Alternating shear rotations in dense suspensions have recently shown the ability to reduce both viscosity and dissipation per strain (at a fixed global shear rate). Here, we study alternating shear rotation, with extensive numerical simulations, at various angles and up to their corresponding jamming points. For increasing shear rotation angles, we find that the jamming point is continuously shifted to higher packing fractions for frictional particles, while it remains constant for frictionless particles. As a consequence, the alternating shear rotation is unable to reduce the dissipation per strain for suspensions composed of frictionless particles. We detail the individual contributions, hydrodynamic or contact, to the shear stress, being uncharted for this protocol. As the angle of rotation increases, the average contact stress decreases. However, we find that the hydrodynamics shows the opposite trend, instead increasing with increasing angle. Hence, hydrodynamic stress will dominate up to much higher packing fractions as the angle of rotation increases. In addition, we report how the microstructure varies and establish a one-to-one mapping between the contact number and its co
We identify a conserved quantity in continuous-time optimization dynamics, termed computational inertia. Defined as the sum of kinetic energy (parameter velocity) and potential energy (loss), this scalar remains invariant under idealized, frictionless training. We formalize this conservation law, derive its analytic decay under damping and stochastic perturbations, and demonstrate its behavior in a synthetic system. The invariant offers a compact lens for interpreting learning trajectories, and may inform theoretical tools for analyzing convergence, stability, and training geometry.
A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a two-dimensional formulation. With a strong analogy to fracture mechanics, it is shown that (i.) a path-independent $J$--integral can be defined for frictionless contact problems, (ii.) which is equal to the energy release rate $G$ associated with an infinitesimal growth in the size of the frictionless constraint, and thus gives the value of the configurational force component along the sliding direction. Furthermore, it is found that (iii.) such a configurational sliding force is the Newtonian force component exerted by the elastic solid on the constraint at the frictionless contact. Assuming the kinematics of an Euler-Bernoulli rod for an elastic body of rectangular shape, the results (i.)--(iii.) lead to a new interpretation from a nonlinear solid mechanics perspective of the configurational forces recently disclosed for one-dimensional structures of variable length. Finally, approximate but closed-form solutions (validated with finite element simulatio
We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic functions and show that the method has a non-trivial accelerated rate as that of Heavy Ball flow. We also propose Frictionless Coordinate Hamiltonian Descent and its parallelizable variant, which turns out to encapsulate the classical Gauss-Seidel method, Successive Over-relaxation, Jacobi method, and more, for solving a linear system of equations. The result not only offers a new perspective on these existing algorithms but also leads to a broader class of update schemes that guarantee the convergence.
Structural superlubricity in van der Waals layered systems holds immense promise for diverse nanoscale contacts devices and energy-efficient applications. While all-direction structural superlubricity has been widely investigated, the understanding towards the more fundamental directional structural superlubricity requires further attentions. In this study, we reveal the physical origins of directional structural superlubricity, which reduces to all-direction superlubricity under certain conditions. By investigating the evolution of incomplete moiré tiles at crystalline interfaces, our general scaling approaches establish the mapping from geometry to tunable directional superlubricity, agreeing with large scale molecular dynamics simulations at both homogeneous or heterogeneous interfaces. Furthermore, diverse programmable frictionless motions of nanoflakes traveling inside double-surface nanoconfinement systems can be achieved. Our work delivers new insights into the design of ultra-low frictional interfaces for future nanoscale tribology and nanoconfinement transport.
Understanding the collisional outcomes of dust aggregates and dependence on material properties of the constituting particles is of great importance toward understanding planet formation. Recent numerical simulations have revealed that interparticle tangential friction plays a crucial role in energy dissipation during collisions between porous dust aggregates; however, the importance of friction on the collisional growth of dust aggregates remains poorly understood. Here we demonstrate the effects of interparticle tangential friction on the collisional growth of dust aggregates. We performed numerical simulations of collisions between equal-mass porous dust aggregates consisting of cohesive and frictionless spheres. We changed the collision velocity and impact angle systematically and calculated the collisional growth efficiency as a function of the collision velocity. We found that the threshold velocity for collisional growth decreases when dust aggregates are made of frictionless spheres as compared to frictional spheres. Our results highlight the importance of tangential interactions on the collisional behavior of dust aggregates and indicate that the predictive equation for th
Predicting the rheology of dense suspensions under inhomogeneous flow is crucial in many industrial and geophysical applications, yet the conventional `$μ(J)$' framework is limited to homogeneous conditions in which the shear rate and solids fraction are spatially invariant. To address this shortcoming, we use particle-based simulations of frictionless dense suspensions to derive new constitutive laws that unify the rheological response under both homogeneous and inhomogeneous conditions. By defining a new dimensionless number associated with particle velocity fluctuations and combining it with the viscous number, the macroscopic friction and the solids fraction, we obtain scaling relations that collapse data from homogeneous and inhomogeneous simulations. The relations allow prediction of the steady state velocity, stress and volume fraction fields using only knowledge of the applied driving force.
We identify a new class of UV-complete instanton solutions that describe the false vacuum\- decay of a real scalar field in a particular curved spacetime background. To this end, we consider a simple scalar theory with a Coleman potential and calculate the Euclidean action $S_{\text{E}}$ by assuming an O(4)-symmetric curved spacetime. The function $a(r)$ dictating the geometry of spacetime may consistently be chosen to be a constant, thereby eliminating the drag forces from the equations of motion and ensuring that the gravitational backgrounds of both the false vacuum and bounce solutions are identical. By employing standard WKB and Gelfand-Yaglom methods, we compute the corresponding prefactor due to quantum fluctuations around this frictionless bounce solution which becomes UV finite after renormalization. The possible consequences of such frictionless UV-finite instantons are discussed.
Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically-stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly four million particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying power laws, we analyze the role of particle size distributions on the structure of jammed packings. The densest packings are obtained for size distributions that balance the relative abundance of large-large/intermediate and small-small particle contacts. Although the proportion of rattler particles and mean coordination number strongly depend on the size distribution, the mean coordination of non-rattler particles attains the frictionless isostatic value of six in all cases. The size distribution of non-rattler particles that participate in the load-bearing network exhibits no dependence on th
Consideration of wave--flow resonance addresses the long-standing problem of how zonal flows (ZF) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. For relevant magnetic geometries, the frequently quoted tertiary instability requires unphysical enhancement of ZF shear and thus is irrelevant to the near-marginal, frictionless regime. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective in the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator--prey model of drift--ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as $L_{ZF}\sim f^{3/16} (1-f)^{1/8} ρ_s^{5/8} l_0^{3/8}$ in the relevant adiabatic limit (i.e., $τ_{ck} k_\|^2 D_\| \gg 1$). $f$ is the fraction of turbulence energy coupled to ZF and $l_0$ is the mixing length absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantl
The statement of the title is shown by numerical simulation of homogeneously sheared packings of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate γ in the limit of small γ and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle ϕ, equal to 5.76 $\pm$ 0.22 degrees in simple shear, is independent on the average pressure P in the rigid limit. It is shown to stem from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, like the effective friction of a frictionless slider on a bumpy surface. Solid fraction Φ remains equal to the random close packing value ≃ 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit, and we conclude that the same friction law for simple shear applies in the large psystem limit if normal stress or density is externally con
We demonstrate that a discontinuous shear thickening (DST) can take place even in a moderately dense inertial suspension consisting of frictionless soft particles. This DST can be regarded as an ignited-quenched transition in the inertial suspension. An approximate kinetic theory well recovers the results of the Langevin simulation in the wide range of the volume fraction without any fitting parameters.
Recently introduced methods which result in shortcuts to adiabaticity, particularly in the context of frictionless cooling, are rederived and discussed in the framework of an approach based on Ehrenfest dynamics. This construction provides physical insights into the emergence of the Ermakov equation, the choice of its boundary conditions, and the use of minimum uncertainty states as indicators of the efficiency of the procedure. Additionally, it facilitates the extension of frictionless cooling to more general situations of physical relevance, such as optical dipole trapping schemes. In this context, we discuss frictionless cooling in the short-time limit, a complementary case to the one considered in the literature, making explicit the limitations intrinsic to the technique when the full three-dimensional case is analyzed.
This paper proposes a frictionless authentication system, provides a comprehensive security analysis of and proposes potential solutions for this system. It first presents a system that allows users to authenticate to services in a frictionless manner, i.e., without the need to perform any particular authentication-related actions. Based on this system model, the paper analyses security problems and potential privacy threats imposed on users, leading to the specification of a set of security and privacy requirements. These requirements can be used as a guidance on designing secure and privacy-friendly frictionless authentication systems. The paper also sketches three potential solutions for such systems and highlights their advantages and disadvantages.
At low volume fraction, disordered arrangements of frictionless spheres are found in un--jammed states unable to support applied stresses, while at high volume fraction they are found in jammed states with mechanical strength. Here we show, focusing on the hard sphere zero pressure limit, that the transition between un-jammed and jammed states does not occur at a single value of the volume fraction, but in a whole volume fraction range. This result is obtained via the direct numerical construction of disordered jammed states with a volume fraction varying between two limits, $0.636$ and $0.646$. We identify these limits with the random loose packing volume fraction $\rl$ and the random close packing volume fraction $\rc$ of frictionless spheres, respectively.
Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect-ratio, quite contrary to what is known from frictionless systems.
The jamming transition is accompanied by a rich phenomenology, such as hysteresis or non-local effects, which is still not well understood. Here we experimentally investigate a model frictionless granular layer flowing down an inclined plane, as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis, yet the layer stability is increased as it gets thinner. Rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting that non-local effects are the consequence of the usual finite-size effects associated to the presence of a critical point. This collapse indicates that the so-called isostatic length $l^*$ governs the effect of boundaries on flow, and rules out other propositions made in the past.
We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.
The almost frictionless transport of the very-high temperature amorphous matter which resembles the color glass condensate (possibly having much of their origin in the RHIC heavy ion collisions) in a confined annular tube with transversely corrugations is investigated by using the verified transition-rate model and boundary perturbation method. We found that for certain activation volume and energy there exist possible frictionless states which might be associated with the perfect fluid formation during the early expansion stage in RHIC Au+Au collisions. We also address the possible similar scenario in LHC Pb+Pb collisions considering the possible perfect fluid formation in ultra-high temperature transport of amorphous matter.
We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings. We focus on two protocols for generating MS packings: 1) isotropic compression and 2) applied simple or pure shear strain $γ$ at fixed packing fraction $φ$. MS packings of frictionless disks occur as geometric families (i.e. parabolic segments with positive curvature) in the $φ$-$γ$ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, $dφ/dγ>0$ and $dφ/dγ<0$. In contrast, MS packings from protocol 2 populate segments with $dφ/dγ<0$ only. For both simple and pure shear, we derive a relationship between the stress anisotropy and dilatancy $dφ/dγ$ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large