that consists of innumerable particles that has diffusive kinetic properties Temporal differential of displacement 1 Temporal differential of Displacement Constitutive coupling dependency ...by which the Sum of state property Sum of state property Discrete heat capacitance Intensive heat capacitance Fluid volumetric capacitance 1 Intensive heat capacitance field Discrete electrical capacitance Shear displacement Shear displacement Heat capacitance 1 Chemical concentration the concentration of a portion of molecules that is the spatial average of the intensive chemical concentration field Intensive electrical capacitance Intensive electrical capacitance field Constitutive parameter ...that quantitatively characterizes a constitutive dependency Resistive process Resistive process ...that proceeds according to a resistive dependency and dissipates energy as heat Electric current dimension ...that is the amount of Charge flowing during an interval of Time Electric current dimension Tensile mechanics domain Physical property attribute ...that characterizes the dimension, value type, or spatial scope of a physical property Portion of fluid ...that is a material substance with fluid kinetic properties. Solid shear velocity Solid shear velocity Force transactor dependency Unbounded surface Cartesian coordinate system 3D 3D-Cartesian coordinate system Interval starting instant ...that is the moment that a process begins Interval ending instant ...that is the moment that a process ends Geometrical spatial dependency Magnetic constant Magnetic constant Chemical potential (chemical affinity = -∆G) Chemical potential Electrical entity 1 is a primitive that entity that is the bearer of electrical charge, is immaterial, and has no spatial extent Fluid kinetic domain ...in which the entities are portions fluids (i.e., liquids, gasses) Fluid domain Unbounded volume shape Transducer process Transducer process Negative quantal charge ...that is the electrical charge of an electron Point location dependency Transformer dependency Rate control dependency ...in which energy is transferred and conserved between physics entities of the same kinetic domain; constrained by the quantitative relationships: E1 = nE2, and nF1 = F2 where E and F are force and flow properties, respectively, of entities 1 and 2 , and n is a positive scalar transformer ratio. Positive quantal charge ...that is the electrical charge of a proton Molecule ...that is a polyatomic entity Material structure ...that has solid kinetic properties Statistical property 1 ...is a <fred?> of a set of physical entities Chemical kinetic parameter Portion of molecules 1 ...that has both chemical and diffusion kinetic properties. Temporal property 1 ...that is the temporal location or duration of a temporal entity within a temporal coordinate system. Temporal location ...that is the amount of time between the origin of a temporal coordinate and a temporal Instant OPB_00403 Portion of material entity Physical dependency ...is a quantitative dependency between the values of physical properties Conservation of energy ...by which Total energy is the algebraic sum of Potential energy and Kinetic energy Conservation of energy Velocity dimension Velocity dimension Property mathematical form --- outsource this class to existing ontology?? Gas constant ...that is the proportionality of the energy of a substance per mole per rise in absolute temperature; the same as Boltzmann's constant times Avogadro's number. Gas constant Charge amount 1 Electrical charge ...is the temporal integral of a Electrical current Temporal integral of force 1 Newton's law ...in which a change of Momentum is the temporal integral of Force Temporal integral of Force Solid inductance 1 Scalar form ...is a physical property whose magnitude or value is expressible as a scalar number that independent of transformations of the spatial coordinate system in which it is measured. Flow transactor dependency Inductance dependency Temporal differential of momentum 1 Newton's law Temporal differential of Momentum Gravitational constant Discrete fluid resistance Universal constitutive property ...that is a measured or defined physical property of matter or space attributable to all kinetic and spatial entities Dynamical process ...that is the flow, control, transformation, or dissipation of thermodynamic energy within or between participating energetic physical entities according to a physical property dependency. Chemical molar amount 1 total amount of a portion of chemical within a spatial region Conservation of charge ...is the law that states that the net rate of electrical charge traversing the Boundary of a Physical entity is exactly equal to the gain or loss of electrical charge within the Boundary. Conservation of charge Vector form ...is a physical property whose value is expressed as a combination of a scalar and a spatial orientation in a spatial coordinate system. Portion of gas Portion of gas ...and is a gas Constitutive coupling parameter ...that is a nondimensional positive scalar Chemical kinetic domain ...in which the entities are portions of molecules Chemical kinetic domain Tensor form ...is a physical property whose value is a multidimensional array of scalars whose values are invariant under spatial coordinate transformation. Statistical domain ...in which statistical properties are related by statistical dependencies. Three dimensional spatial region ...that consists of point regions in a three spatial dimensions in space Property spatial scope ...that is the spatial region for which a physical property is defined Portion of electrical charge ....that is a uncountable set of quantal charges whose net charge is a continuous scalar quantity Electrical capacitance 1 Temporal coordinate system ...is a temporal entity that is a system for assigning a numbers or scalars to temporal moments relative to reference moment. Length dimension ...is proportional to the extent of Space Length dimension Mean of property magnitude Bounded line 2 Mass density Mass density Bendng mechanics domain Cylindrical coordinate system Cylindrical coordinate system Two dimensional spatial region ...that consists of point regions in a two spatial dimensions in space Avagadro constant ...that is the number particles, usually, atoms or molecules in one mole of a chemical entity. Avagadro constant Particle amount 1 Particle amount ...is the temporal integral of a Particle flow Physical domain Physics domain ... is a domain of physics science in which physical properties are related by physical dependencies. Discrete intensive scope ...that is measured or applies to the entirety of a physical entity but is independent of the spatial extent or mass of the entity; Resistive dependency 1 Resistive dependency ...in which a flow depends on a force differential applied to the entity. Discrete extensive scope A physical property has discrete extensive if it's value applies to the entire spatial region occupied by a physical entity and is the spatial integral of a property and is proportional to the spatial extent or mass of the entity. Solid angle dimension Solid angle dimension Heat kinetic domain ...in which the entities are portions of thermal energy Thermal transfer domain Discrete heat resistance Continuum point scope A physical property has continuum point scope if it has the value at an arbitrarily small spatial region surrounding a spatial point within a spatial region; an intensive property. Spatial region ..is a bounded or unbounded region of space. Rotational displacement Rotational displacement Discrete electrical resistance Inductive process ...that is an Inductive dependency Inductive process Momentum property ...is the temporal integral of a force Continuum field scope A physical property has continuum field scope if it is the spatially distributed values of the property throughout a spatial region; the spatial distribution of an intensive property. Zero dimensional spatial region ...that is an arbitrarily small spatial region surrounding a spatial point Origin of spatial coordinate system Centroidal point Solid angular velocity Solid angular velocity Cumulative dynamical process ...that proceeds according to an axiomatic physical dependency. Heat amount 1 Heat amount ...is the temporal integral of a Heat flow Area dependency Area dependency Portion of solid substance Locus of points in line region Spherical coordinate system Spherical coordinate system Spatial property 1 ...that is a measure of the spatial extent or location of a spatial entity referred to a spatial coordinate system. Discrete solid mass ...that is the proportionality between solid momentum and velocity of a solid entity Electrochemical potential Electrochemical potential Fluid pressure Fluid pressure Temporal entity 1 Temporal entity ...is a moment or span of time Capacitance parameter ...is the derivative of displacement versus force in a capacitive dependency; reciprocal of elastance property Thermodynamic entity ...that is the capacity of a energetic entity to perform work and has thermodynamic properties Electrostatic field ...by which electrical charges that are immobile with respect to each other exert force on each other Electrostatic field Volume of volume region Summation dependency ...that is a summation of the magnitudes of individual Kinetic properties of one class across a Set of energetic physical entities Kinetic summation dependency Temporal interval ...is a period of time bounded by two temporal moments (that may be the same moment). Temporal interval Physical analytical entity Physical analytical entity The OPB is an ontology of the abstract concepts created by the science of systems dynamics and thermodynamics. Aside from its dependence on classical physics, the OPB does not purport to be a philosophically-based representation of physical "reality". We are motivated by utilitarian goal of facilitating and expediting the annotation and cross-referencing of physics-based analytical models in the realm of biomedicine. The OPB does not include quantum or relativistic physics, nor is it intended to recapitulate the axiomatic basis of physics as a theoretical framework. Whereas the foundational theory of the OPB encompasses both discrete systems analysis (using ordinary differential equations; ODEs) and continuum systems analysis (using partial differential equations; PDEs), the first version of the OPB is targeted solely to discrete systems analysis. A physics analytical entity is a formal abstraction of the real world created within the science of classical physics for the description of physical entities and the analysis of physical processes. Plane angle dimension Plane angle dimension Particle diffusion coefficient 1 Unbounded line 1 Chemical reaction rate constant Physiochemical constant NIST>Physiochemical constant Inductive dependency 1 1 ...in which the momentum of an entity depends on its flow rate. Inductive dependency Constitutive dependency ...that is a dependency between the magnitudes of dynamical physical properties that depends on the structure and material composition of physical entities. Particle flow rate ...is the temporal derivative of a Particle amount Particle flow Material constitutive property Material constitutive property ...is a constitutive property that is independent of an entity's spatial extent or its mass; can be determined at a point within the entity Spatial domain Spatial domain ...in which spatial properties are related by spatial dependencies. Three dimensional spatial coordinate system 3D-coordinate system Two dimensional spatial coordinate system 2D-coordinate system Resistance dependency Volume dependency Volume dependency Potential field dependency Gravitational potential dependency Electrostatic potential dependency Entropy property Energy amount ...that is a measure of the amount of energy in a portion of energy Energy flow rate Entropy flow rate Entropy amount ...that is a measure of the amount of entropy in a portion of entropy Dynamical property 1 ...that is a property of an energy-bearing physical entity whose value determined the amount or rate of change of the amount of thermodynamic energy inhering in as entity as defined by a thermodynamic dependency Dynamical state property ...that is the temporal integral of a rate property Flow rate property ......that is the sum of flow rates entering an energetic physical entity and is the temporal differential of its amount Force property ...is a determinant of potential energy, AND is a participant in a resistive dependency and a capacitive dependency, AND is a temporal differential on momentum Chemical molar flow rate measured in concentration per unit time; moles/s Chemical concentration flow rate measured in concentration per unit time; M/s Particle potential Process domain ...in which process properties are related by process dependencies. State transactor dependency Rate transactor dependency Amount transactor dependency Momentum transactor dependency Transactor dependency Transactor process Spatial integral dependency