As part of my work, I'm making use of the familiar properties of function minima/maxima in a way which I can't seem to find in the literature. I was hoping that by describing it here, someone else might recognise it and be able to point me to a citation. I think it's highly unlikely that I'm the...
Is it possible to introduce a distinction between "no replies" and "unanswered"? What I mean is, I made a thread the other day, and for reasons of clarity made a 2nd post, which now means my thread no longer shows up in "unanswered threads" despite in no way actually being answered. It seems...
It's probably better to talk explicitly in terms of ##\mathbf{s}(u,v,q)## and ##\mathbf{f}(u,v,q)##, and restate that the path "##\mathrm{d}\mathbf{s}##" is actually a path through ##u,v## (where the path itself depends on ##q## due to ##q##'s impact on ##\mathbf{s}(u,v,q)## and on the unstated...
As part of the work I'm doing, I'm evaluating a contour integral:
$$\Omega \equiv \oint_{\Omega} \mathbf{f}(\mathbf{s}) \cdot \mathrm{d}\mathbf{s}$$
along the border of a region on a surface ##\mathbf{s}(u,v)##, where ##u,v## are local curvilinear coordinates, and where the surface itself is...
Of course they are how they are for a lot of good reasons (some of which I explicitly enumerate). My point is simply that these resources are not especially useful for actually Modern Fortran.
If one wishes to actually use Fortran in 2018, and is not strictly forced to use an older version of the language standard, I would certainly strongly recommend familiarising yourself with truly Modern Fortran, i.e. F2003 and F2008, both of which are now "almost entirely" implemented in gfortran...
If the book has been listed on ResearchGate, you will usually get this information as part of whatever aggregation process they do behind-the-scenes (assuming also that the citers/citees are in the same databases).
Yet further analysis raises the following points about the possible extreme cases of ##\cos(\theta)##:
1. ##\Delta \mathbf{X}_{GD} \perp \Delta \mathbf{X}_{NR} \Leftrightarrow \cos(\theta) = 0~,##
and this can only occur either for ##\mathbf{F}=0##, or when either...
In light of @FactChecker 's post talking about the properties of objective functions, I feel the need to re-emphasise that my ultimate goal is not merely to minimise a merit function, but indeed actually to solve ##\mathbf{F}(\mathbf{X})=\mathbf{0}## a system of nonlinear equations. This is...
I would like to come back to this topic, as this is becoming a subsection of my thesis work, so it's of utmost importance that I can address the topic concisely and correctly.
Let us continue to suppose that we have a function ##\vec{F}(\vec{X})## where both are of length (dimension) ##N##, and...
I think your comment on N-R being a case of quadratic programming has already set me in the right direction. From what I'm seeing so far, it's never so much that you "need N-R to solve the higher dimensional problem" but rather that "if you know you're in a region of essentially quadratic...
I am of course using existing tools for solving my actual problems, my question was more to ensure that I have a thorough understanding of what I'm doing and why I'm using the tools I am, and why they do what they do, along with the ability to provide comprehensive arguments and citations...
Hi @Taylor_1989
There are a few options which should let you preserve the syntax highlighting without having to resort to screenshots. For example, this stackexchange entry demonstrates how to use LaTeX for this. Mentioned in the discussion are another program ostensibly useful just for...
@moebot Are you able to provide some comments to your code, such as
What the equation is, whose root(s) you're trying to find
What you are intending each section of code to do
Why you're writing in F77 (fixed) style with GOTOs instead of loops
?
I would just like to chip into contest the frequently asserted claim that "Fortran is a language where calls are intrinsically by-reference", by "referring" to a blog post by Steve Lionel a.k.a. Doctor Fortran (formerly?) of Intel...
I wasn't sure into which category I should post this, so feel free to move it into a more appropriate place.
As part of my work I'm solving a system of nonlinear equations, of a usual form:
$$\vec{F}(\vec{X})=\begin{pmatrix}F_1(X_1, X_2, \cdots X_N) \\ F_2(\cdots) \\ \vdots \\...
Hi there @Taylor_1989
I saw you doing Fortran programming in gedit and winced visibly, so I felt as if it might be a good idea to give you two recommendations for development environments to use.
1) Geany (should be available in your package manager, also check for "geany-plugins" and...
I am more than aware of this, which is exactly why I had said locality in configuration space, because that's what I meant. So I don't see the relevance of your objection?
Also, saying "to be compatible" is a bit of a disingenuous representation, as if to say that it's necessarily some sort...
Arguably in the same place we've been several times before in scientific history, where we've thought that we had a complete description of reality (with a few tiny holes that will surely be patched up soon...), before eventually some bright spark works out that something underneath helps...
My understanding of 'textbook', de Broglie-Bohm(-like), and Everett(-like) QM and QFT is that, other details aside, evolution of \Psi is 100% local... in configuration space at the very least. I would be utterly unsurprised if many 'realist' theoretical physicists consider, at least in some...
The phase(s) of the decomposition of \psi in the energy basis evolve, yes.
I expect that it is straightforward to show that a Gaussian in position-space would evolve outwards, by considering the Gaussian's representation in Fourier space (the momentum basis is equivalent to the energy basis for...
My understanding of this has been that a Dirac delta function in the position space would actually be unphysical, since technically speaking there is no mathematical mechanism by which such a function could be said to "spread out". I recall reading in a series of papers which happened to be...
I know it's been a month since this thread was last bumped, but I really can't read this and let it slide.
You don't have to simply assume that the initial distribution goes as |ψ|2. Running dynamics simulations with unrelated initial conditions results in the distribution dropping out...
After a lengthy dialogue with my supervisor, I solved the problem!
I had been implicitly assuming that since I was conserving the values of E and H at each interface, I was therefore automatically conserving energy flow through the structure. This of course was not the case.
So I...
Homework Statement
I'm implementing the transfer matrix method (manually) for an EM wave through a 1D layered structure. Basically I'm just considering a plane wave in the positive-x direction, conserving E and H across each material interface, and constructing interface matrices, the...