Fig. 4 | Nature Communications

Fig. 4

From: Characterizing rare fluctuations in soft particulate flows

Fig. 4

Scaling of effective and kinetic temperatures. a When rescaled with the critical exponents q = 1.5(1) and y = 1.44(15) the effective and granular temperatures collapse onto a scaling function. However, to achieve a data collapse we had to adopt slightly different critical densities, ϕ c  = 0.83 and ϕ c  = ϕ J  = 0.84 for T e and T g , respectively. In the fluid state and in the critical state the temperatures match. For the fluid state they exhibit Bagnoldian scaling with exponent 2. In the critical state they still share same non-trivial scaling for \(\dot{\gamma }/\delta {\phi }^{y/q}\gtrapprox 10\). In the jammed state the temperatures segregate into two different branches; T e approaches a constant and T g follows a power-law behavior with exponent 1.5(1). Different system sizes are given by different symbols in which filled and hollow symbols refer to T g and T e , respectively. The color code corresponds to different shear rates \(\dot{\gamma }=0.02\) (purple), 0.04 (magenta), 0.06 (blue), 0.08 (golden), and 0.1 (yellow). b The collapse of all data presented in Fig. 4a when the vertical axis is multiplied by a factor of T g /τ with τ = 0.28. In these data, we cover a large range of packing fractions around jamming, 0.7 < ϕ < 0.9. Error bars correspond to square root of variance

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