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<phys>.sum(expr) evaluates the sum of the expression expr over the particles. The sum includes all particles that are active, frozen, or stuck to boundaries. It excludes particles that have not yet been released and those that have disappeared.
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<phys>.sum_all(expr) evaluates the sum of the expression expr over all particles, including particles those that are not yet released or have disappeared. Since the coordinates of unreleased and disappeared particles are not-a-number (NaN), the sum may return NaN if the model includes unreleased or disappeared particles. An expression such as pt.sum_all(isnan(qx)) can be used to compute the total number of unreleased and disappeared particles.
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<phys>.ave(expr) evaluates the average of the expression expr over the active, frozen, and stuck particles. Unreleased and disappeared particles contribute to neither the numerator nor the denominator of the arithmetic mean.
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<phys>.ave_all(expr) evaluates the average of the expression expr over all particles. It is likely to return NaN if the model includes unreleased or disappeared particles.
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<phys>.max(expr) evaluates the maximum value of the expression expr over all active, frozen, and stuck particles.
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<phys>.max_all(expr) evaluates the maximum value of the expression expr over all particles.
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<phys>.min(expr) evaluates the minimum value of the expression expr over the active, frozen, and stuck particles.
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<phys>.min_all(expr) evaluates the minimum value of the expression expr over all particles.
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<phys>.max(expr, evalExpr) evaluates the expression evalExpr for the particle that has the maximum value of the expression expr out of all active, frozen, and stuck particles. For example, in a model that uses the Mathematical Particle Tracing interface with name pt, the expression pt.max(pt.V, qx) would evaluate the x-coordinate qx of the particle with the greatest velocity magnitude pt.V.
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<phys>.max_all(expr, evalExpr) evaluates the expression evalExpr for the particle that has the maximum value of the expression expr for all particles, including disappeared and unreleased particles.
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<phys>.min(expr, evalExpr) evaluates the expression evalExpr for the particle that has the minimum value of the expression expr out of all active, frozen, and stuck particles. For example, in a model that uses the Mathematical Particle Tracing interface with name pt, the expression pt.min(pt.V, qx) would evaluate the x-coordinate qx of the particle with the smallest velocity magnitude pt.V.
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<phys>.min_all(expr, evalExpr) evaluates the expression evalExpr for the particle that has the minimum value of the expression expr for all particles, including disappeared and unreleased particles.
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