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φ i , φ j = h i j 6

since two different hat function can overlap on at most one leg (otherwise two legs of a hat function could cover the same support).

Next, we can create our K matrix, which requires knowledge of both a φ i , φ j and our P i matrix between nodes i and j , P i j . Starting with P i j , if we have done our bookkeeping correctly, we have all the variables we need to compute

P i j = k i j [ ( s i j - 1 ) I - v i j v i j T ] ,

after which we only need a φ i , φ j for | i - j | 1 . For i = j on our main diagonal, the energy inner product is just the sum of the integrals ( φ i ' ' ( x i ) ) 2 d x i evaluated for each leg of the hat function. If each leg lives on a support of length h i j , the energy inner product is

a φ i , φ i = j N i 1 h i j .

For | i - j | = 1 , two hat functions can share support on at most one leg, so our energy inner product is

a φ i , φ j = - 1 h i j

which again is analogous to our single-string case.

Damping

The case of the damped network wave equation is worth examining as well, especially in the mathematical modeling of a spider's web. The material properties of spiderwebs also make it ideal for simulation via the second order wave equation. These include minimal torsion (twisting) in vibrations, low stiffness, no hysteresis under small strains, and a loss of energy primarily through aerodynamic damping. The wave equation assumes negligible torsion and low stiffness, is meant to model string movement specifically under small strains, and is easy to add a constant aerodynamic/viscous damping term to.

Since the structure of our damping matrix G is built from the same inner products as our M matrix; the only difference is that we now have to keep track of one more constant, the damping coefficient on a connection between two nodal points a i j . The i j th block of G is then just the i j th block of M scaled by a i j . This allows us to again vary damping from connection to connection, which proves useful in the simulation of spider webs, since the radial and axial fibers of a spiderweb are often subject to different levels of damping.

Matlab gui

With this last bit of information, we know each block entry of our N blocks by N blocks discretization matrices, and can construct a finite element discretization for a web given only a list of nodes, their positions, and their connectivity. To implement this in an accessible way, a Matlab“point-and-click" GUI was developed to allow users to trace and experiment with their own webs through numerical simulations of web motion and analysis of the eigenvalues and fundamental modes.

A screenshot of the GUI. With the web outline drawn, we can continue to refine our grid until we achieve a desired size.

Setting up the web

Using a GUI to wrap around our framework which allows the user to point and click to place nodes down, then to click from one node to another to specify the connection pattern. Endpoints (where the nodes are pinned down, enforcing Dirichlet boundary conditions) are assumed to be nodes with only one neighbor (i.e., not a link in a chain). Once the initial pattern is set, the user can change the discretization fineness as desired, as well as rescale the size of the web to a larger or small grid. When the user is done, the positions and connection pattern of the nodes can be used to create a finite element discretization of the network of strings.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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