Seth Putterman’s research while affiliated with University of California, Los Angeles and other places

Cavitation is a process where bubbles form and collapse within a fluid with dynamic, spatially varying pressure. This phenomenon can concentrate energy density by 12 orders of magnitude, creating light-emitting plasma or damaging nearby surfaces. A key question in cavitation theory and experiments is: what are the upper limits of energy density achievable through this spontaneous multiscale process? Among the many physical processes at play, we focus on fluid compressibility, modeled using the Tait-Murnaghan equation of state for a homentropic Euler fluid. We examine spherical cavities corresponding to experimentally realizable sonoluminescing bubbles, whose radius changes by a factor of over 100. These bubbles reach velocities exceeding the speed of sound of the surrounding fluid. However, all-Mach hydrodynamic solvers, such as those implemented using the Basilisk software, can exhibit unphysical behavior even at early times when motion is nearly incompressible. To accurately capture high Mach number motion and resolve dynamics in the sonoluminescence regime, we introduced a uniform bubble approximation for the ideal gas inside the bubble. This leading-order approximation clarifies the significant effects of compressibility. Our results reproduce the equation-of-state-dependent asymptotic power-law region predicted by analytic calculations. This confirms our method's ability to capture high Mach number motion and suggests that the asymptotic regime could be experimentally observed. Convergence of this method is demonstrated for bubbles in both water and liquid lithium, showing that compressibility slows collapse. Additionally, an outgoing shock wave in the compressible fluid is resolved.

Hydrodynamic equations for a one-component plasma are derived as a unification of the Euler equations with long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify thermodynamics, dispersion laws, nonlinear motion, and conservation laws. In the moderate and strong coupling limits, it is argued that these equations work down to the length scale of the interparticle spacing. The use of a variational principle also ensures that closure is achieved self-consistently. Hydrodynamic equations are evaluated in both the Eulerian frame, where the fluid variables depend on the position in the laboratory, and the Lagrangian frame, where they depend on the position in some reference state, such as the initial position. Each frame has its advantages and our final theory combines elements of both. The properties of longitudinal and transverse dispersion laws are calculated for the hydrodynamic equations. A simple step function approximation for the pair distribution function enables simple calculations that reveal the structure of the equations of motion. The obtained dispersion laws are compared to molecular dynamics simulations and the theory of quasilocalized charge approximation. The action, which gives excellent agreement for both longitudinal and transverse dispersion laws for a wide range of coupling strengths, is elucidated. Agreement with numerical experiments shows that such a hydrodynamic approach can be used to accurately describe a one-component plasma at very small length scales comparable to the average interparticle spacing. The validity of this approach suggests considering nonlinear flows and other systems with long-range interactions in the future.

Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify thermodynamics, dispersion laws, nonlinear motion, and conservation laws. In the moderate and strong coupling limits, it is argued that these equations work down to the length scale of the average interparticle spacing. Closure and self-consistency of these nonlocal equations are achieved via the implementation of a variational principle. Hydrodynamic equations are evaluated in both the Eulerian frame, where the dependent variables depend on the position in the laboratory, and the Lagrangian frame, where they depend on the position in some reference state, such as the initial position. Each frame has its advantages and our final theory combines elements of both. The properties of longitudinal and transverse dispersion laws are calculated for the hydrodynamic equations. A simple step function approximation for the pair distribution function is used that allows for simple calculations that reveal the structure of the equations of motion. The obtained dispersion laws are compared to molecular dynamics simulations and the theory of quasilocalized charge approximation. The action, which gives excellent agreement for both longitudinal and transverse dispersion laws for a wide range of coupling strengths, is elucidated. Agreement with numerical experiments shows that such a hydrodynamic approach can be used to accurately describe a one-component plasma at very small length scales comparable to the average interparticle spacing. The validity of this approach suggests considering nonlinear flows and other systems with long-range interactions in the future.

Motivated by the high energy focusing found in rapidly collapsing bubbles, which is relevant to implosion processes that concentrate energy density, such as sonoluminescence, we consider a calculation of an empty cavity collapse in a compressible Euler fluid. We review and then use the method based on similarity theory that was previously used to compute the power law exponent n for the collapse of an empty cavity in water during the late stage of the collapse. We extend this calculation by considering different fluids surrounding the cavity, all of which are parametrized by the Tait–Murnaghan equation of state through parameter γ. As a result, we obtain the dependence of n on γ for a wide range of γ, and indeed see that the collapse is sensitive to the equation of state of an outside fluid.

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schrödinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.

The performance of ultrasonic transducers is largely determined by the piezoelectric properties and geometries of their active elements. Due to the brittle nature of piezoceramics, existing processing tools for piezoelectric elements only achieve simple geometries, including flat disks, cylinders, cubes and rings. While advances in additive manufacturing give rise to free-form fabrication of piezoceramics, the resultant transducers suffer from high porosity, weak piezoelectric responses, and limited geometrical flexibility. We introduce optimized piezoceramic printing and processing strategies to produce highly responsive piezoelectric microtransducers that operate at ultrasonic frequencies. The 3D printed dense piezoelectric elements achieve high piezoelectric coefficients and complex architectures. The resulting piezoelectric charge constant, d33, and coupling factor, kt, of the 3D printed piezoceramic reach 583 pC/N and 0.57, approaching the properties of pristine ceramics. The integrated printing of transducer packaging materials and 3D printed piezoceramics with microarchitectures create opportunities for miniaturized piezoelectric ultrasound transducers capable of acoustic focusing and localized cavitation within millimeter-sized channels, leading to miniaturized ultrasonic devices that enable a wide range of biomedical applications.

Motivated by the high energy focusing found in rapidly collapsing bubbles that is relevant to implosion processes that concentrate energy density, such as sonoluminescence, we consider a calculation of an empty cavity collapse in a compressible Euler fluid. We review and then use the method based on similarity theory that was previously used to compute the power law exponent n for the collapse of an empty cavity in water during the late stage of the collapse. We extend this calculation by considering different fluids surrounding the cavity, all of which are parametrized by the Tait-Murnaghan equation of state through parameter γ. As a result, we obtain the dependence of n on γ for a wide range of γ, and indeed see that the collapse is sensitive to the equation of state of an outside fluid.

Convection in radial force fields is a fundamental process behind weather on Earth and the Sun, as well as magnetic dynamo action in both. Until now, benchtop experiments have been unable to study convection in radial force fields due to the inability to generate radial forces of sufficient strength. Recently, it has been appreciated that sound, when averaged over many cycles, exerts a force on density gradients in the gas it travels through. The acoustic radiation pressure on thermal gradients draws cooler gas to regions with large time-averaged acoustic velocity and can be modeled as an effective acoustic gravity. We have constructed a system which generates a high amplitude, spherically symmetric acoustic wave in a rotating spherical bulb containing weakly ionized sulfur gas. Without sound, the gas stratifies itself into an initial state with the warmest gas near the center of the bulb, and the coolest gas near the bulb surface. When the sound is initiated, the acoustic radiation pressure is not balanced and a convective instability is triggered. With high speed videography, we observe the initial shape and growth rate of the most unstable mode at various acoustic amplitudes. Acoustic and rotational forces both contribute to the detailed mode shape, which changes qualitatively at low amplitudes where acoustic forces no longer surpass rotational ones everywhere in the bulb.

The performance of ultrasonic transducers is largely determined by the piezoelectric properties and geometries of their active elements. Due to the brittleness of piezoceramics, existing processing tools for piezoelectric elements only achieve simple geometries, including flat disks, cylinders, cubes and rings. While advances in additive manufacturing give rise to free-form fabrication of piezoceramics, the resultant transducers suffer from high porosity, weak piezoelectric responses, and limited geometrical flexibility. We introduce optimized piezoceramic printing and processing strategies to produce highly responsive piezoelectric microtransducers that operate at ultrasonic frequencies. The 3D printed dense piezoelectric elements achieve high piezoelectric coefficients and complex architectures. The resulting piezoelectric charge constant, d33, and coupling factor, kt, of the 3D printed piezoceramic reach 583 pC/N and 0.65, approaching the properties of pristine ceramics. The integrated printing of transducer packaging materials enables miniaturized ultrasonic transducers capable of localized cavitation within millimeter-sized channels, paving the way for intravascular drug delivery.

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-hermitian effective hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly non exponential and when implemented will enable faster readout, such as on time scales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on time scales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the SSE is elucidated.