Modeling non-equilibrium electromagnetic fluctuations with buff-neq

buff-neq is an application code in the buff-em suite for studying non-equilibrium (NEQ) electromagnetic-fluctuation-induced phenomena--specifically, for computing radiative heat-transfer rates and non-equilibrium Casimir forces and torques for bodies of arbitrary shapes and arbitrary (linear, isotropic, piecewise homogeneous) frequency-dependent permittivity and permeability. buff-neq implements the fluctuating-volume current (FVC) approach to numerical modeling of non-equilibrium fluctuation phenomena.

Mechanically, working with buff-neq is similar in many ways to working with the non-equilibrium Casimir code scuff-neq in the scuff-em code suite. In particular,

  • As in scuff-neq, you can request either (a) frequency-resolved information on heat-transfer rates and NEQ Casimir forces (in which case you will specify a list of frequencies and will get back a list of frequency-specific values of energy and momentum fluxes) or (b) frequency-integrated information, in which case you will assign temperatures to each body in your geometry and buff-neq will numerically integrate the fluxes, weighted by appropriate Bose-Einstein factors, to obtain the total heat-transfer rate or NEQ Casimir force. (For more details, see What buff-neq actually computes.)

  • As in scuff-neq, you can specify an optional list of geometrical transformations describing various displacements and rotations of the bodies in your geometry; in this case you will get back values of the frequency-resolved or frequency-integrated quantities for each transformation you specify.

For Casimir forces and torques, the quantities computed by buff-neq are only the non-equilibrium contributions to the total force and torque---that is, the contributions arising from the temperature differences between individual bodies and the surrounding environment. To get the total force, these must be added to the equilibrium contributions, which are the Casimir forces and torques for the case in which all bodies are at the temperature of the environment. (For heat-transfer rates there is of course no equilibrium contribution, as there is no net power transfer between bodies at thermal equilibrium.)

Table of Contents

1. What buff-neq actually computes

buff-neq implements the FVC approach to non-equilibrium fluctuation phenomena. This is an algorithm for computing the thermal averages of power, force, and torque (PFT) quantities in geometries consisting of compact material bodies at various temperatures embedded in an finite-temperature or zero-temperature environment.

2. buff-neq command-line options

Common options

buff-neq recognizes the following subset of the list of commonly accepted options to buff-em command-line codes; these all have the same meaning as the corresponding options in scuff-em. (In general, almost everything mentioned in the General reference for scuff-em command-line applications pertains to buff-em command-line applications as well.)

--geometry --TransFile --Omega --OmegaFile --OmegaQuadrature --OmegaMin --AbsTol --RelTol --FileBase

Options requesting output quantities

--PAbs --PRad --XForce --YForce --ZForce --XTorque --YTorque --ZTorque

Specifies the quantities in which you are interested: absorbed power (--PAbs), radiated power (--PRad), Cartesian force components, or Cartesian torque components. You may specify none, all, or any subset of these options, but each option you specify will generally increase the computation time (you can scrutinize the .log file to see how much additional time each extra output quantity takes to compute).

Options specifying object temperatures

--Temperature UpperSphere 300 --Temperature LowerSphere 100

--TEnvironment 100

--TemperatureFile MyTemperatureFile.SVTensor

The first two options here set the temperatures of the objects labeled UpperSphere and LowerSphere in the .buffgeo file. Temperature specifications are interpreted in units of Kelvin, so 300 corresponds to room temperature.

The --TEnvironment option here sets the temperature of the environment in which the objects are embedded.

The --TemperatureFile option here may be used to define spatially inhomogeneous temperature profiles. In this case, MyTemperatureFile.SVTensor should be a .SVTensor file describing an isotropic but possibly spatially inhomogeneous tensor whose scalar value is the temperature in Kelvin; for example, MyTemperatureFile.SVTensor might contain the line

bash Q = 300*z + 100*(1-z)

This describes a temperature profile that varies linearly from 100 Kelvin at z=0 to 300 Kelvin at z=1. (Here Q is just the conventional name used in the .SVTensor file specification for assigning formulas for tensor components.)

Note that the temperatures of all objects, and of the environment, are zero by default. This means that, if you request a full frequency-integrated calculation (which you do by omitting the --omega or --omegaFile option) and you do not specify any --temperature options, the code will chug for a while (computing temperature-independent fluxes at various frequencies) before reporting strictly zero values for all quantities! This is probably not what you want.

Options controlling the computation of power, force, and torque

buff-neq implements several algorithms for computing powers, forces, and torques (PFTs). You may request the computation of PFTs via more than one method.

--JDEPFT

Requests that PFTs be computed using the method.

--MomentPFT

Requests that PFTs be computed using the moment method.

--DSIPoints 302 --DSIMesh BoundingMesh.msh

--DSIPoints2 590

--DSIRadius 5.0

These options request PFT calculations via the displaced-surface-integral (DSI) method.

To request a DSIPFT calculation using N cubature points a over a bounding sphere of radius R, say --DSIPoints N --DSIRadius R. To see the allowed values of N, type buff-neq --help.

Alternatively, you can say --DSIMesh BoundingMesh.msh to request a DSIPFT calculation using a one-point cubature over each triangular panel of BoundingMesh.msh.

To get a "second opinion," you can request a second DSIPFT calculation by saying --DSIPoints2 N. This will perform a DSIPFT calculation over bounding sphere with N points (with the sphere radius set by --DSIRadius). This calculation will be performed in addition to the first DSIPFT calculation you requested by specifying --DSIPoints or --DSIMesh.

3. Examples of calculations using buff-neq