exchemist

22 hours ago, Sensei said:

One of your unique posts that I can agree with..

Drinking Technetium-99[m] is widely used medial technique..

https://www.google.com/search?q=Technetium-99[m]

My father had a bone scan using this, to check whether his (very slow-moving) prostate cancer was progressing. All rather absurd, as he was 90 at the time and showing no symptoms. I had to take him to the hospital and wait while they dosed him, left it to migrate into the bones and then tested him.  But while I was waiting I was very intrigued to find Tc99m was used. I had not even realised excited states of radioisotopes were a thing - though of course it makes sense.   

3 minutes ago, swansont said:

I think it’s the use of K-G instead of Schrödinger

OK. I'm afraid the pop-sci version is all we got as chemists at university (e.g. in my copy of Cotton and Wliklnson's Inorganic Chemistry), since while we were familiar with the Schrödinger equation, the Klein-Gordon one would have been out of scope. I know just about enough to realise it's rather handwavy and unsatisfactory, but that's it.    

1 minute ago, swansont said:

The whole relativistic mass explanation is a pop-sci retelling of the physics; the solutions to the equations are in terms of the energy, for which you get a correction in the relativistic case (and this is how the journal article I once looked up treated it). It’s in the pop-sci retelling they talk about relativistic mass, or take the kinetic energy and get a velocity.

Is that on the basis of still using Schrödinger's equation, in which case I suppose you must mean some correction to the Hamiltonian (?) , or would it be on the basis of the Klein-Gordon equation, as @Mordred suggests.

1 hour ago, CrypticFish said:

I should clarify I am just a layman by the way, so sorry if anything I say seems silly. 

The 0.7c thing mainly comes from the various sources I have seen recently which attribute some velocity to an electron, but you are right to say it probably doesn't have velocity in the traditional sense, I think the 0.7c thing comes from people attributing a traditional orbit to an electron on further reading. 

Can you clarify on why the sum of momenta is zero in the local frame of a system? I interpret that as the total value of momentum equalling zero because momentum in any one direction is negated by momentum in the opposite direction thus it essentially averages out to zero. Or is it due to the components having equal relative velocity? 

So am I being misguided in focusing too much on the relative velocity between quarks/gluons and electrons due to the lack of defined position or motion for an electron?

There are real physicists on the forum who are better qualified than I on this but I think so, yes. As I say, the Schrödinger equation almost always works for electrons in the atom and that does not consider relativistic effects, which would not be so if the electron were treated as moving at a significant fraction of c.

To treat a case like gold in  terms of the Schrödinger equation, my understanding is one has to resort to "relativistic mass" to account for the observed absorption in the blue part of the spectrum that makes gold appear yellow, i.e. the electrons behave as if they are heavier due to effectively travelling at relativistic - though undefined - "speeds". But this explanation is not very rigorous (modern physics does not use the concept of relativistic mass any more). I'm sure the real physicists would do the whole thing over using other mathematics.

As for motion of quarks within the nucleus, that is out of my league.   

17 minutes ago, CrypticFish said:

To clarify, what I am getting at is that I am a bit confused on how an atom or larger body can be said to have a momentum of 0 and thus be in its own reference frame when it's components do not have a momentum of zero. Obviously, functionally, a larger mass can be considered as being in its own reference frame that can be compared to other reference frames. Just confused on how it works out on the tiniest level.

 

Just used perception for simplifications sake. Ultimately I'm trying to get at a comparison of the frame of a fundamental particle and the frame of a larger mass, i.e the timing of events, their relative position and the difference in these traits between frames (and ultimately if I am correct in saying the components of a larger mass exist in a significantly different frame to a larger mass).

You can in principle choose anything, of any size, and consider it either from the point of view of its own frame of reference or that of one of its components (if it is a composite entity) , depending on what you are trying to do. In the case of an atom, one would normally take the frame of reference of the nucleus as the reference frame of the atom, as that is quite pointlike for most purposes and happens to be where the centre of mass is  - and the centre of any electric field, in the case of an ion. The electron is problematic, as it has neither defined position nor a defined path of motion. 

54 minutes ago, CrypticFish said:

I'll try to keep this concise:

Elementary particles have very different relative velocities, with quarks and gluons moving at or near C, and electrons being much slower (eg sometimes ~0.7% C). With this in mind, an atom or larger mass is typically considered to be in its own reference frame, despite its components being at very different relative velocities. Why is this?

For example, a human does not perceive any time dilation or length contraction between the particles of their own body. Is this because the experience of a larger mass is more or less the average of its component particles? Would it be true that if a quark or electron could perceive the world, there would be a high degree of difference to how it perceives the world compared to a human that can be attributed to relativity, in essence, experiencing a significantly different degree of length contraction, time dilation, and events that seem simultaneous to us may not be simultaneous to the particle, etc? 

In an atom, the nucleus does not move much relative to the reference frame of the molecule it is part of, and the electrons' wave-particle behaviour is modelled successfully in most cases by Schrödinger's equation which is non-relativistic.  (There are exceptions with the electrons in some heavy elements with very high nuclear charge, for which relativistic treatment is needed. Famously, the colour of gold is accounted for by this.) So actually relativity does not come into biochemistry that much (unless you are a purist who demands that particle "spin" be  treated ab initio rather than as a given feature.)

Where do you get 0.7c from, for the electron? In an atom one can't really speak of the electron's velocity (Heisenberg etc), so that sounds a bit dodgy to me. 

8 minutes ago, Alfred001 said:

That's precisely my point. Maybe now that I've stated it for the 100th time you'll understand what I'm saying.

Good, so there's no burning issue, then and doctors can go on prescribing it for serious infections where there is no good alternative.  I'm glad that's settled. 

1 hour ago, Alfred001 said:

So how much does a 14 day course of metronidazole, commonly used for H pylori therapy, increase a person's cancer risk? Presumably you know, since you claim the risk-reward balance breaks in favor of using metronidazole rather than alternative antibiotics that don't have a suspected cancer risk associated.

It increases it by 2/10ths of F-all, to judge by the studies you cite.  

2 hours ago, Alfred001 said:

That the risk indicated by the studies I cited does not apply to short courses of treatment.

Yes, but most drugs we use are not suspected to be carcinogens.

That’s not what I claimed. If it had been, it would have made no sense for me to go on and discuss the balance of risk.

1 hour ago, Alfred001 said:

I've cited evidence of a possible correlation, you've just flatly stated there is no increased risk when the course of treatment is short, providing no evidence, even though I've already referenced a study that found "limited correlation" with a short course specifically and never mentioned a long course of metro.

Additionally, there's a cohort study (Beard et al. 1988) which found the incidence of lung cancer (bronchogenic carcinoma) was significantly increased in women exposed to metronidazole, and the excess remained after an attempt to adjust for smoking.

So what's your evidence for your claim?

What claim would that be?

35 minutes ago, icarus2 said:

 

The phrase I wrote is this.

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

ET=∑imic2+∑i<j−Gmimjrij=Mc2−35GM2R

And, it is a matter of interpreting mass-energy as a being with mass-energy. It's just a summary of a 24-pages thesis.

And, in the introduction of the thesis, there are the following passages:
In addition, although there are electric charges, spins, and various physical quantities, it is necessary to analyze the problem of expanding the universe due to gravitational interactions because the object will be a being with at least energy (mass) even in various situations.
 

I misunderstood this sentence(As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.) you wrote. I am so sorry.

The total energy E_{T} of the system
And, it is a matter of interpreting mass-energy as a being with mass-energy. 

OK so you start with a "being" (I assume this is a language issue and you mean just an entity of some kind) that has energy as one of its properties.

But that means you don't start "from nothing", then.  

2 hours ago, icarus2 said:

 

I think this claim( It isn't something that exists on its own.) about potential energy is false. Potential energy should be treated as real energy, not virtual energy. Potential energy must have a specific value under specific circumstances.

1. In the calculation of potential energy, not only the calculation through the amount of change is successful. Calculations with own values(I don't know what to choose as the right word. own value?) also succeed. In other words, even if the calculation through the change is successful, it does not guarantee that it is correct.

U=mgh or U=-GMm/r

 

2. Looking at the electromagnetic potential energy similar to the gravitational potential energy,
+ + or - - : When the same kind of charge exists,

U++=+kq1q2r+c1
+ - : When charges of different species exist,

U+−=−kq1q2r+c2

1)The situation where +Q+Q and +Q-Q exist seems to be a symmetrical situation, should c1, c2 exist?

2)Let's assume that the constants are the same as c1=c2,
+ + : When same kind charges exist, U=+kq1q2/r +c1
+ - : When charges of different kinds exist, U=-kq1q2/r + c1
Does this asymmetry look right?

 

3. In elementary particle physics, invariant mass includes either binding energy or potential energy, depending on how the system is defined.

It is well known that when proton-neutrons make up a nucleus, they have less mass than they do in their free state.

Since these protons and neutrons do not change their mass in the coordinate system of their center of mass, they are rest mass and invariant mass in this situation.

However, when they form one nucleon, the mass decreases by the difference in binding energy. In other words, the constant mass of one nucleon has a negative binding energy.

Now there's the matter of combining nucleons with other nucleons, then the individual nucleons have an invariant mass. This is because, in the coupling problem of two nucleons, individual nucleons are assumed to be invariant in the coordinate system of the center of mass of the individual nucleons. I think we need to think about the meaning of the fact that the binding energy is included in the rest mass of the composite particle.

In composite particles, binding energy is also a component of invariant mass. Should we treat these objects as objects that do not have any own value (fixed value), as objects that have values only when changes occur without substance?

Since almost all problems related to potential energy are problems of calculating the amount of change, the idea that the amount of change is important in potential energy and that only the amount of change has meaning has been established.

Even if the calculation through amount of change is successful, it does not guarantee that it does not have any energy value. The reason is that even if the energy has an own value, it still succeeds in explaining the problem by calculating the change.

U=mgh, U=-GMm/r : Both give the correct values in the change calculation problem.

4. Regarding gravitational potential energy, some physicists think differently than you.

I've talked a lot about potential energy, but the notion acquired by education is strong, and I'm not capable enough to break it. So, a little bit of other people's opinions.

1) Alan Guth said
The energy of a gravitational field is negative!
The positive energy of the false vacuum was compensated by the negative energy of gravity.

2) Stephen Hawking also said
The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

3) Gravitation and Spacetime (Book) : 25~29P

Different forms of energy as source of gravity : Gravitational energy in Earth

If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6×10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.

4) Explanation of GRAVITY PROBE B team
https://einstein.stanford.edu/content/relativity/a11278.html

Do gravitational fields produce their own gravity?

Yes.
A gravitational field contains energy just like electromagnetic fields do. This energy also produces its own gravity, and this means that unlike all other fields, gravity can interact with itself and is not 'neutral'. The energy locked up in the gravitational field of the earth is about equal to the mass of Mount Everest, so that for most applications, you do not have to worry about this 'self-interaction' of gravity when you calculate how other bodies move in the earth's gravitational field.

i,j, are subscripts used a lot in physics, and are not subscripts used only in the case of Euler coordinates.
And, in the symbol of summation, there is also an explanation of gravitational potential energy. So, I don't think anyone interprets it as Euler coordinates.

∑−Gmimjrij

When obtaining the potential energy of the mass system, the potential terms of all pairs are summed using the summation symbol. Then, since overlapping terms occur, i<j or a<b is used. It is used to avoid overlapping ordered pairs in ordered pairs.


In the major books I used, the notation "m_0" was always used to indicate rest mass. The same notation can be seen in the display of the wiki you linked to. When I use a rest mass, I use the notation m_0. The "m" I used is total mass, or equivalent mass.

E2=(m0c2)2+(pc)2


 

Well you would be wrong, then. Energy is just a property of a system denoting, as @Mordred says, the ability to do work. You won't find anyone with competent physical science training who claims energy can exist on its own. That sort of thinking is Star Trek, not science. There are many quantities in science like this: momentum, temperature, entropy, electric charge.....    Energy is just one of those.

In fact, your (1) illustrates the problem immediately. You can't talk about "change" without saying what is changing. And then you give a formula including mass. Mass of what? None of this makes sense until you specify some physical system to which it can be applied. 

1 hour ago, Externet said:

Greetings. 

Those solar sails proposed for space probes collect the impact of photons to provide propulsion.  I think.   The photons stop moving when reach/hit the 'solar sail' or always bounce and keep going at the speed of light ?  Is the collision to those sail surfaces the one that creates a force as reaction from their action ?   How different is from a boat sail and wind ?

The photons from the sun reaching earth provide some push ?  How many photons hit the earth per unit of time; is there a tiny shift of the orbit due to reaction to photons ? -Explain as simplistic as possible, please-

It's not mass but momentum, p. For a photon, E=pc. The change of momentum when a photon is reflected at normal incidence will be 2p. A boat sail uses Bernoulli's principle, i.e. that of an aerofoil, so that is very different.

2 hours ago, Alfred001 said:

Perhaps my search of the literature has been inadequate, but as best as I can tell, the situation with metronidazole is that it was conclusively demonstrated to be carcinogenic in animals, genotoxic in humans in vitro and in vivo and "reasonably anticipated to be a human carcinogen" and in spite of this, the drug continues to be in wide use with seemingly no urgency to run a study to settle the question of its carcinogenic potential in humans. Am I missing something or is this insane?

You can maybe say there's no evidence of carcinogenicity in humans, but absence of evidence is not evidence that it's not carcinogenic, not if adequately powered, well designed studies haven't been done. And in fact, as shown in one of the passages I quote later, a "limited-correlation" has been found.

How is it safe for humans to be taking this drug that has so strongly been suggested to be potentially carcinogenic and has not been proven not to be? Shouldn't we stop giving this to people?

Again, perhaps I'm missing some significant literature?

Here's what I looked at:

Association of Metronidazole with Cancer: A Potential Risk Factor or Inconsistent Deductions? (2018 review article)

 

A review on metronidazole: an old warhorse in antimicrobial chemotherapy (2019)

 

No, it's not insane and yes, you are missing something. Nobody takes metronidazole for more than about 2 weeks in a course of treatment. It tends to be used to treat serious protozoan or bacterial infections that would otherwise be very debilitating or ultimately lethal, and then stopped. Nobody takes this stuff prophylactically. I've used it twice, in both cases to treat giardiasis I picked up on travels in the Far East. One was a 3 day course and the other 7 days.

There is no drug on Earth that has no risks attached to it. The evidence for metronidazole being carcinogenic in practice is very weak, whereas its benefits are great. Taking it out of the medical arsenal would certainly result in more deaths, and would thus be counterproductive.   

14 minutes ago, Phi for All said:

You got down into the dermis, like a tattoo needle. Ouch!

That sounds like a long-haul, painful recovery. Triple ouch! Glad you're still with us.

Your explanation, of the way skin grows from the bottom, accounts for objects embedded  in the skin being expelled. But what about objects that are further inside the body? Can they also work their way out and if so how does occur?

22 minutes ago, icarus2 said:

One of humanity's ultimate questions is "How did the universe come into existence?"

Since energy is one of the most fundamental physical quantities in physics, and particles and the like can be created from this energy, this question is "How did energy come into existence?" It is related to the question you are asking.

Cosmology can be largely divided into a model in which energy has continued to exist and a model in which energy is also created. Each model has its strengths and weaknesses, but in the model that assumes the existence of some energy before the birth of our universe, "How did that energy come into existence?" Since the question still exists, the problem has not been resolved and, therefore, I do not personally prefer it.

In order to explain the source of energy in our universe, there have been models that claim the birth of the universe from nothing, or a Zero Energy Universe. However, the key point, the specific mechanism of how being was born from nothing, is lacking, presupposes an antecedent existence such as the Inflaton Field, or is described in a very poor state. *The nothing mentioned here is not a complete nothing, but a state of zero energy.

I would like to suggest a solution to this ultimate problem.

 

1. Changes in the range of gravitational interactions over time

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

a

ET=∑imic2+∑i<j−Gmimjrij=Mc2−35GM2R

b

<math> {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} </math>

c

[tex] {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} [/tex]

Since there is an attractive component (Mass-energy) and a repulsive component (Gravitational potential energy or Gravitational self-energy), it contains elements that can explain the accelerated expansion and decelerated expansion of the universe.

In the case of a uniform distribution, comparing the magnitudes of mass energy and gravitational potential energy, it is in the form of -kR^2. That is, as the gravitational interaction radius increases, the negative gravitational potential energy value becomes larger than the positive mass energy.

2. The inflection point at which the magnitudes of mass energy and gravitational potential energy are equal

The inflection point is the transition from decelerated expansion to accelerated expansion.

If R < R_gs , then the positive mass-energy is greater than the negative gravitational potential energy, so the universe is dominated by attractive force and is decelerating.

If R > R_gs, then the negative gravitational potential energy is greater than the positive mass-energy, so the universe is dominated by the repulsive (anti-gravity) force and accelerated expansion.

Therefore, by matching R_gs with the time of accelerated expansion in the early universe, we can create a new inflation model.

3. When entering accelerated expansion within the Planck time

This means that, in Planck time, a universe born with an energy density of ρ_0 passes through an inflection point where positive energy and negative gravitational potential energy (gravitational self-energy) become equal. And, it means entering a period of accelerated expansion afterwards.

4. Birth and Expansion of the Universe from the Uncertainty Principle

4.1 The Uncertainty Principle - Inflating in Planck time

During Planck time, fluctuations in energy

During Planck time, energy fluctuation of ΔE=(1/2)m_pc^2 is possible.

However, when the mass distribution of an object is approximated in the form of a spherical mass distribution, Δx from the uncertainty principle corresponds to the diameter, not the radius. So Δx=2R'=cΔt, this should apply.

In this case, from the values obtained above in "When entering accelerated expansion within the Planck time", the density is quadrupled, the radius is 1/2 times, and thus the mass is (1/2) times. Therefore, the mass value is M'=(5/6)m_p

It means,

If Δt occurs during the Planck time t_p, the energy fluctuation ΔE can occur more than (1/2)m_pc^2. And, the energy of the inflection point where the mass distribution enters accelerated expansion is (5/6)m_pc^2.

In short,

According to the uncertainty principle, it is possible to change (or create) more than (1/2)m_pc^2 energy during the Planck time,

If an energy change above (5/6)m_pc^2 that is slightly larger than the minimum value occurs, the total energy of the mass-energy distribution reaches negative energy, i.e., the negative mass state, within the time Δt where quantum fluctuations can exist.

However, since there is a repulsive gravitational effect between negative masses, the corresponding mass distribution expands instead of contracting. Thus, the quantum fluctuations generated by the uncertainty principle cannot return to nothing, but can expand and create the present universe.

 

4.2. The magnitude at which the minimum energy generated by the uncertainty principle equals the minimum energy required for accelerated expansion

In the above analysis, the minimum energy of quantum fluctuation possible during Planck time is ΔE≥(1/2)m_pc^2, and the minimum energy fluctuation for which expansion after birth can occur is ΔE≥(5/6)m_pc^2. Since (5/6)m_pc^2 is greater than (1/2)m_pc^2, the birth and coming into existence of the universe in Planck time is a probabilistic event.

For those unsatisfied with probabilistic event, consider the case where the birth of the universe was an inevitable event.

Letting Δt=kt_p, and doing some calculations, we get the k=(3/5)^(1/2)

To summarize,

If Δt ≤ ((3/5)^(1/2))t_p, then ΔE ≥ ((5/12)^(1/2))m_pc^2 is possible. And, the minimum magnitude at which the energy distribution reaches a negative energy state by gravitational interaction within Δt is ΔE=((5/12)^(1/2))m_pc^2. Thus, when Δt < ((3/5)^(1/2))t_p, a state is reached in which the total energy is negative within Δt.

In other words, when quantum fluctuation occur where Δt is smaller than (3/5)^(1/2)t_P = 0.77t_p, the corresponding mass distribution reaches a state in which negative gravitational potential energy exceeds positive mass energy within Δt. Therefore, it can expand without disappearing.

In this case, the situation in which the universe expands after birth becomes an inevitable event.

 

[Abstract]

There was a model claiming the birth of the universe from nothing, but the specific mechanism for the birth and expansion of the universe was very poor.

According to the energy-time uncertainty principle, during Δt, an energy fluctuation of ΔE is possible, but this energy fluctuation should have reverted back to nothing. By the way, there is also a gravitational interaction during the time of Δt, and if the negative gravitational self-energy exceeds the positive mass-energy during this Δt, the total energy of the corresponding mass distribution becomes negative energy, that is, the negative mass state. Because there is a repulsive gravitational effect between negative masses, this mass distribution expands. Thus, it is possible to create an expansion that does not go back to nothing.

Calculations show that if the quantum fluctuation occur for a time less than Δt = ((3/10)^(1/2))t_p ~ 0.77t_p, then an energy fluctuation of ΔE > ((5/6}^(1/2))m_pc^2 ~ 0.65m_pc^2 must occur. But in this case, because of the negative gravitational self-energy, ΔE will enter the negative energy (mass) state before the time of Δt. Because there is a repulsive gravitational effect between negative masses, ΔE cannot contract, but expands. Thus, the universe does not return to nothing, but can exist.

Gravitational Potential Energy Model provides a means of distinguishing whether the existence of the present universe is an inevitable event or an event with a very low probability. And, it presents a new model for the process of inflation, the accelerating expansion of the early universe. This mechanism also provides an explanation for why the early universe started out in a high dense state. Additionally, when the negative gravitational potential energy exceeds the positive mass energy, it can produce an accelerated expansion of the universe. Through this mechanism, inflation, which is the accelerated expansion of the early universe, and dark energy, which is the cause of the accelerated expansion of the recent universe, can be explained at the same time.

 

* The above is a summary of some of the key arguments of the paper, and for more details, please refer to the paper linked below.

# The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism

https://www.researchgate.net/publication/371951438

# Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field

https://www.researchgate.net/publication/360096238

The first problem with this is that energy is just a property of a system, not a free-standing entity in its own right. So starting with energy immediately begs the question “energy of what?”. In other words, it solves nothing, since you must first postulate some system, before you can speak of energy.

23 minutes ago, studiot said:

I have very scanty knowledge of biochemistry, mainly through reaction kinetics, so I am only guessing what Amy is after, I suspect she has mixed up some terminology somewhere, hence my questions.

 

Anyway here is a short discussion about the maths, set at upper high school level calculus.

 

The diffusion equation and the wave equation connect the distribution in space and time of some quantity and it derivatives with respect to space and time.

The 'solution'' of the equation is an algebraic equation describing the values of this function in time and/or space.

The derivatives involved are first and second derivatives.

The connection enables the evolution in time of a system obeying these equations to be determined. That is the spatial distribution at a given time t.

In general we are looking for continuous functions so functions such as x = t² and x = sin(t) are acceptable but x = tan(t) is not

x = t² is not periodic, but x = sin(t) and x = tan(t) are periodic.

However x = tan(t) is discounted as it is non continuous.

OK so the first derivative will be continuous (but may be zero).

For periodicity to occur there must be 'turning points'.
This involve the second derivative being zero at the points.
Further there must be more than one turning point x = t² has one turning point but this is clearly not enough to generate periodicity.

Now the wave equation involves only second derivatives,
So it is not surprising that periodic solutions predominate.

The diffusion equation involves both first and second derivatives.
So it nis not surprising that non periodic solutions occur most frequently in practice.

But the periodicity or non periodicity is built right into the equation it is not a separate cake as chenbeier puts it.

 

I hope this helps somebody.

In fact this discussion reminds me that Schrodinger’s “wave” equation in its time-dependent form is actually a diffusion equation. The time-independent form however is a standing wave equation, I understand, hence the way it is often named. But I expect this is straying a long way from the OP question.

33 minutes ago, studiot said:

The diffusion equation is not only impossible to solve, it is actually meaningless without the boundary conditions, (and I include initial conditions in this).

 

The link Amy provided pays attention to this and describes in some detail some of the possible circumstances including multiple sources   and/ or sinks both time and space and the possibility of both diffusing and transmission media interacting.

It is true that the simple quadratic formula it calculates refers to a single source with no sinks and and an unbounded transmission medium.

Thus it is a very simplistic formula (It is not the diffusion equation) which simply comes up with a rough estimate of how far (x) a diffusing medium would get in time (D), all other things being equal.

but it depends upon these conditions which are  part of the diffusion equation, not something separate from it.

 

To see how diffusion can lead to chemical oscillation read this

 

That’s very interesting. I was not aware of these.  I actually think the Briggs-Rauscher reaction may be an even better example as that one does seem to exhibit regular, rather than chaotic, periodicity: https://en.wikipedia.org/wiki/Briggs–Rauscher_reaction

However these processes are not in fact examples of diffusion, but of chemical reactions, in which diffusion inevitably plays a part. I struggle to believe  there are any examples of purely diffusive processes that exhibit periodicity.

1 hour ago, studiot said:

@chenbeier  @exchemist

Surely you should also consider the boundary conditions.

Even the simple diffusion equation has periodic solutions with the right conditions.

There are plenty of learned maths papers on the subject.

eg 

Diffusion equation if f and φ are periodic the solution is also periodic - Mathematics Stack Exchange

Periodic solutions in reaction–diffusion equations with time delay - ScienceDirect

 

The point is to find out from Amy what she is trying to do as I still don't follow this and she hasn't responded to my last post.

 

Again a medical example, with more complicated conditions is the calculation of the rate and size of periodic dosing to achieve a 'steady state concentration' in the body.

This also happens when considering Fourier solutions to the heat equation, which is a form of the simple diffusion equation.

 

So @amy1vaulhausen, please,

Why are you working with a physiological calculator and why are you measuring distance in light seconds ?

What conditions are you setting

What real life scenario would such periodic behaviour correspond to?
 

Or is this just an abstract artifact of the maths that has no real life application?

6 hours ago, amy1vaulhausen said:

 I realize diffusion itself is not periodic, but wouldnt the average "rate" of diffusion through a substance with known parameters be something that could be averaged, ie we could know the time period it takes for diffusion to occur? Wouldnt the time frame be essentially the same for a given solute to diffuse through similiar units of spatial size, viscosity, etc?

Diffusion will continue so long as a concentration gradient remains. So it doesn’t generally stop after a definite time interval. It will gradually slow down, asymptotically, as equilibrium concentration throughout is approached.

The concept of the diffusion coefficient is that there is indeed a constant, for given substances and a given concentration gradient, at a given temperature.

1 hour ago, amy1vaulhausen said:

Thank you very much for your reply studiot!   

the reason behind my question is based on the diffusion rate in time.

 

Formula ;  t=x^2/2D 

 

see reference ; https://www.physiologyweb.com/calculators/diffusion_time_calculator.html

 

Since a solute will take a range of time to diffuse for a spacial unit with known viscosity and related parameters

and since that time range can be computed in seconds, then if light seconds are used as a distance value and

we convert the distance to a value in hertz, wouldnt we end up with a means to covert rate to a hertzian frequency? 

Am just wondering if there is a standard way to approach this?  A formula to use?  A cycle of time can be converted to

a frequency in hertz.  If we know the amount of time in seconds it takes a solute to diffuse in a specific unit of space

with know characteristics then there must be a way to convert this time period to a hertzian value or at least a range

of frequency values?

You can’t express a distance , which has dimensions of L , in units of 1/T. A light second still has dimensions of distance. The speed of light has dimensions L/T. So a light second, c x t, has dimensions L/T  x T = L, i.e. distance.

There is no cycle of time in a diffusion process. It is not a periodic phenomenon.

12 hours ago, swansont said:

Vaporizing liquid microthruster

https://www.sciencedirect.com/science/article/abs/pii/S0924424799003891

“Experimental testing produced thruster force magnitudes ranging from 0.15 mN to a maximum force output of 0.46 mN”

That’s not very much thrust.

AFAIK resistojets are used for station-keeping, not propulsion.

 

Why does it have to be a Non Neumann probe? Is that in any way relevant?

https://beyondnerva.com/resistojet-electrothermal-thrusters/

Thanks. 

6 hours ago, amy1vaulhausen said:

How to Convert Diffusion Rate to Hertz - Hi, new here.  Does anyone know if it is possible to convert the molecular diffusion rate

to a frequency in hertz?

This question does not make sense. Ask yourself this question: how can a rate of transfer of a substance, say dissolved salt spreading out through an unstirred liquid, have a frequency? 

7 hours ago, Michael_123_ said:

I know that ramscoop designs are no longer considered feasible. Which of the following would be best, and how might it work in this context?

-Vaporizing liquid micro-thruster

-Laser ablation plasma

Electrothermal resistojets

What is an “electrothermal resistojet”?

47 minutes ago, Phi for All said:

While I can easily see alternatives to Christo-Fascism gaining in popularity as the white supremacists in the US are taking off their hoods, I do wonder how the recent rise in social media, YouTube video followings, and TikTok lifestyle livestreams have affected the numbers. Certainly it's much easier to count your following today than it was in 1990. How many of these new pagans have always been pagans, just uncounted or misnamed as "free spirits"?

That could be it, but then again the thing about the internet is that it makes everything very readily available to everyone. So it could equally be that people can for the first time easily “shop around” for worldviews/lifestyles/belief systems they find personally appealing, at least to try them out for a bit, to a degree that previous generations would have found much more difficult.