Bulbul Chakraborty

Tuning shear thickening behavior is a longstanding problem in the field of dense suspensions. Acoustic perturbations offer a convenient way to control shear thickening in real time, opening the door to a new class of smart materials. However, complete control over shear thickening requires a quantitative description for how suspension viscosity varies under acoustic perturbation. Here, we achieve this goal by experimentally probing suspensions with acoustic perturbations and incorporating their effect on the suspension viscosity into a universal scaling framework where the viscosity is described by a scaling function, which captures a crossover from the frictionless jamming critical point to a frictional shear jamming critical point. Our analysis reveals that the effect of acoustic perturbations may be explained by the introduction of an effective interparticle repulsion whose magnitude is roughly equal to the acoustic energy density. Furthermore, we demonstrate how this scaling framework may be leveraged to produce explicit predictions for the viscosity of a dense suspension under acoustic perturbation. Our results demonstrate the utility of the scaling framework for experimentally manipulating shear thickening systems.

Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a ''stress-only'' formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this gauge-theoretic formulation. Here, we extend this framework by incorporating scale-dependent screening that captures both dielectric and Debye-type behaviour. This introduces a characteristic length scale in stress correlations as well as in the response to external forces. Through numerical simulations of soft-sphere packings, we show that this length scale is set by the particle size, thus providing a natural ultraviolet cutoff while preserving long-wavelength emergent elasticity. We show that this lengthscale remains finite for all pressures, with no evidence for an emergent Debye-like screening near the frictionless unjamming transition. We demonstrate that although individual realisations show strong fluctuations, disorder averaging at fixed macroscopic conditions yields a robust dielectric-like response that persists up to unjamming. Finally, we also provide a physical interpretation of the gauge field within the electrostatic mapping: relative grain displacements in response to localised external perturbations correspond to difference in the gauge field, linking the field-theoretic description to particle-level mechanics.

We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks arises in at least two steps, reminiscent of the two-step melting transition in two dimensional crystals. In particular, our simulations demonstrate that the percolation of stress-supporting bonds happens at different critical volume fractions along different directions. By examining each independent component of the elasticity tensor, we determine universal exponents and develop universal scaling functions to analyze isotropic rigidity percolation as a multicritical point. We expect that these results will be important for elucidating the underlying mechanical phase transitions governing the properties of biological materials ranging from the cytoskeletons of cells to the extracellular networks of tissues such as tendon where the networks are often preferentially aligned.

The onset and growth of rigid clusters in a two-dimensional (2D) suspension in shear flow are studied by numerical simulation. The suspension exhibits the lubricated-to-frictional rheology transition but is studied at stresses above the levels that cause extreme shear thickening. At large solid area fraction, $\phi$, but below the jamming fraction, we find that there is critical $\phi_c$ beyond which the proportion of particles in rigid clusters grows sharply, as $f_{\rm rig} \sim (\phi-\phi_c)^{\beta}$ with $\beta=1/8$, and at which the fluctuations in the net rigidity grow sharply, with a susceptibility measure $\chi_{\rm rig} \sim |\phi-\phi_c|^{-\gamma}$ with $\gamma = 7/4$. By applying finite size scaling, the correlation length, arising from the correlation of rigid domains, is found to scale as $\xi \sim |\phi-\phi_c|^{-\nu}$ with $\nu = 1$. The system is thus found to exhibit criticality, with critical exponents consistent with the 2D Ising transition. This behavior occurs over a range of stresses, with $\phi_c$ increasing as the stress decreases, consistent with the known increase in jamming fraction with reduction of stress for shear-thickening suspensions.

Recently, we proposed a universal scaling framework that shows shear
thickening in dense suspensions is governed by the crossover between two
critical points: one associated with frictionless isotropic jamming and a
second corresponding to frictional shear jamming. Here, we show that orthogonal
perturbations to the flows, an effective method for tuning shear thickening,
can also be folded into this universal scaling framework. Specifically, we show
that the effect of adding in orthogonal shear perturbations (OSP) can be
incorporated by simply altering the scaling variable to include a
multiplicative term that decreases with the normalized OSP strain rate. These
results demonstrate the broad applicability of our scaling framework, and
illustrate how it can be modified to incorporate other complex flow fields.

The theory of mechanical response and stress transmission in disordered,
jammed solids poses several open questions of how non-periodic networks --
apparently indistinguishable from a snapshot of a fluid -- sustain shear. We
present a stress-only theory of emergent elasticity for a non-thermal amorphous
assembly of grains in a jammed solid, where each grain is subjected to
mechanical constraints of force and torque balance. These grain-level
constraints lead to the Gauss's law of an emergent $U(1)$ tensor
electromagnetism, which then accounts for the mechanical response of such
solids. This formulation of amorphous elasticity has several immediate
consequences. The mechanical response maps exactly to the static, dielectric
response of this tensorial electromagnetism with the polarizability of the
medium mapping to emergent elastic moduli. External forces act as vector
electric charges whereas the tensorial magnetic fields are sourced by momentum
density. The dynamics in the electric and magnetic sectors, naturally translate
into the dynamics of the rigid jammed network and ballistic particle motion
respectively. The theoretical predictions for both stress-stress correlations
and responses are borne out by the results of numerical simulations of
frictionless granular packings in the static limit of the theory in both 2D and
3D.

Dry granular materials such as sand, gravel, pills, or agricultural grains, can become rigid when compressed or sheared. At low density, one can distort the shape of a container of granular material without encountering any resistance. Under isotropic compression, the material will reach a certain {\itjamming} density and then resist further compression. {\em Shear jamming}
occurs when resistance to shear emerges in a system at a density lower than the jamming density, and the elastic properties of such states have important implications for industrial and geophysical processes. We report on experimental observations of changes in the mechanical properties of a shear-jammed granular material subjected to small-amplitude, quasi-static
cyclic shear. We study a layer of plastic discs confined to a shear cell, using photoelasticimetry to measure all inter-particle vector forces. For sufficiently small cyclic shear amplitudes and large enough initial shear, the material evolves to an unexpected "ultra-stable" state in which all the particle positions and inter-particle contact forces remain unchanged after each complete shear cycle for thousands of cycles. The stress response of these states to small imposed shear is nearly elastic, in contrast to the original shear jammed state.

We study a model of microtubule assembly/disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that only consider a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative rescue mechanism, and enhances fluctuations of filament lengths. Our results also show that in the presence of remnants microtubule dynamics can be regulated by changing the depolymerisation rate.