# The Memristor

Isn't this equation equivalent to a regular resistor? R = dv/di?

What would be the unit of memristance? Ohms?
If so, this is not really a fourth fundamental circuit element as it is being told.

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Isn't this equation equivalent to a regular resistor? R = dv/di?
The equation looks more akin to inductance to me ($$L=\frac{d\Phi_{m}}{dq/dt}$$). It appears that the defining feature of the memristor is that it has some memory of the past current so that the memory resistance is a function of both present and past current rather than just current.

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wolram
Gold Member
May be instead of having to (reset) a machine this device would remember where it stopped and carry on from there.

May be instead of having to (reset) a machine this device would remember where it stopped and carry on from there.
That's the impression I got as well. The press release mentioned something about instantly-booting computers.

jhicks,

it seems to me that your equation is not correct.
$$L=\frac{d\Phi}{di}$$
but
$$di\neq\frac{dq}{dt}$$

Now from the resistor equation:
$$R=\frac{v}{i}$$

$$iR=v$$

$$idtR=vdt$$

$$\int{idt}R=\int{vdt}$$

$$qR=\Phi$$

$$R=\frac{\Phi}{q}$$

just like the equation of the memristor.
Its been a long time since the last time I played with equations like these, so tell me if I got it wrong.
But this memristor seems to me to be just a resistor with histeresis.

Yes nathan you are correct; it was a mistype of what I meant to put (obviously $$I=\frac{dq}{dt}\neq dI$$, and I believe your analysis of what a memristor is compared to a resistor is spot on as well after having read the Nature article ( http://www.nature.com/nature/journal/v453/n7191/pdf/nature06932.pdf if you have a subscription )

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I just heard about these, and emailed 2 of my professors about them. I can't wait to hear what they have to say about it.

I'm sure they will be widely used once they're mass produced.

Perhaps the reset function will thus be more 'complicated' than is now?

The memristor equation almost looks like what we signaling guys call the small signal, or AC resistance, as opposed to the DC, or large signal resistance. A nonlinear resistor (like a FET) that is voltage sensitive, for instance, can have different resistance values so that:

R(v) = V/I

The only thing that makes it a "mem" resistor is the (q) in the equation:

M(q) = $$\frac{d\phi}{dq}$$

Why not a R(q) = V/I ? Also, V is always a "difference", I mean, its always really dV, its referenced to something, right? Just from where you measure it makes a difference.

It sounds like the trick was to find a device where current shuttled oxygen "holes" between the titanium oxide layers to remember how much current (charge) had passed. And it is reversible. It sounds like a solid-state integrator (capacitor) that is read not by its voltage, but by its resistance.

From what I understand, you always alter its resistance with DC current, but you can read it with balanced (AC) current, and not change its state.

The interesting thing is that it can slowly change between states, if you run current lightly through it, and since it has a sigmoidal-shaped resistance change (a typical hysteresis effect), it can then be used as a classical neural network neuron device. What makes it really interesting is that it is passive, doesn't require constant power, shut it off and the atoms stay put.

my only question is to this being a "fundamental" property like resistance, inductance, and capacitance. It sounds like a special type of resistor rather than a separate property. Why do we mathematically model transmission lines, components, and all other electrical characteristics only with resistance, inductance, and capacitance, but not with memristance? Is it really valid to say its a fundamental component? I guess if its a passive device, it seems more believable to be fundamental, but it still had to be created artificially in a lab, whereas the other properties show up everywhere naturally.

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There are only two things that I can think of that one can argue to make it "fundamental".

1. Mathematically - that was Leon Chua's first idea that it was necessary. It was the fourth leg, based on the relationships of the ratios of fluxes, charges, etc.
2. It will explain hysteresis that exists everywhere.

However, these are the similar things that were claimed for Chaos Theory a few years ago (don't get me started on Fuzzy Logic). I think Dr. Chua has a few papers on Chaos theory, by the way. (Chaos explained nonlinearity everywhere, gee, that's really helped.)

I think it's a neat device, I share TheAnalogKid's skepticism about the fundamental claims, just because I just somehow don't see it suddenly being something that I've been needing in my modeling. Not just yet.

my only question is to this being a "fundamental" property like resistance, inductance, and capacitance. It sounds like a special type of resistor rather than a separate property. Why do we mathematically model transmission lines, components, and all other electrical characteristics only with resistance, inductance, and capacitance, but not with memristance? Is it really valid to say its a fundamental component? I guess if its a passive device, it seems more believable to be fundamental, but it still had to be created artificially in a lab, whereas the other properties show up everywhere naturally.
It is impossible to construct a device from any combination of resistor, capacitor, and inductor that will output a hysteresis loop. This according to R. Stanley Williams of Hewlett Packard here:
There are only two things that I can think of that one can argue to make it "fundamental".

1. Mathematically - that was Leon Chua's first idea that it was necessary. It was the fourth leg, based on the relationships of the ratios of fluxes, charges, etc.
2. It will explain hysteresis that exists everywhere.

However, these are the similar things that were claimed for Chaos Theory a few years ago (don't get me started on Fuzzy Logic). I think Dr. Chua has a few papers on Chaos theory, by the way. (Chaos explained nonlinearity everywhere, gee, that's really helped.)

I think it's a neat device, I share TheAnalogKid's skepticism about the fundamental claims, just because I just somehow don't see it suddenly being something that I've been needing in my modeling. Not just yet.
The effect of the platinum on either side of a doped and non-doped center of Titanium dioxide lets the boundary move under the influence of a voltage thus altering resistance. The effect occurs over time and is quite sensitive to voltage once the voltage is high enough, but not so high that the device self destructs. At the quicker switching rates the device is said to have a "geologic" lifetime.

The device may be trivially used as thumbdrive memory unit but after being tooled up the nature of the logic that it can support, the smallness of size (comparable to a nerve synapse in a non motor neuron), and the great similarity to the function of the synapse will give the first functioning analog computer that computes using synthetic man made "logic" components that function in the same manner and purpose as a biologic organism.
http://physicsworld.com/cws/article/news/36497

There are three synapses I know of: chemical, immunological, and electrical.
How close will a memristor be in size to the synapse?

• chemical 20 nm
• electrical 3 nm
• immunological ????
Other size comparisons:
• biologic virus 100 nm
• most advanced transistor 30-40 nm
• memristor (after only two years in development) 3 nm
Prepare for the New Luddites once the capabilities become known. If Cylons are capable of being a boon to mankind, they are capable of being a plague.

In any case it will be the architecture of these that limits the spatial/temporal ratio, number of memristors in a cubic unit divided by the percent of light speed thru put, that will determine the intelligence capabilities of the baby CYbernetic LOgic uNit (CYLON.)

HP is using a cross bar arrangement in its experimental device to discover properties and engineering parameters. Construction architecture looking to replicate that of the human brain should be pursued by looking to the brain and its 6 tier pyramid architecture. There is none better at emulating this now with software than Jeff Hawkins, author of OnIntelligence. http://www.ted.com/talks/jeff_hawkins_on_how_brain_science_will_change_computing.html

Combine the functional and material parameters of the memristor with the understanding of brain architecture and (IF you can make it small enough) you will have a CYLON that will be capable; every bit as capable as some teen that becomes smarter than his parents by virtue of his receiving a high school diploma. :yuck:

Should we allow it to self replicate?

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I'm thinking of doing some in depth research for a school project on the memristor, does anybody have any input on whether or not this is a good idea? The reason I ask is because since there are little to no available consumer memristors out there, my project would be solely research, mathematics, fancy poster boards and I would really have very little to show for it. It's a very interesting topic to me and I feel like if I follow through my senior year as an undergrad I may be able to make more sense out of the topic and perhaps do a year of graduate school based on this component and more in depth research.

Thoughts?

I'm thinking of doing some in depth research for a school project on the memristor, does anybody have any input on whether or not this is a good idea? The reason I ask is because since there are little to no available consumer memristors out there, my project would be solely research, mathematics, fancy poster boards and I would really have very little to show for it. It's a very interesting topic to me and I feel like if I follow through my senior year as an undergrad I may be able to make more sense out of the topic and perhaps do a year of graduate school based on this component and more in depth research.

Thoughts?
You may be able to program the hysteresis loop that is characteristic of the memristor. Chou presented this loop as the characteristic output of the memristor to balance the output of the other three basic electronic elements, capacitor, inductor, resistor. If you believe HP's head of memristor research, the memristor would be whatever it is that gave that hysteresis loop, no matter whether created by a program or an assembly of elements as Hewlett Packard has done with titanium and others are doing with silicon, though with silicon the 10,000 cycle limit would likely limit its application to thumb drives at its present state of development. The titanium iteration has no known cycle limits but is more expensive.

You could create a virtual memristor with a program that emulated the hysteresis loop and explain the advantages of how a single memristor could function as multiple "and" gates and able to act as a memory cell or as a member of a cpu all depending on the requirements of the user. There need be no dedicated memory sticks, or hard drives, or optical storage units given a dense enough bank of memristors properly organized to enhance programming.

It is a lack of programming that will hold back the capabilities, I believe. Lots to learn about analog programming per a particular memristor architecture construction assembly that ultimately will be determined by cost versus engineering requirements, as usual.

http://demonstrations.wolfram.com/CurrentVoltageCharacteristicsOfAMemristor/" [Broken]

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Thanks for the reply, while this is or at least will be an important topic in the near future, I just want to start to focus my studies on the non-linear properties this component has. I know in many SPICE simulators you can define components based upon mathematical equations, which is hopefully what I will be doing. As for the programming half, I've worked with a few MATLAB explanations and models for the memristor's qualities and I've got to say this is some really interesting stuff.

Thanks for the reply, while this is or at least will be an important topic in the near future, I just want to start to focus my studies on the non-linear properties this component has. I know in many SPICE simulators you can define components based upon mathematical equations, which is hopefully what I will be doing. As for the programming half, I've worked with a few MATLAB explanations and models for the memristor's qualities and I've got to say this is some really interesting stuff.
The future of programming the new memorized resistance units will need to be developed to take advantage of the reduced component count and the proportional density increase in computing capacity. Presently their is a trend to http://emotion.inrialpes.fr/BP/" [Broken]
The reasoning here is best expressed by physicist James C. Maxwell.

The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on.

Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.​
and also
Probability is an alternative to logic to rationally reason with incomplete and uncertain knowledge.​

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So...he's saying that it would be possible for me to determine a person's logic by statistically doing calculus? And then assimilating that with memristance logic? I'm not quite sure I understood that or how it would go for a project.

So...he's saying that it would be possible for me to determine a person's logic by statistically doing calculus? And then assimilating that with memristance logic? I'm not quite sure I understood that or how it would go for a project.
I'm not the one to be asking about calculus. You could be right, just that I'm not able to tell your intent since I couldn't pass it to keep my *** out of 'Nam. In a human endeavor that uses reason the use of logic involving only three conditions has been available in the raw materials of computer construction. The binary conditions of true or not true, or indeterminate (overuns, does not compute failures.) Whereas the real world is one of dynamic uncertainty exemplified by the condition known as turbulence, that has some expression in the pop Butterfly Effect. There is just to much data at fine levels to be analyzed and so statistical states must be used. Quantum theory has this down to a, hmm, science.

What I think Maxwell is saying, and it addresses the problems with any field type theory, is that any equation must be NOT of simple yes or no algorithms but must be expressed in terms of probabilities. This is very relevant to a lot more than scientific endeavors. In our courts a jury that does not understand the subtleties of Bayesian logic can be fooled into thinking DNA evidence and other probability expressions are of the simple yes or no propositions and can even be tricked by unscrupulous or ignorant attorneys. Even few doctors know how to figure the real odds that a certain test shows you have of having a disease based on the error rates and full analysis of the testing procedures. Best read on Bayesian analysis and examples in the medical field as well as Bayesian logic that deals with probabilities. Bayesian reasoning often is counter to "common sense" logic.

Say you know a family has two children, and further that at least one of them is a girl. What is the probability that they have two girls? Boy/girl, girl/boy, and girl/girl give a .33 chance (1 in 3) that at least one is a girl. How then does the fact that the one girl that they do have is named Florida alter the chances to .5 (1 in two?) http://bblais.blogspot.com/2010/01/there-once-was-girl-named-florida-aka.html

The memristive type computer is inherently a probability computer when fully realized. There are other efforts in the same area to get rid of the right wrong dualities that digital computers have so far relied on programming schemes to counter.

I'm not the one to be asking about calculus. You could be right, just that I'm not able to tell your intent since I couldn't pass it to keep my *** out of 'Nam. In a human endeavor that uses reason the use of logic involving only three conditions has been available in the raw materials of computer construction. The binary conditions of true or not true, or indeterminate (overuns, does not compute failures.) Whereas the real world is one of dynamic uncertainty exemplified by the condition known as turbulence, that has some expression in the pop Butterfly Effect. There is just to much data at fine levels to be analyzed and so statistical states must be used. Quantum theory has this down to a, hmm, science.

What I think Maxwell is saying, and it addresses the problems with any field type theory, is that any equation must be NOT of simple yes or no algorithms but must be expressed in terms of probabilities. This is very relevant to a lot more than scientific endeavors. In our courts a jury that does not understand the subtleties of Bayesian logic can be fooled into thinking DNA evidence and other probability expressions are of the simple yes or no propositions and can even be tricked by unscrupulous or ignorant attorneys. Even few doctors know how to figure the real odds that a certain test shows you have of having a disease based on the error rates and full analysis of the testing procedures. Best read on Bayesian analysis and examples in the medical field as well as Bayesian logic that deals with probabilities. Bayesian reasoning often is counter to "common sense" logic.

Say you know a family has two children, and further that at least one of them is a girl. What is the probability that they have two girls? Boy/girl, girl/boy, and girl/girl give a .33 chance (1 in 3) that at least one is a girl. How then does the fact that the one girl that they do have is named Florida alter the chances to .5 (1 in two?) http://bblais.blogspot.com/2010/01/there-once-was-girl-named-florida-aka.html

The memristive type computer is inherently a probability computer when fully realized. There are other efforts in the same area to get rid of the right wrong dualities that digital computers have so far relied on programming schemes to counter.
Alright thank you, that made a bit more sense, at least from how I understood it. Simple gate logic today is solely based on, zeros and ones, however this new non-linear component (memristor) shows for itself that this 1 & 0 (and X,Z...) is not true logic of this world. The extra probabilities, say for example past current and voltage levels across the memristor are what will truly reason with the next event(s)?

This makes much more sense when trying to figure out how to tie human logic into these memristors, I'll for sure be reading up on some Bayesian reasoning. So for the calculus based within a memristance function, which bases its current state on past differentials of the sort and those "extra probabilities," it must be safe to say that the human brain functions remarkably close to that of a memristor's function if all that is behind true world reasoning and logic is the calculus behind probability.

Since a memristor isn't linear, these changes are going to be some sort of function between current and voltage which are also past events. Similar to this is human logic, also based upon past events but is human logic based upon probabilities? I can't even think in that magnitude right now...

Alright thank you, that made a bit more sense, at least from how I understood it. Simple gate logic today is solely based on, zeros and ones, however this new non-linear component (memristor) shows for itself that this 1 & 0 (and X,Z...) is not true logic of this world. The extra probabilities, say for example past current and voltage levels across the memristor are what will truly reason with the next event(s)?

This makes much more sense when trying to figure out how to tie human logic into these memristors, I'll for sure be reading up on some Bayesian reasoning. So for the calculus based within a memristance function, which bases its current state on past differentials of the sort and those "extra probabilities," it must be safe to say that the human brain functions remarkably close to that of a memristor's function if all that is behind true world reasoning and logic is the calculus behind probability.

Since a memristor isn't linear, these changes are going to be some sort of function between current and voltage which are also past events. Similar to this is human logic, also based upon past events but is human logic based upon probabilities? I can't even think in that magnitude right now...
If it was easy there'd be 9 year olds doing it.

My hope is that the memristor computer will be amenable to turning off and turning on the type of memory that humans have which give signs of being altered just from being recalled. If the computer could do both then it would have the advantage over us. Presuming, of course, that the brain is stuck with altering memories by remembering. Things in the field are proceeding at a lightning pace. I can't keep up. http://plato.stanford.edu/entries/language-thought/ And I'm retired.

I was hoping for a little more input on this...
After emailing HP in hopes of being able to get some more information and perhaps speaking with an engineer about the memristor, I had no luck. They do not provide such information, which I expected.
I tried sending Hynix (the partner to HP in this effort) an email but they don't really have any good contact information and are based somewhere in Asia.
So I'm rather stuck with a lot of data and very little to show except for my binder. I've used some SPICE simulation models of the memristor to demonstrate my knowledge of its properties however I'm in need of something more physical, and don't really know where to turn.

bump :)

bump :)
You got me. You want a project. Get a Wofram Mathematica 7 memristor simulator going and somehow see if you can have the output feed the input to another instance of Mathematica and see if you can get the damn thing to play a half *** competent game of tic-tac-toe. In other words how do you program a memristor circuit analog computer? Can you make two memristors do addition? Or do you only need one? http://demonstrations.wolfram.com/CurrentVoltageCharacteristicsOfAMemristor/

It also seems like I've seen an active circuit configured to achieve the hysteresis loop but it was pretty complicated and I can't seem to find it now.

If the loop can be simulated with hydraulics then you could make a column of water trip some check valves and hold a level in tube depending on the pressure (voltage) of the water or oil in a hydraulic simulation of a memristor. A cork with a magnetic could be the sensor of the level (height) of the water column which position was read as an output by a series of reed switches up the column and could digitize the position of the column onto a graphing program. You could then talk about how the memristor works in a voltage range low enough that it won't short out, (blow up a balloon or fragile light bulb representation that high pressure would rupture, thus emulating a high voltage insulation breakdown in electric conductors.

I'm thinking a hydraulic representation would be a visual with colored fluids in transparent tubes with check valve spring calibrated by spring tensions to allow pressure into the tube and alter the floats position.

Enough for you to get started? Just make the levels of one, two, or three tubes change in accordance with the Mathematica simulator by adjusting spring values and such and the positions of the floats be in front of a scale(like on a thermometer) that when adding three columns values would give a result or better have a fourth column connected to the base of the three columns "read" the pressures of the column height and achieve the additive of those, perhaps on a logarithmic readout or straight 1:1. Whatever, you'll have to adapt.

You got me. You want a project. Get a Wofram Mathematica 7 memristor simulator going and somehow see if you can have the output feed the input to another instance of Mathematica and see if you can get the damn thing to play a half *** competent game of tic-tac-toe. In other words how do you program a memristor circuit analog computer? Can you make two memristors do addition? Or do you only need one? http://demonstrations.wolfram.com/CurrentVoltageCharacteristicsOfAMemristor/

It also seems like I've seen an active circuit configured to achieve the hysteresis loop but it was pretty complicated and I can't seem to find it now.

If the loop can be simulated with hydraulics then you could make a column of water trip some check valves and hold a level in tube depending on the pressure (voltage) of the water or oil in a hydraulic simulation of a memristor. A cork with a magnetic could be the sensor of the level (height) of the water column which position was read as an output by a series of reed switches up the column and could digitize the position of the column onto a graphing program. You could then talk about how the memristor works in a voltage range low enough that it won't short out, (blow up a balloon or fragile light bulb representation that high pressure would rupture, thus emulating a high voltage insulation breakdown in electric conductors.

I'm thinking a hydraulic representation would be a visual with colored fluids in transparent tubes with check valve spring calibrated by spring tensions to allow pressure into the tube and alter the floats position.

Enough for you to get started? Just make the levels of one, two, or three tubes change in accordance with the Mathematica simulator by adjusting spring values and such and the positions of the floats be in front of a scale(like on a thermometer) that when adding three columns values would give a result or better have a fourth column connected to the base of the three columns "read" the pressures of the column height and achieve the additive of those, perhaps on a logarithmic readout or straight 1:1. Whatever, you'll have to adapt.
Thanks minorwork, those are all very good suggestions. After reading the latter over a couple of times some ideas started popping into my head, such as using Labview for a differential simulation export, and using some sort of FPGA to control the external visual whether it be a tube-based water system or perhaps a radio's volume? Even as simple as rows of LEDs which illuminate 1:1 with kOhms of resistance.

Those are just a few I thought of quickly, since this is turning more into an emulation there is room for cleverness. I'm going to keep a note pad with me and think of some ideas over the next bit. Thanks for the help it is appreciated, suggestions welcome, of course.