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18-924: SWU may refer to: Science & technology [ edit ] Separative Work Unit , the amount of separation done by an enrichment process Labor Unions [ edit ] Seychelles Workers Union Starbucks Workers Union Universities [ edit ] South-West University "Neofit Rilski" (Blagoevgrad, Bulgaria) Southwest University (Chongqing, China) Srinakharinwirot University (Bangkok, Thailand) Seoul Women's University Showa Women's University (Tokyo, Japan) Southern Wesleyan University Southwestern University (Philippines) Miscellaneous [ edit ] StandWithUs , pro-Israel organization SWU Swimwear, Australian online retailer Star Wars universe SWU Music & Arts , Brazilian music festival Swiss European Air Lines (ICAO airline designator) Topics referred to by

36-432: A mass P {\displaystyle P} of product assay x p {\displaystyle x_{p}} , and tails of mass T {\displaystyle T} and assay x t {\displaystyle x_{t}} is given by the expression: where V ( x ) {\displaystyle V\left(x\right)} is the value function , defined as: Given

54-427: A net electrical capacity of 1300 MW requires about 25 tonnes per year (25 t / a ) of LEU with a U concentration of 3.75%. This quantity is produced from about 210 t of NU using about 120 kSWU. An enrichment plant with a capacity of 1000 kSWU/a is, therefore, able to enrich the uranium needed to fuel about eight large nuclear power stations. Value function The value function of an optimization problem gives

72-460: A tails assay of 0.3%. The number of separative work units provided by an enrichment facility is directly related to the amount of energy that the facility consumes. Modern gaseous diffusion plants typically require 2,400 to 2,500 kilowatt-hours (kW·h), or 8.6–9 gigajoules , (GJ) of electricity per SWU while gas centrifuge plants require just 50 to 60 kW·h (180–220 MJ) of electricity per SWU. Example: A large nuclear power station with

90-618: A typical optimal control problem is to subject to with initial state variable x ( t 0 ) = x 0 {\displaystyle x(t_{0})=x_{0}} . The objective function J ( t 0 , x 0 ; u ) {\displaystyle J(t_{0},x_{0};u)} is to be maximized over all admissible controls u ∈ U [ t 0 , t 1 ] {\displaystyle u\in U[t_{0},t_{1}]} , where u {\displaystyle u}

108-453: Is not a unit of energy, but serves as a measure of the enrichment services . In the early 2020s the cost of 1 SWU was approximately $ 100. The unit was introduced by Paul Dirac in 1941. The work W S W U {\displaystyle W_{\mathrm {SWU} }} necessary to separate a mass F {\displaystyle F} of feed of assay x f {\displaystyle x_{f}} into

126-1132: Is a Lebesgue measurable function from [ t 0 , t 1 ] {\displaystyle [t_{0},t_{1}]} to some prescribed arbitrary set in R m {\displaystyle \mathbb {R} ^{m}} . The value function is then defined as V ( t , x ( t ) ) = max u ∈ U ∫ t t 1 I ( τ , x ( τ ) , u ( τ ) ) d τ + ϕ ( x ( t 1 ) ) {\displaystyle V(t,x(t))=\max _{u\in U}\int _{t}^{t_{1}}I(\tau ,x(\tau ),u(\tau ))\,\mathrm {d} \tau +\phi (x(t_{1}))} with V ( t 1 , x ( t 1 ) ) = ϕ ( x ( t 1 ) ) {\displaystyle V(t_{1},x(t_{1}))=\phi (x(t_{1}))} , where ϕ ( x ( t 1 ) ) {\displaystyle \phi (x(t_{1}))}

144-572: Is different from Wikidata All article disambiguation pages All disambiguation pages Separative Work Unit The same amount of separative work will require different amounts of energy depending on the efficiency of the separation technology. Separative work is measured in Separative work units SWU, kg SW, or kg UTA (from the German Urantrennarbeit – literally uranium separation work ) Separative work unit

162-510: Is the "scrap value". If the optimal pair of control and state trajectories is ( x ∗ , u ∗ ) {\displaystyle (x^{\ast },u^{\ast })} , then V ( t 0 , x 0 ) = J ( t 0 , x 0 ; u ∗ ) {\displaystyle V(t_{0},x_{0})=J(t_{0},x_{0};u^{\ast })} . The function h {\displaystyle h} that gives

180-558: The Hamiltonian , H ( t , x , u , λ ) = I ( t , x , u ) + λ ( t ) f ( t , x , u ) {\displaystyle H\left(t,x,u,\lambda \right)=I(t,x,u)+\lambda (t)f(t,x,u)} , as with ∂ V ( t , x ) / ∂ x = λ ( t ) {\displaystyle \partial V(t,x)/\partial x=\lambda (t)} playing

198-431: The value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system , the value function represents the optimal payoff of the system over the interval [t, t 1 ] when started at the time- t state variable x(t)=x . If the objective function represents some cost that is to be minimized, the value function can be interpreted as

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216-449: The HJB equation with respect to x {\displaystyle x} , which after replacing the appropriate terms recovers the costate equation where λ ˙ ( t ) {\displaystyle {\dot {\lambda }}(t)} is Newton notation for the derivative with respect to time. The value function is the unique viscosity solution to

234-645: The cost to finish the optimal program, and is thus referred to as "cost-to-go function." In an economic context, where the objective function usually represents utility , the value function is conceptually equivalent to the indirect utility function . In a problem of optimal control , the value function is defined as the supremum of the objective function taken over the set of admissible controls. Given ( t 0 , x 0 ) ∈ [ 0 , t 1 ] × R d {\displaystyle (t_{0},x_{0})\in [0,t_{1}]\times \mathbb {R} ^{d}} ,

252-400: The current state x ( t ) {\displaystyle x(t)} as "new" initial condition must be optimal for the remaining problem. If the value function happens to be continuously differentiable , this gives rise to an important partial differential equation known as Hamilton–Jacobi–Bellman equation , where the maximand on the right-hand side can also be re-written as

270-414: The desired amount of product P {\displaystyle P} , the necessary feed F {\displaystyle F} and resulting tails T {\displaystyle T} are: For example, beginning with 102 kilograms (225 lb) of natural uranium (NU), it takes about 62 SWU to produce 10 kilograms (22 lb) of Low-enriched uranium (LEU) in U content to 4.5%, at

288-500: The optimal control u ∗ {\displaystyle u^{\ast }} based on the current state x {\displaystyle x} is called a feedback control policy, or simply a policy function. Bellman's principle of optimality roughly states that any optimal policy at time t {\displaystyle t} , t 0 ≤ t ≤ t 1 {\displaystyle t_{0}\leq t\leq t_{1}} taking

306-580: The role of the costate variables . Given this definition, we further have d λ ( t ) / d t = ∂ 2 V ( t , x ) / ∂ x ∂ t + ∂ 2 V ( t , x ) / ∂ x 2 ⋅ f ( x ) {\displaystyle \mathrm {d} \lambda (t)/\mathrm {d} t=\partial ^{2}V(t,x)/\partial x\partial t+\partial ^{2}V(t,x)/\partial x^{2}\cdot f(x)} , and after differentiating both sides of

324-403: The same term [REDACTED] This disambiguation page lists articles associated with the title SWU . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=SWU&oldid=1092832326 " Category : Disambiguation pages Hidden categories: Short description

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