## Drude weight definition

As discussed in Lesson 2, crude oil is a complex mixture of hydrocarbon molecules. As engineers, we are interested in the bulk large scale properties of the crude oil and natural gas. As discussed earlier, these properties are typically measured in the laboratory PVT cell. A PVT cell is essentially a piston which allows the volume to be either increased or decreased. It is fitted with a pressure gauge to allow for pressures to be recorded; a measuring device to allow for the determination of the volume of the cell; and temperature control to ensure the test is conducted at the desired temperature.

For reservoirs containing black oils, the laboratory experiment used to determine PVT properties is the Differential Liberation Test. This test is illustrated in Figure 3. In a differential liberation test, a crude oil sample green is introduced into the cell at the initial reservoir pressure and temperature Step 1 in Figure 3. The volume of the cell is then increased by extending the piston outward Step 2and the pressure and volume are recorded. This process is continued for several pressure steps until the first bubble of gas red is observed through a window in the cell Step 3.

This pressure is the bubble-point pressure of the crude oil. Up until the bubble-point pressure is reached, all measurements have been single-phase liquid hydrocarbon measurements. After the bubble-point pressure has been reached, the volume is increased further until a significant volume of free gas has developed Step 4. At this point, the pressure and the oil and gas volumes in the cell are measured.

The gas is then expelled from the piston under isobaric constant pressure conditions by reducing the piston volume and allowing the gas to escape through a valve in the system Step 5. This process is then repeated until the desired final pressure is reached Step 8.

The pressure, liquid volume, and gas volume are then used in the calculation of the appropriate properties for black oils. What is the differential liberation test trying to model? In the reservoir, as gas comes out of solution, it typically has a much lower viscosity than the oil phase. Consequently, as gas evolves from the oil, this difference in the viscosity allows the gas to move faster than the oil and to separate from the source oil from which it evolved.

This is illustrated in Figure 3. In addition, due to the density differences between oil and gas phases, gravity will also act to separate the two phases. It is the properties of the separated phases that we are most interested in, as these are more representative of the processes occurring in the reservoir. In the oil and gas industry, crude oils are characterized by the API gravity American Petroleum Institute gravity of the oil.

The API gravity is defined as:. The API gravity scale acts as an inverse relationship to density and specific gravitythat is, as density increases, the API gravity decreases.

Crude oils are often graded by their API gravity:. Samples of the crude oil taken during the differential liberation test can be extracted from the PVT cell, and the compositions of the crude oil samples can be measured as functions of pressure. If laboratory data are unavailable, then the Cragoe [7] correlation can be used to estimate the molecular weight:. As already discussed, the bubble-point pressure is the pressure that first bubble of gas evolves from an undersaturated crude oil during pressure reduction.

The laboratory method for calculating the bubble-point pressure, p bof a crude oil was discussed earlier in the context of the differential liberation test. Other PVT tests, such as the Constant Composition Expansion Testcan be used to determine the bubble-point pressure of the crude oil. The constant composition expansion test is similar to the differential liberation test, however, the evolved gas is not expelled from the PVT cell during the test.

For all measurements made up to and including the bubble-point pressure, the constant composition expansion test and the differential liberation test give identical results. This dissolved natural gas consists mostly of the low-end molecular weight hydrocarbons methane, ethane, propane, and butane and some inorganic impurities nitrogen, carbon-dioxide, hydrogen-sulfide, etc.

The volume of this dissolved gas is quantified by the Solution Gas-Oil RatioR so sometimes simply referred to as R s.

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A typical plot of R so is illustrated in Figure 3. In this figure, we can see that the reservoir is an undersaturated oil reservoir.Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics.

It only takes a minute to sign up. I have been trying to understand the Drude Weight quantity that is used in the Metal-Insulator transition and Spin chain literature, and I have not been able to find any clear intuitive explanations of what it means, where it comes from and when it is useful. The constant value simply because there is no dissipation in Drude theory. You can refer to the paper by PRB 47, Thanks to the feedback of guangcun I have changed parts of this answer. As I understand it now, the Drude weight distinguishes between an insulator and a metal in a clean model system.

This means, for example, a lattice model with no impurities. These two things mean there are no dissipation mechanisms and so the currents do not decay, which is distinct from superconducting currents that are dissipationless at finite temperatures below the critical temperature and when there are some impurities.

Consider a simple 1D example without any consideration of spatial dependence of the response. Sign up to join this community.

The best answers are voted up and rise to the top. What is the 'Drude Weight' and why is it important? Ask Question. Asked 4 years, 3 months ago.

Active 3 years, 3 months ago. Viewed 2k times. Improve this question. Add a comment.

The Real Definition of Weight

Active Oldest Votes. Improve this answer. I also see now how that would be relevant to a clean model system. Before, I was coming at it imagining an experimental setup where dissipationless currents would as I understand it imply superconductivity rather than a clean theoretical metal.

Download PDF. A short summary of this paper. The same expression also appears in the defini- tion of the Meissner weight, the quantity which indicates superconductivity, as well as in the definition of non-classical rotational inertia of bosonic su- perfluids. It is shown that the difference between these quantities depends on the interpretation of the average momentum term, which can be under- stood as the expectation value of the total momentum Drude weightthe sum of the expectation values of single momenta rotational inertia of a su- perfluidor the sum over expectation values of momentum pairs Meissner weight.

This distinction appears naturally when the current from which the particular transport quantity is derived is cast in terms of shift operators. Moreover, the inverse of the rotational iner- tia of a rotating bosonic superfluid non-classical rotational inertia NCRI is also proportional to the second derivative of the ground state energy, i. Here these quantities will be collectively called transport susceptibilities.

A fundamental question thus arises: there are three distinct physical phe- nomena, but they appear to be described by a single mathematical expression. They pointed out that the derivative with respect to the flux is ambiguous. In the absence of level crossings the two are identical.

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SWZ conclude that the difference between the Drude and superfluid weights is that the former latter corresponds to the adiabatic envelope derivative. Up to now this appears to be the last word on this topic. There are a number of weaknesses in this interpretation.

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Moreover, as discussed in a recent paper of the author [5] and summarized below, the application of these ideas to variational wavefunctions is ambiguous. The usual way [6, 7] to calculate the Drude weight is to take the second derivative of the variational ground state en- ergy. However, this quantity can be cast in terms of an average of the true energy eigenvalues.

Turning on the perturbation can cause level crossings. If we insist on SWZ, then these level crossings should be excluded, and the usual approach [6, 7] would be invalidated. In the limit of a perfect variational wavefunction one which corresponds to the exact ground state for any value of the perturbation the result would be what according to SWZ is the Meissner weight, not the Drude weight.

We stress though that this usual approach would only be invalidated if we as- sume SWZ is correct. In this paper a different approach to distinguishing the Drude weight, Meissner weight, and the rotational inertia of a superfluid is developed, which does not make any reference to whether the derivative is adiabatic or envelope. In a periodic system this expression includes an expectation value which can be interpreted in a number of ways.

It can be taken to mean A the expectation value of the sum over all momenta, B the sum over expecta- tion values of single momenta, or C any other break up of the total momentum operator pairs, triplets, etc.

In fact, this ambiguity disappears if the current, from which Eq. Case A is shown to correspond to the Drude weight, which distinguishes metallic conductors from insulators.Your normal weight without any extra fluid in your body is called "dry weight. When you have kidney failure, your body depends on dialysis to get rid of the extra fluid and wastes that build up in your body between treatments.

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When first starting dialysis, finding your dry weight may take a few treatments. Be sure to tell your dialysis care team if you experience cramping, dizziness, or nausea during or after treatment. If you have too much extra fluid in your body, you may need longer or more frequent hemodialysis treatments.

There is a limit to how much fluid can safely be removed during each dialysis treatment. Your dry weight is measured in kilograms. One kilogram is 2. Most hemodialysis patients are advised to limit their weight gain per treatment to no more than 1 kilogram per day 2.

Skip to main content. What Is Dry Weight? What is dry weight? How is my dry weight calculated? How do I know if I am at my dry weight?

Your blood pressure may be within your normal range after dialysis or before your next session. You do not experience lightheadedness or cramping between dialysis sessions. You do not have swelling in your legs, feet, arms, hands, or around your eyes. Your breathing is comfortable and easy. How do I maintain dry weight after dialysis? Watch your fluid intake. Your healthcare team can tell you what is right for you.

Ask your healthcare team how much fluid is right for you. Follow a kidney-friendly diet. Work with your healthcare team to come up with a meal plan that is right for you. Avoid salty foods. Salt makes your body hold on to extra fluid. It will also make you thirstier, which makes it harder to control your fluid intake between treatments.

Keep track of your daily weight. Keeping track of your weight is important between dialysis sessions.

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If you see sudden weight gain between sessions, you should tell your healthcare provider immediately. What happens if I lose or gain weight?The Drude model of electrical conduction was proposed in [1] [2] by Paul Drude to explain the transport properties of electrons in materials especially metals. The model, which is an application of kinetic theoryassumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions.

The latter expression is particularly important because it explains in semi-quantitative terms why Ohm's lawone of the most ubiquitous relationships in all of electromagnetism, should hold. The model was extended in by Hendrik Antoon Lorentz and hence is also known as the Drude—Lorentz model [ citation needed ] to give the relation between the thermal conductivity and the electric conductivity of metals see Lorenz numberand is a classical model. Later it was supplemented with the results of quantum theory in by Arnold Sommerfeld and Hans Betheleading to the Drude—Sommerfeld model.

### Drude model

German physicist Paul Drude proposed his model in when it was not clear whether atoms existed, and it was not clear what atoms were on a microscopic scale. Drude starts from the discovery of electrons in by J. Thomson and assumes as a simplistic model of solids that the bulk of the solid is composed of positively charged scattering centers, and a sea of electrons submerge those scattering centers to make the total solid neutral from a charge perspective.

In modern terms this is reflected in the valence electron model where the sea of electrons is composed of the valence electrons only, [6] and not the full set of electrons available in the solid, and the scattering centers are the inner shells of tightly bound electrons to the nucleus. The scattering centers had a positive charge equivalent to the valence number of the atoms.

Whenever people tried to give more substance and detail to the nature of the scattering centers, and the mechanics of scattering, and the meaning of the length of scattering, all these attempts ended in failures.

The scattering lengths computed in the Drude model, are of the order of 10 to inter-atomic distances, and also these could not be given proper microscopic explanations. In modern terms, there are experiments in which electrons can travel for meters in a solid in the same manner as they would travel in free space, and this shows how a purely classical model cannot work. Drude scattering is not electron-electron scattering which is only a secondary phenomenon in the modern theory, neither nuclear scattering given electrons can be at most be absorbed by nuclei.

The model remains a bit mute on the microscopic mechanisms, in modern terms this is what is now called the "primary scattering mechanism" where the underlying phenomenon can be different case per case. The model gives better predictions for metals, especially in regards to conductivity, [note 6] and sometimes is called Drude theory of metals.

This is because metals have essentially a better approximation to the free electron modeli. The same Drude theory, despite inconsistencies which baffled most physicists of the period, was the major one accepted to explain solids until the introduction in of the Drude-Sommerfeld model.

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A few more hints of the correct ingredients of a modern theory of solids was given by the following:. Drude used Maxwell—Boltzmann statistics for the gas of electrons and for deriving the model, which was the only one available at that time.

By replacing the statistics with the correct Fermi Dirac statisticsSommerfeld significantly improved the predictions of the model, although still having a semi-classical theory that could not predict all results of the modern quantum theory of solids. Nowadays Drude and Sommerfeld models are still significant to understanding the qualitative behaviour of solids and to get a first qualitative understanding of a specific experimental setup.

It is less common to use a full-blown quantum field theory from first principles, given the complexities due to the huge numbers of particles and interactions and the little added value of the extra mathematics involved considering the incremental gain in numerical precision of the predictions.Plus it spreads the word by giving search engines important links to our reviews.

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