skip to main content


Title: Adjustable Constrained Soft‐Tissue Dynamics
Abstract

Physically based simulation is often combined with geometric mesh animation to add realistic soft‐body dynamics to virtual characters. This is commonly done using constraint‐based simulation whereby a soft‐tissue simulation is constrained to geometric animation of a subpart (or otherwise proxy representation) of the character. We observe that standard constraint‐based simulation suffers from an important flaw that limits the expressiveness of soft‐body dynamics. Namely, under correct physics, the frequency and amplitude of soft‐tissue dynamics arising from constraints (“inertial amplitude”) are coupled, and cannot be adjusted independently merely by adjusting the material properties of the model. This means that the space of physically based simulations is inherently limited and cannot capture all effects typically expected by computer animators. For example, animators need the ability to adjust the frequency, inertial amplitude, gravity sag and damping properties of the virtual character, independently from each other, as these are the primary visual characteristics of the soft‐tissue dynamics. We demonstrate that independence can be achieved by transforming the equations of motion into a non‐inertial reference coordinate frame, then scaling the resulting inertial forces, and then converting the equations of motion back to the inertial frame. Such scaling of inertia makes it possible for the animator to set the character's inertial amplitude independently from frequency. We also provide exact controls for the amount of character's gravity sag, and the damping properties. In our examples, we use linear blend skinning and pose‐space deformation for geometric mesh animation, and the Finite Element Method for soft‐body constrained simulation; but our idea of scaling inertial forces is general and applicable to other animation and simulation methods. We demonstrate our technique on several character examples.

 
more » « less
Award ID(s):
1911224
NSF-PAR ID:
10202879
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley-Blackwell
Date Published:
Journal Name:
Computer Graphics Forum
Volume:
39
Issue:
7
ISSN:
0167-7055
Page Range / eLocation ID:
p. 69-79
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT

    Modelling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, and planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve adaptively, in any high-dynamic range simulation, but this poses unique challenges of consistency, conservation, and accuracy, especially in multiphysics simulations where species with different ‘softening laws’ may interact. We therefore derive a generalized form of the energy-and-momentum conserving gravitational equations of motion, applicable to arbitrary rules used to determine the force softening, together with consistent associated time-step criteria, interaction terms between species with different softening laws, and arbitrary maximum/minimum softenings. We also derive new methods to maintain better accuracy and conservation when symmetrizing forces between particles. We review and extend previously discussed adaptive softening schemes based on the local neighbour particle density, and present several new schemes for scaling the softening with properties of the gravitational field, i.e. the potential or acceleration or tidal tensor. We show that the ‘tidal softening’ scheme not only represents a physically motivated, translation and Galilean invariant and equivalence-principle respecting (and therefore conservative) method but also imposes negligible time-step or other computational penalties, ensuring that pairwise two-body scattering is small compared to smooth background forces and can resolve outstanding challenges in properly capturing tidal disruption of substructures (minimizing artificial destruction) while also avoiding excessive N-body heating. We make all of this public in the GIZMO code.

     
    more » « less
  2. Abstract

    Weak but persistent synoptic-scale ascent may play a role in the initiation or maintenance of nocturnal convection over the central United States. An analytical model is used to explore the nocturnal low-level jets (NLLJ) and ascent that develop in an idealized diurnally varying frictional (Ekman) boundary layer in a neutrally stratified barotropic environment when the flow aloft is a zonally propagating Rossby wave. Steady-periodic solutions are obtained of the linearized Reynolds-averaged Boussinesq-approximated equations of motion on a beta plane with an eddy viscosity that is specified to increase abruptly at sunrise and decrease abruptly at sunset. Rayleigh damping terms are used to parameterize momentum loss due to radiation of inertia–gravity waves. The model-predicted vertical velocity is (approximately) proportional to the wavenumber and wave amplitude. There are two main modes of ascent in midlatitudes, an afternoon mode and a nocturnal mode. The latter arises as a gentle but persistent surge induced by the decrease of turbulence at sunset, the same mechanism that triggers inertial oscillations in the Blackadar theory of NLLJs. If the Rayleigh damping terms are omitted, the boundary layer depth becomes infinite at three critical latitudes, and the vertical velocity becomes infinite far above the ground at two of those latitudes. With the damping terms retained, the solution is well behaved. Peak daytime ascent in the model occurs progressively later in the afternoon at more southern locations (in the Northern Hemisphere) until the first (most northern) critical latitude is reached; south of that latitude the nocturnal mode is dominant.

     
    more » « less
  3. null (Ed.)
    Flapping-wing insects, birds and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy that may enable high dynamic efficiency. However, recent experiments highlight losses due to damping in the insect thorax that could reduce the benefit of those elastic elements. We performed experiments on, and simulations of, a dynamically scaled robophysical flapping model with an elastic element and biologically relevant structural damping to elucidate the roles of body mechanics, aerodynamics and actuation in spring-wing energetics. We measured oscillatory flapping-wing dynamics and energetics subject to a range of actuation parameters, system inertia and spring elasticity. To generalize these results, we derive the non-dimensional spring-wing equation of motion and present variables that describe the resonance properties of flapping systems: N , a measure of the relative influence of inertia and aerodynamics, and K ^ , the reduced stiffness. We show that internal damping scales with N , revealing that dynamic efficiency monotonically decreases with increasing N . Based on these results, we introduce a general framework for understanding the roles of internal damping, aerodynamic and inertial forces, and elastic structures within all spring-wing systems. 
    more » « less
  4. ABSTRACT

    We present fundamental scaling relationships between properties of the optical/UV light curves of tidal disruption events (TDEs) and the mass of the black hole that disrupted the star. We have uncovered these relations from the late-time emission of TDEs. Using a sample of 63 optically selected TDEs, the latest catalogue to date, we observed flattening of the early-time emission into a near-constant late-time plateau for at least two-thirds of our sources. Compared to other properties of the TDE light curves (e.g. peak luminosity or decay rate) the plateau luminosity shows the tightest correlation with the total mass of host galaxy (p-value of 2 × 10−6, with a residual scatter of 0.3 dex). Physically this plateau stems from the presence of an accretion flow. We demonstrate theoretically and numerically that the amplitude of this plateau emission is strongly correlated with black hole mass. By simulating a large population (N = 106) of TDEs, we determine a plateau luminosity-black hole mass scaling relationship well described by $\log _{10} \left({{M_{\bullet }}/M_\odot }\right) = 1.50 \log _{10} \left({ L_{\rm plat}}/10^{43} \, {\rm erg\, s^{-1}}\right) + 9.0$ (here Lplat is measured at 6 × 1014 Hz in the rest frame). The observed plateau luminosities of TDEs and black hole masses in our large sample are in excellent agreement with this simulation. Using the black hole mass predicted from the observed TDE plateau luminosity, we reproduce the well-known scaling relations between black hole mass and galaxy velocity dispersion. The large black hole masses of 10 of the TDEs in our sample allow us to provide constraints on their black hole spins, favouring rapidly rotating black holes. Finally, we also discover two significant correlations between early time properties of optical TDE light curves (the g-band peak luminosity and radiated energy) and the TDEs black hole mass.

     
    more » « less
  5. Abstract Englacial water transport is an integral part of the glacial hydrologic system, yet the geometry of englacial structures remains largely unknown. In this study, we explore the excitation of fluid resonance by small amplitude waves as a probe of englacial geometry. We model a hydraulic network consisting of one or more tabular cracks that intersect a cylindrical conduit, subject to oscillatory wave motion initiated at the water surface. Resulting resonant frequencies and quality factors are diagnostic of fluid properties and geometry of the englacial system. For a single crack–conduit system, the fundamental mode involves gravity-driven fluid sloshing between the conduit and the crack, at frequencies between 0.02 and 10 Hz for typical glacial parameters. Higher frequency modes include dispersive Krauklis waves generated within the crack and tube waves in the conduit. But we find that crack lengths are often well constrained by fundamental mode frequency and damping rate alone for settings that include alpine glaciers and ice sheets. Branching crack geometry and dip, ice thickness and source excitation function help define limits of crack detectability for this mode. In general, we suggest that identification of eigenmodes associated with wave motion in time series data may provide a pathway toward inferring englacial hydrologic structures. 
    more » « less