Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

1) Assume a fluid (say, water) occupies a domain D⊂ R3 and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and would be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let Φ= Φ(x,t) be the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.

B(x)ut dV= -∫∂B(x)Φ.n0dS.

Fick's law for diffusion states that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that Φ= -k∇+uV.
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
ut= ∇.(k∇u)+ ∇.(uV).
in the absence of diffusion (k=0), this is the higher- dimensional transport equation. If the fluid is motionless, it is known as diffusion equation.

2) find out the causality principle for the Klein- Gordon equation in one dimension. Deduce that the speed of propagation is at most c.
3) Drive causality principle for weave equation in R2 utt= c22u.

Math, Academics

  • Category:- Math
  • Reference No.:- M91016

Have any Question? 


Related Questions in Math

1 which is the better deal 10000 invested at 5 compounded

1 . Which is the better deal, $10,000 invested at 5%, compounded yearly, for 20 years, or $5,000 invested at 10%, compounded continuously, for 20 years? 2. What must be invested today, to be worth $20,000 in 10 years, if ...

Atmospheric pressure decreases by about 116 for every 1000

Atmospheric pressure decreases by about 11.6% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a g ...

A certain forest covers an area of 3900km2 suppose that

A certain forest covers an area of 3900km2. Suppose that each year this area decreases by 4.25%. What will the area be after 6years? Use the calculator provided and round your answer to the nearest square kilometer.

Problem -in deltapqr pq 174 m and pr 76 m k lies on qr

Problem - In ΔPQR, PQ = 17.4 m and PR = 7.6 m. K lies on QR such that ∠PKQ = 137 o . Find (i) ∠QPK, (ii) the length of QK.

What are the best ways to mitigate risk in health care

What are the best ways to mitigate risk in health care settings? Consider a focus on patient safety/satisfaction, data, and culture of the institution. Analyze at least three methods to mitigate risk, providing examples ...

In 450 words with referencesdiscuss why productivity is

In 450 words with references: Discuss why productivity is important, particularly in a healthcare organization. How do staffing models and labor optimization algorithms contribute towards productivity? During project man ...

You are tasked with choosing a corporation and discussing

You are tasked with choosing a corporation and discussing the importance of ethics and social responsibility in relation to that particular corporation. Think about the stakeholders associated with the corporation and ho ...

A collection of dimes and quarters is worth 650 there are

A collection of dimes and quarters is worth $6.50. There are 35 coins in all. How many dimes are there? Write the correct system of equations and answer in a complete sentence thank you

Resolve the given vector into its x-component and

Resolve the given vector into its x-component and y-component. The given angle θ is measured counterclockwise from the positive x-axis (in standard position). Magnitude 2.76 mN, θ =237.65° The x-component A Subscript x = ...

Your goal is to describe the details of a more-or-less

Your goal is to describe the details of a more-or-less feasible business in the renewable energy or more general sustainability sector. Do not propose a major enterprise: propose something that is feasible (or close to f ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen