Escuela de Ingeniería civil Industrial

El dueño del Supermercado Las Brisas, localizado en la Región de Valparaíso, le solicitó a uno de sus colaboradores que obtuviera información sobre las compras que efectuaban clientes en un día cualquiera. Para tal efecto, eligió el día 20 de Octubre y consideró los siguientes datos por cada compra efectuada ese día: Rut cliente. Código artículo. Descripción artículo. Cantidad. Monto de la compra Sector donde estaba ubicado el artículo adquirido. Periodo del día cuando compró.

Steady laminar flow in a circular duct of variable section in the axial direction is modeled, assuming that the working fluid is an incompressible Newtonian fluid with constant properties. The behavior of the velocity and the pressure fields are presented. The method used to solve the problem makes use of regular perturbations around the shape factor ε parameter. The results of this research can be used for the design of new important industrial devices that help to optimize fluid transport processes.

In many biomedical and industrial technological applications it is necessary to drive fluids that exhibit plastic or elasto-plastic behaviour. Particularly for cases in which fast results are demanded, or only small fluid samples are available, micro-channels are used. These normally have cross-section geometries determined by the manufacturing procedures and may be of square, rectangular, triangular and other shapes. In order to obtain the expected results, such as protein separation, particle concentrations, and the like, the rate of flow and time-dependent pattern of it must be carefully determined. In this paper it is presented an analytically rigorous method for calculating the friction coefficient in channels of arbitrary cross-section contours for plastic flow that may be described by the Bingham model. Results are presented for a variety of shapes and for different values of the yield stress.

In this paper the Graetz problem is addressed for the case of steady laminar flow of Newtonian fluids in tubes of arbitrary cross-section. The method herein presented models the velocity field in a general way so that the non-slip boundary condition is met by a wide variety of cross-section contours. The energy equation is next solved for the temperature field, which is also mathematically modeled so that the thermal condition at the wall is met, for all cases, in the corresponding tube contours. Main results are the temperature distribution for different tube geometries that include the triangular and square cases.

A method to model and minimize resonant structural oscillations using magnetorheological dampers is presented. The response of the magnetorheological fluid flowing in a circular tube under a pressure gradient to the applied variable magnetic field is tailored to determine the optimum stress field in the fluid to mitigate resonance effects.

Presentación en webinar de SOCLIMPACT el 23/09/2020 para la comunidad online Principales temas: Riesgos energéticos por cambio climático. (Cadenas de impacto) Estrategia para la maximización de EERR Metodología general para realizar estudios eléctricos de potencia (Estudio de estabilidad) Modelado de redes eléctricas Análisis para el estudio de eventos derivados del cambio climático

The linear programs in Chapters 1 and 2 are all examples of classical ''activity'' models. In such models the variables and constraints deal with distinctly different kinds of activities-tons of steel produced versus hours of mill time used, or packages of food bought versus percentages of nutrients supplied. To use these models you must supply coefficients like tons per hour or percentages per package that convert a unit of activity in the variables to the corresponding amount of activity in the constraints. This chapter addresses a significantly different but equally common kind of model, in which something is shipped or assigned, but not converted. The resulting constraints, which reflect both limitations on availability and requirements for delivery, have an especially simple form. We begin by describing the so-called transportation problem, in which a single good is to be shipped from several origins to several destinations at minimum overall cost. This problem gives rise to the simplest kind of linear program for minimum-cost flows. We then generalize to a transportation model, an essential step if we are to manage all the data, variables and constraints effectively. As with the diet model, the power of the transportation model lies in its adaptability. We continue by considering some other interpretations of the ''flow'' from origins to destinations, and work through one particular interpretation in which the variables represent assignments rather than shipments. The transportation model is only the most elementary kind of minimum-cost flow model. More general models are often best expressed as networks, in which nodes-some of which may be origins or destinations-are connected by arcs that carry flows of some kind. AMPL offers convenient features for describing network flow models, including node and arc declarations that specify network structure directly. Network models and the relevant AMPL features are the topic of Chapter 15. 43

Profesor: Basso, Cleveland y Yáñez P1. a) [2.0 ptos] Considere una CDMD con un número finito de estados. Considere la siguiente afirmación: "Si la cadena está formada por unaúnica clase de estados, entonces tiene unaúnica distribución límite tal que lim n→∞ P (n) ij = π j para cualquier par de estados i, j". Indique si la frase anterior es verdadera o falsa, justificando claramente su respuesta b) Considere una CDMD con estados {1, 2, 3, 4} y matriz de transición dada por: P =     1 4 3 4 0 0 1 0 0 0 2 3 0 1 3 0 0 0 2 3 1 3     (i) [2.0 ptos] Dibuje el grafo de la cadena y clasifique sus estados según su recurrencia o transiencia. ¿Es la cadena irreducible? (ii) [1.0 pto] Calcule P 4 42 y f 4 42. ¿Intuitivamente, cuál de estas probabilidades debería ser mayor o igual que la otra? (iii) [1.0 pto] Calcule la probabilidad de que alguna vez el sistema ingrese al estado 3, considerando que el estado inicial es 4. Solución: a) La afirmación es falsa, pues podemos tomar que esaúnica clase sea periódica, por ejemplo: En esta cadena podemos ver que lim n→∞ P (2n) 22 = 1 = lim n→∞ P (2n) 12 = 0, por lo tanto, no hay distribución límite, pues lim n→∞ P (n) ij depende del estado inicial i. b) (i) El grafo es el siguiente Tenemos que existen 3 clases. Una clase son los estados 1 y 2 que son recurrentes; la otra está representada por el 3 que es transiente. Finalmente, laúltima clase contiene solo al 4 y es también transiente. La cadena tiene más de una clase por lo que no es irreductible. (ii) Siempre P 4 42 ≥ f 4 42 P 4 42 = P 44 · P 43 · P 31 · P 12 + P 43 · P 33 · P 31 · P 12 + P 43 · P 31 · P 11 · P 12 f 4 42 = P 44 · P 43 · P 31 · P 12 + P 43 · P 33 · P 31 · P 12 + P 43 · P 31 · P 11 · P 12 En este caso son iguales, P 4 42 = f 4 42