Accessibility and Ease of Use in Neuromodulation Devices

BACKGROUND

The utilization of neuromodulation therapy continues to grow as therapeutic indications expand. These conditions often present with comorbid physical, visual, and auditory impairments. Patients with disabilities in these categories may have difficulty operating their devices. Thus, reviewing the accessibility and inclusive design of neuromodulation devices is imperative to ensure equal access for patients of all ability levels. To date, the literature provides little insight into this topic.

MATERIALS AND METHODS

Manufacturers of Food and Drug Administration-approved neuromodulation devices in the United States completed our electronic survey to assess neuromodulation device features, universal/inclusive design guidelines, and methods used to make the device accessible to patients with disabilities.

RESULTS

We assessed 11 devices from seven manufacturers. Of those, there were six spinal cord, two peripheral nerve, and three deep brain stimulators. Of all respondents, 91% used universal inclusive design guidelines. Of the studied devices, 91% have an interface that uses visual feedback, and 82% have an interface that uses auditory feedback. All surveyed devices were reported to have an interface that requires physical handling.

DISCUSSION

Our study found that most devices incorporate auditory signals, buttons with raised indentations, speech commands, or other useful features to assist those with visual disabilities. Visual interfaces may be sufficient for a patient with hearing impairment to use all the surveyed devices. However, dual sensory impairment presents a significant limitation in all devices surveyed. Furthermore, the biggest barrier to using neuromodulation devices was physical impairment because all surveyed devices require physical handling.

CONCLUSIONS

Manufacturers have awareness of universal inclusive design principles. However, our study was unable to find a device that is accessible to all users regardless of ability. As such, it is critical to involve universal design principles to ensure that inclusive devices are available to improve patient adherence, treatment efficacy, and outcomes.

Durable responses at 24 months with high-frequency spinal cord stimulation for nonsurgical refractory back pain

OBJECTIVE

The objective of this study was to evaluate the 24-month durability of pain relief, function, quality of life, and safety outcomes for patients with nonsurgical refractory back pain (NSRBP) treated with high-frequency spinal cord stimulation (SCS) within a large, national, multicenter randomized controlled trial (RCT).

METHODS

Following the completion of an RCT comparing high-frequency SCS plus CMM with CMM alone for the treatment of NSRBP, patients gave additional consent for a follow-up extension to 24 months. Presented is the cohort analysis of all patients treated with high-frequency SCS following the optional crossover at 6 months. The outcomes assessed to 24 months included responder rate of ≥ 50% pain relief measured according to the visual analog scale [VAS]), disability (Oswestry Disability Index [ODI]), quality of life (EQ-5D 5-level [EQ-5D-5L]), opioid reduction.

RESULTS

Of the 125 patients who received a permanent implant, 121 completed the 12-month follow-up, 101 gave additional consent for extended follow-up, and 98 completed the 24-month follow-up. At 24 months after implantation, the mean back pain VAS score was reduced by 73% and the responder rate was 82%. ODI and EQ-5D-5L both improved by at least double the minimal clinically important difference for each measure. No unexpected adverse events were observed, and the rates of serious adverse events (3.4%) and device explantations (4.8%) were low.

CONCLUSIONS

The addition of high-frequency SCS to CMM in patients with NSRBP offers profound improvements at 24 months in pain, function, quality of life, and reduced opioid use. This study provides much-needed evidence to inform current clinical practice for managing patients with NSRBP.

Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Implementation and Preliminary Effectiveness of a Multidisciplinary Telemedicine Pilot Initiative for Patients with Chronic Non-Cancer Pain in Rural and Underserved Areas at a Major Academic Medical Center

Background

Arkansas lacks adequate access to high-quality pain care, as evidenced, in part, by it having the second highest opioid prescribing rate in the United States. To improve access to high-quality treatment of chronic pain, we developed the Arkansas Improving Multidisciplinary Pain Care and Treatment (AR-IMPACT) Telemedicine Clinic, a multidisciplinary and interprofessional team of specialists who provide evidence-based pain management for patients with chronic pain.

Methods

We conducted a single-arm pilot trial of the AR-IMPACT Telemedicine Clinic with rural, university-affiliated primary care clinics. We assessed the AR-IMPACT Telemedicine Clinic using an implementation framework and preliminary effectiveness measures. Specifically, we assessed 5 of the 8 implementation outcomes of the framework (ie, penetration, adoption, acceptability, appropriateness, and feasibility) using a mixed methods approach. To evaluate implementation outcomes, we used surveys, interviews, and administrative data. We used electronic health record data to measure preliminary effectiveness (ie, changes in average morphine milligram equivalents per day and pain and depression scores).

Results

The AR-IMPACT team saw 23 patients that were referred by 13 primary care physicians from three rural, university-affiliated primary care clinics over one year. Of the 19 patients willing to participate in the pilot study, 12 identified as women, 31.6% identified as Black, and over 50% had less than a bachelor's level education. Patients rated the clinic positively with high overall satisfaction. Referring physicians indicated high levels of appropriateness, acceptability, and feasibility of the program. AR-IMPACT team members identified several barriers and facilitators to the feasibility of implementing the program. No changes in preliminary effectiveness measures were statistically significant.

Conclusion

Overall, the AR-IMPACT Telemedicine Clinic obtained moderate penetration and adoption, was highly acceptable to patients, was highly acceptable and appropriate to providers, and was moderately feasible to providers and AR-IMPACT team members.

Federal and Statewide Coverage for Opioid-Sparing Chronic Pain Treatments

BACKGROUND

With increased hospitalizations and deaths related to opioid use disorder, there is an impetus for federal and private insurance companies to provide coverage for integrative treatments that address pain. The Centers for Disease Control and Prevention (CDC) and the current literature recommend that nonpharmacological and nonopioid treatments must be considered for chronic pain management. The continued examination of potential coverage and cost-effectiveness for opioid-sparing alternatives with proven efficacy is critical for physicians who treat chronic pain.

STUDY DESIGN

Qualitative analysis of coverage policies for 10 alternative chronic back pain therapies was completed using the most up-to-date publicly available information from federal and state databases until September 2021.

OBJECTIVES

To determine coverage for opioid-sparing treatments for chronic back pain across federal and state healthcare systems.

METHODS

We selected the alternative therapies from the National Institute of Health's National Center for Complementary and Integrative Health (NCCIH) (www.nccih.nih.gov). We then collected and analyzed coverage policies for federal and state healthcare plans, including Medicare, Veterans Health Administration (VHA), Indian Health Services (IHS), and Medicaid, by accessing federal databases and state policy databases via the department of health and human services (HHS).

RESULTS

The 2 most commonly covered nonpharmacologic therapies for chronic back pain are physical therapy and cognitive behavioral therapy. Other more novel therapies have a heterogenous distribution among federal and state healthcare coverage. Assessment of regional differences determined that the median number of treatments in the Northeast and Midwest was 3, while in the South and West, it was 2.

LIMITATIONS

Several provider manuals included varying degrees of information regarding their services. Some states included all pertinent information, such as the definition of treatment, the exact number of service visits allowed annually, and whether prior authorization was necessary. Many manuals provided less information than this. Each state's Medicaid document contained inherent variability, especially with respect to when they were updated or published. Some states had updated information available for 2021, while the most updated policies for other states included documents that were last updated in 2008.

CONCLUSIONS

Integrative treatments for chronic back pain are currently available, yet coverage varies widely depending on the patient's Medicare or Medicaid status. Different states cover different therapies, which may lead to unequal healthcare outcomes for patients with chronic pain.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Leveraging the Prescription Drug Monitoring Program to Curb Opioid Prescribing in Arkansas

Effective means of accurately identifying problematic opioid prescribing are needed. Using an iterative approach with the Arkansas State Medical Board Pain Subcommittee, we modified existing opioid prescriber criteria to create seven metrics to be deployed in Arkansas. These included metrics of dose and days' supply, concomitant use of opioid and benzodiazepines, solid dosage units, and numbers of opioid patients and certain opioid prescriptions. Two of these metrics (average MME daily dose per prescription and total oxycodone 30 mg or hydromorphone prescriptions) were weighted by 2, creating a maximum score of 9 of which each prescriber could receive. Twenty prescribers with a score of 7 or greater were identified and referred to the Arkansas State Medical Board Pain Subcommittee for review and subsequent investigation if deemed necessary. Of those 20 prescribers, four were previously investigated and under disciplinary action, and three were under current investigation for misconduct related to prescribing practices. Five prescribers had new investigations opened due to the findings from the metrics, and disciplinary action was taken. Therefore, 12 of the 20 prescribers referred to the Arkansas State Medical Board were deemed worthy of investigation and disciplinary action. The Arkansas opioid prescriber metrics are able to accurately identify prescribers with potentially problematic opioid prescribing.

Treatment of nonsurgical refractory back pain with high-frequency spinal cord stimulation at 10 kHz: 12-month results of a pragmatic, multicenter, randomized controlled trial

OBJECTIVE

Spinal cord stimulation (SCS) at 10 kHz (10-kHz SCS) is a safe and effective therapy for treatment of chronic low-back pain. However, it is unclear from existing evidence whether these findings can be generalized to patients with chronic back pain that is refractory to conventional medical management (CMM) and who have no history of spine surgery and are not acceptable candidates for spine surgery. The authors have termed this condition "nonsurgical refractory back pain" (NSRBP) and conducted a multicenter, randomized controlled trial to compare CMM with and without 10-kHz SCS in this population.

METHODS

Patients with NSRBP, as defined above and with a spine surgeon consultation required for confirmation, were randomized 1:1 to patients undergoing CMM with and without 10-kHz SCS. CMM included nonsurgical treatment for back pain, according to physicians' best practices and clinical guidelines. Primary and secondary endpoints included the responder rate (≥ 50% pain relief), disability (Oswestry Disability Index [ODI]), global impression of change, quality of life (EQ-5D-5L), and change in daily opioid use and were analyzed 3 and 6 months after randomization. The protocol allowed for an optional crossover at 6 months for both arms, with observational follow-up over 12 months.

RESULTS

In total, 159 patients were randomized; 76 received CMM, and 69 (83.1%) of the 83 patients who were assigned to the 10-kHz SCS group received a permanent implant. At the 3-month follow-up, 80.9% of patients who received stimulation and 1.3% of those who received CMM were found to be study responders (primary outcome, ≥ 50% pain relief; p < 0.001). There was also a significant difference between the treatment groups in all secondary outcomes at 6 months (p < 0.001). In the 10-kHz SCS arm, outcomes were sustained, including a mean 10-cm visual analog scale score of 2.1 ± 2.3 and 2.1 ± 2.2 and mean ODI score of 24.1 ± 16.1 and 24.0 ± 17.0 at 6 and 12 months, respectively (p = 0.9). In the CMM arm, 74.7% (56/75) of patients met the criteria for crossover and received an implant. The crossover arm obtained a 78.2% responder rate 6 months postimplantation. Five serious adverse events occurred (procedure-related, of 125 total permanent implants), all of which resolved without sequelae.

CONCLUSIONS

The study results, which included follow-up over 12 months, provide important insights into the durability of 10-kHz SCS therapy with respect to chronic refractory back pain, physical function, quality of life, and opioid use, informing the current clinical practice for pain management in patients with NSRBP.

Individual and Health Policy Factors Associated With Positive Heroin and Opioid Treatment Response: United States, 2018

Objectives. To identify client- and state-level factors associated with positive treatment response among heroin and opioid treatment episodes in the United States. Methods. We used national data from 46 states using the Treatment Episode Dataset‒Discharges (2018) to identify heroin and opioid treatment episodes (n = 162 846). We defined positive treatment response as a decrease in use between admission and discharge. We used multivariable regression, stratified by race/ethnicity, to identify demographic, pain-related, and state-level factors associated with positive treatment response. Results. Lower community distress was the strongest predictor of better treatment outcomes across all racial/ethnic groups, particularly among White and American Indian/Alaska Native episodes. A primary opioid of heroin was associated with worse outcomes among White and Hispanic episodes. Legislation limiting opioid dispensing was associated with better outcomes among Hispanic episodes. Buprenorphine availability was strongly associated with better outcomes among Black episodes. Conclusions. State-level variables, particularly community distress, had greater associations with positive treatment outcomes than client-level variables. Public Health Implications. Changes in state-level policies and increased resources directed toward areas of high community distress have the potential to improve opioid use disorder treatment and reduce racial/ethnic disparities in treatment outcomes. (Am J Public Health. 2022;112(S1):S66-S76. https://doi.org/10.2105/AJPH.2021.306503).

Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity η(ω), which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare η(ω) obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and η(ω) was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so η(ω) could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of η(ω). For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with ω and the imaginary part increasing with ω, as expected for viscoelastic liquids. Quantitatively, the values of η(ω) obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of η(ω) are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

Shock width measured under liquid and solid conditions in a two-dimensional dusty plasma

Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystallinelike solid and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was four to six lattice constants. These measurements were based on the high-gradient region of density profiles. The profiles were obtained from particle coordinates, measured by high-speed video imaging. The spatial resolution was improved by combining particle coordinates, in the shock's frame of reference, from a sequence of images.

Fluctuation theorem convergence in a viscoelastic medium demonstrated experimentally using a dusty plasma

The convergence of the steady-state fluctuation theorem (SSFT) is investigated in a shear-flow experiment performed in a dusty plasma. This medium has a viscoelastic property characterized by the Maxwell relaxation time τ_{M}. Using measurements of the time series of the entropy production rate, for subsystems of various sizes, it is discovered that the SSFT convergence time decreases with the increasing system size until it eventually reaches a minimum value of τ_{M}, no matter the size of the subsystem. This result indicates that the convergence of the SSFT is limited by the energy-storage property of the viscoelastic medium.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Patient selection

Sacroiliac joint fusion has become a mainstay of the treatment of low back pain for both surgeons and interventionalists. This chapter discusses proper patient selection for both open and minimally invasive sacroiliac joint fusion techniques. Topics covered are indications and contraindications for surgery as well as imaging modalities that the provider can use to ascertain the integrity of the sacroiliac joint when fusion is being considered. It is important to assess each patient’s psychiatric history and current psychiatric symptoms, weigh the benefits and the risks of the procedure, and then use clinical judgment before proceeding with surgery. A brief overview of the two most common surgical approaches (lateral and posterior), along with survivorship data, is provided. Other patient considerations include bone density, previous lumbar spine surgery, smoking history, and comorbidities such as diabetes mellitus.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Comparisons of Monopolar Lesion Volumes with Hypertonic Saline Solution in Radiofrequency Ablation: A Randomized, Double-Blind, Ex Vivo Study

BACKGROUND

Chronic degeneration of the zygapophyseal joints in the cervical or lumbar spine are common causes of axial back pain. Radiofrequency (RF) ablation is a treatment modality in the denervation of facet joint-related pain. Although multiple factors have been theorized to contribute to the size of the optimal RF lesion, the addition of hypertonic saline solution has been posited to create larger RF lesion sizes.

OBJECTIVES

This study compares lesion of 20-gauge RF monopolar probe using 2% lidocaine, 0.9% normal saline solution, and 3% saline solution administered through the RF needle prior to ablation, with subsequent lesion sizes recorded.

STUDY DESIGN

Randomized, double-blinded, ex vivo study using clinically relevant conditions.

SETTING

Procedural laboratory in an academic institution.

METHODS

RF ablation lesions were reproduced in room temperature (21°C ± 2°C) chicken breast specimens with 20-gauge monopolar RF probes inserted. RF was applied for 90 seconds at 80°C after injection of 1 mL of either 2% lidocaine, 2% lidocaine and 0.9% normal saline solution in a 1:1 ratio, or 2% lidocaine and 3% saline solution in a 1:1 ratio. Tissues were dissected, measured, and ellipsoid volumes of burn calculated. Homogeneity of variances was assessed via the Bartlett's test, and heteroskedasticity with the studentized Breusch-Pagan test. One-way analysis of variance (ANOVA) (alpha of 0.05) was used to evaluate statistical significance between volume means across groups. When the null hypothesis of no difference in burn volume between samples could not be rejected, a predefined equivalence volume of ± 0.05 cm3 was used with Welch's 2 one-sided t-tests (TOST) with a Bonferroni adjusted alpha of 0.0167 to evaluate for null acceptance.

RESULTS

The mean lesion volume for monopolar RF with 1 mL 2% lidocaine was 0.16 cm3. Monopolar RF with 1 mL 2% lidocaine + 0.9% normal saline solution had a mean lesion volume of 0.15 cm3, and treatment with 1 mL 2% lidocaine + 3% saline solution measured 0.17 cm3. ANOVA failed to reject the null, and TOST accepted as equivalent all 3 comparisons.

LIMITATIONS

In vivo anatomy and physiology of a human organism was not used for this study. Samples were not warmed to physiologic temperature. Randomization resulted in slightly unequal sample sizes, although all groups were of sufficient size that the central limit theorem should apply.

CONCLUSIONS

Three commonly used solutions were found to have equivalent lesion sizes from monopolar probe RF ablation.

KEY WORDS

Radiofrequency, ablation, lesion shape, lesion size, monopolar RF, hypertonic saline solution.

Dusty plasma experiment to confirm an expression for the decay of autocorrelation functions

Statistical physicists recently proposed an expression for an autocorrelation function (ACF) [Belousov and Cohen, Phys. Rev. E 94, 062124 (2016)2470-004510.1103/PhysRevE.94.062124] that has, until now, not been tested experimentally. The expression captures the early behavior of the ACF decay, when the ACF is flattened. Using experimental data from a nonequilibrium steady-state dusty plasma, we confirm that the expression's use extends to liquidlike strongly coupled plasmas. A transition in the shape of the ACF is identified, and we suggest that it corresponds to the onset of collisional scattering.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-μm sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment

The Green-Kubo (GK) method is widely used in simulations of strongly coupled plasmas to obtain the viscosity coefficient. However, the method's applicability, which is often taken for granted, has not been tested experimentally. We report an experimental test using a two-dimensional strongly coupled dusty plasma. We find that the GK viscosity is ≈60% larger than the result of a benchmark hydrodynamic method, obtained in the same experiment with the same conditions except for the presence of shear.

Characterization of three-dimensional structure using images

The pair correlation function g(r) and the number density n for particles in a three-dimensional (3D) sample can be determined from a single two-dimensional (2D) image. The 2D image is obtained experimentally with a simple setup: a cross-sectional slab of particles is illuminated with a laser sheet and imaged with a single camera. After image analysis, to find positions of particles in two dimensions, along with their brightness, one obtains g(r), also known as the radial distribution function. The key for attaining high accuracy is to use only the particles that are brighter than a filter level, which we refine to achieve greater accuracy. The density n is obtained from g(r). This method is demonstrated in a dusty plasma experiment. Accuracy is quantified using simulation data; errors of 2% for both the pair correlation function and the number density are achievable. The method is useful for dusty plasmas and colloids.

Superdiffusion of two-dimensional Yukawa liquids due to a perpendicular magnetic field

Stochastic transport of a two-dimensional (2D) dusty plasma liquid with a perpendicular magnetic field is studied. Superdiffusion is found to occur especially at higher magnetic fields with β of order unity. Here, β = ω(c)/ω(pd) is the ratio of the cyclotron and plasma frequencies for dust particles. The mean-square displacement MSD = 4D(α)t(α) is found to have an exponent α > 1, indicating superdiffusion, with α increasing monotonically to 1.1 as β increases to unity. The 2D Langevin molecular dynamics simulation used here also reveals that another indicator of random particle motion, the velocity autocorrelation function, has a dominant peak frequency ω(peak) that empirically obeys ω(peak)(2) = ω(c)(2) + ω(pd)(2)/4.

Experimental measurement of velocity correlations for two microparticles in a plasma with ion flow

Velocity correlations are measured in a dusty plasma with only two microparticles. These correlations allow a characterization of the oscillatory modes and an identification of the effects of ion wakes. Ion wake effects are isolated by comparing two experiments with the microparticles aligned parallel vs perpendicular to the ion flow. From records of microparticle velocities, the one- and two-particle distribution functions f(1) and f(2) are obtained, and the two-particle correlation function g(2) ≡ f(2)-f(1)f(1) is calculated. Comparing the two experiments, we find that motion is much more correlated when the microparticles are aligned with the ion flow and the character of the oscillatory modes depends on the ion flow direction due to the ion wake.

Perpendicular diffusion of a dilute beam of charged dust particles in a strongly coupled dusty plasma

The diffusion of projectiles drifting through a target of strongly coupled dusty plasma is investigated in a simulation. A projectile's drift is driven by a constant force F. We characterize the random walk of the projectiles in the direction perpendicular to their drift. The perpendicular diffusion coefficient Dp⊥ is obtained from the simulation data. The force dependence of Dp⊥ is found to be a power law in a high force regime, but a constant at low forces. A mean kinetic energy Wp for perpendicular motion is also obtained. The diffusion coefficient is found to increase with Wp with a linear trend at higher energies, but an exponential trend at lower energies.

Mobility in a strongly coupled dusty plasma with gas

The mobility of a charged projectile in a strongly coupled dusty plasma is simulated. A net force F, opposed by a combination of collisional scattering and gas friction, causes projectiles to drift at a mobility-limited velocity up. The mobility μp=up/F of the projectile's motion is obtained. Two regimes depending on F are identified. In the high-force regime, μp∝F0.23, and the scattering cross section σs diminishes as up-6/5. Results for σs are compared with those for a weakly coupled plasma and for two-body collisions in a Yukawa potential. The simulation parameters are based on microgravity plasma experiments.

Effect of strong coupling on the dust acoustic instability

In a plasma containing charged dust grains, the dust acoustic instability (DAI) can be driven by ions streaming through the dust with speed less than the ion thermal speed. When the dust is strongly coupled in the liquid phase, the dispersion relation of the dust acoustic modes changes in a way that leads to an enhancement of the growth rate of the DAI. In this paper, we show how strong coupling enhances the DAI growth rate and consider application to microgravity experiments where subthermal ion flows are in general possible.

Longitudinal viscosity of two-dimensional Yukawa liquids

The longitudinal viscosity η(l) is obtained for a two-dimensional (2D) liquid using a Green-Kubo method with a molecular dynamics simulation. The interparticle potential used has the Debye-Hückel or Yukawa form, which models a 2D dusty plasma. The longitudinal η(l) and shear η(s) viscosities are found to have values that match very closely, with only negligible differences for the entire range of temperatures that is considered. For a 2D Yukawa liquid, the bulk viscosity η(b) is determined to be either negligibly small or not a meaningful transport coefficient.

Observation of temperature peaks due to strong viscous heating in a dusty plasma flow

Profound temperature peaks are observed in regions of high velocity shear in a 2D dusty plasma experiment with laser-driven flow. These are attributed to viscous heating, which occurs due to collisional scattering in a shear flow. Using measurements of viscosity, thermal conductivity, and spatial profiles of flow velocity and temperature, we determine three dimensionless numbers: Brinkman, Br = 0.5; Prandtl, Pr = 0.09; and Eckert, Ec = 5.7. The large value of Br indicates significant viscous heating that is consistent with the observed temperature peaks.

Energy transport in a shear flow of particles in a two-dimensional dusty plasma

A shear flow of particles in a laser-driven two-dimensional (2D) dusty plasma is observed in a study of viscous heating and thermal conduction. Video imaging and particle tracking yields particle velocity data, which we convert into continuum data, presented as three spatial profiles: mean particle velocity (i.e., flow velocity), mean-square particle velocity, and mean-square fluctuations of particle velocity. These profiles and their derivatives allow a spatially resolved determination of each term in the energy and momentum continuity equations, which we use for two purposes. First, by balancing these terms so that their sum (i.e., residual) is minimized while varying viscosity η and thermal conductivity κ as free parameters, we simultaneously obtain values for η and κ in the same experiment. Second, by comparing the viscous heating and thermal conduction terms, we obtain a spatially resolved characterization of the viscous heating.

Two-particle distribution and correlation function for a 1D dusty plasma experiment

Experimentally measured velocities are used to obtain the one- and two-particle distribution functions f(1) and f(2) and the two-particle correlation function g(2)≡f(2)-f(1)f(1). The fluctuating velocities of interacting charged microparticles were recorded by tracking their motion while they were immersed in a dusty plasma. The phase space was reduced by having only two particles in a harmonic one dimensional confining potential. In statistical theory, g(2) is usually said to be dominated by the randomness of collisions, but here we find that it is dominated by collective oscillatory modes.

Waves and instability in a one-dimensional microfluidic array

Motion in a one-dimensional (1-D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row. Due to their hydrodynamic interactions, the spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.

Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity η(ω). The real part of η(ω) (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for η(ω), yielding the Maxwell relaxation time τ(M)=0.10 s. Results for η(ω) are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

Cutoff wave number for shear waves and Maxwell relaxation time in Yukawa liquids

Because liquids cannot resist shear except over very short distances comparable to the atomic spacing, shear sound waves (i.e., transverse phonons) propagate only for very short wavelengths. A measure of this limit is the cutoff wave number k(c), which is sometimes called the critical wave number. Previously k(c) was determined in molecular dynamics (MD) simulations by obtaining the dispersion relation. Another approach is developed in this paper by identifying the wave number at the onset of a negative peak in the transverse current correlation function. This method is demonstrated using a three-dimensional MD simulation of a Yukawa fluid, which mimics dusty plasmas. In general, k(c) is an indicator of conditions where elastic and dissipative effects are approximately balanced. Additionally, the crossover frequency for the real and imaginary terms of the complex viscosity of a dusty plasma is obtained; this crossover frequency corresponds to the Maxwell relaxation time.

Synchronization mechanism and Arnold tongues for dust density waves

The nonlinear phenomenon of synchronization is characterized experimentally for dust density waves, i.e., dust acoustic waves, which are self-excited due to an ion streaming instability. The waves propagate in a dust cloud with a natural frequency of 22 Hz. We synchronize these waves to a different frequency using a driving electrode that sinusoidally modulates the ion density. We study four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, we find that synchronization of our waves exhibit the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, synchronization of our waves exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. The latter state appears to be a nonlinear oscillation; it is neither at the natural frequency nor a synchronized state.

Particle chains in a dilute dusty plasma with subsonic ion flow

Chains of charged dust particles are observed aligned with a subsonic ion flow. These chains are found in dilute regions, near the midplane of a parallel-plate radio-frequency plasma under microgravity conditions. The argon ion flow speed near these chains was estimated to be of order 10(2) m/s, corresponding to an ion acoustic Mach number M<0.1. The chains were observed to be stable in both the longitudinal and transverse directions. This stability suggests that there is a transverse restoring force. The transverse components of the ion-drag force or electrostatic wake-field forces could provide such a stabilizing effect. The chain appears to terminate with a final dust particle that is located in a dilute region; this observation suggests a possible attractive force in the longitudinal direction in the presence of a subsonic ion flow.

Green-Kubo relation for viscosity tested using experimental data for a two-dimensional dusty plasma

The theoretical Green-Kubo relation for viscosity is tested using experimentally obtained data. In a dusty plasma experiment, micron-sized dust particles are introduced into a partially ionized argon plasma, where they become negatively charged. They are electrically levitated to form a single-layer Wigner crystal, which is subsequently melted using laser heating. In the liquid phase, these dust particles experience interparticle electric repulsion, laser heating, and friction from the ambient neutral argon gas, and they can be considered to be in a nonequilibrium steady state. Direct measurements of the positions and velocities of individual dust particles are then used to obtain a time series for an off-diagonal element of the stress tensor and its time autocorrelation function. This calculation also requires the interparticle potential, which was not measured experimentally but was obtained using a Debye-Hückel-type model with experimentally determined parameters. Integrating the autocorrelation function over time yields the viscosity for shearing motion among dust particles. The viscosity so obtained is found to agree with results from a previous experiment using a hydrodynamical Navier-Stokes equation. This comparison serves as a test of the Green-Kubo relation for viscosity. Our result is also compared to the predictions of several simulations.

Polygon construction to investigate melting in two-dimensional strongly coupled dusty plasma

The polygon construction method of Glaser and Clark is used to characterize melting and crystallization in a two-dimensional (2D) strongly coupled dusty plasma. Using particle positions measured by video microscopy, bonds are identified by triangulation, and unusually long bonds are deleted. The resulting polygons have three or more sides. Geometrical defects, which are polygons with more than three sides, are found to proliferate during melting. Pentagons are found in liquids, where they tend to cluster with other pentagons. Quadrilaterals are a less severe defect, so that disorder can be characterized by the ratio of quadrilaterals to pentagons. This ratio is found to be less in a liquid than in a solid or a superheated solid. Another measure of disorder is the abundance of different kinds of vertices, according to the type of polygons that adjoin there. Unexpectedly, spikes are observed in the abundance of certain vertex types during rapid temperature changes. Hysteresis, revealed by a plot of a disorder parameter vs temperature, is examined to study sudden heating. The hysteresis diagram also reveals features suggesting a possibility of latent heat in the melting and rapid cooling processes.

Errors in particle tracking velocimetry with high-speed cameras

Velocity errors in particle tracking velocimetry (PTV) are studied. When using high-speed video cameras, the velocity error may increase at a high camera frame rate. This increase in velocity error is due to particle-position uncertainty, which is one of the two sources of velocity errors studied here. The other source of error is particle acceleration, which has the opposite trend of diminishing at higher frame rates. Both kinds of errors can propagate into quantities calculated from velocity, such as the kinetic temperature of particles or correlation functions. As demonstrated in a dusty plasma experiment, the kinetic temperature of particles has no unique value when measured using PTV, but depends on the sampling time interval or frame rate. It is also shown that an artifact appears in an autocorrelation function computed from particle positions and velocities, and it becomes more severe when a small sampling-time interval is used. Schemes to reduce these errors are demonstrated.

Identifying anomalous diffusion and melting in dusty plasmas

Anomalous diffusion in liquids and the solid-liquid phase transition (melting) are studied in two-dimensional Yukawa systems. The self-intermediate scattering function (self-ISF), calculated from simulation data, exhibits a temporal decay, or relaxation, with a characteristic relaxation time. This decay is found to be useful for distinguishing normal and anomalous diffusion in a liquid, and for identifying the solid-liquid phase transition. For liquids, a scaling of the relaxation time with length scale is found. For the solid-liquid phase transition, the shape of the self-ISF curve is found to be a sensitive indicator of phase. Friction has a significant effect on the timing of relaxation, but not the melting point.

Mode coupling for phonons in a single-layer dusty plasma crystal

New modes in a dusty plasma result from coupling of differently polarized phonons. A single horizontal layer of charged microparticles, confined so that vertical as well as horizontal motions are possible, usually exhibits three modes. An experiment shows that mode coupling leads to a new hybrid mode and another new mode. Coupling also leads to a recently reported hybrid mode and nondispersive mode, shown here to occur in an unmelted lattice. A linear theory based on ion wakes is able to predict some, but not all, of these modes. Other multiphase systems could exhibit similar mode coupling.

Viscoelasticity of 2D liquids quantified in a dusty plasma experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wave-number-dependent viscosity η(k), which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, η(k) is computed from the transverse current autocorrelation function, which is found by tracking random particle motion. The transverse current autocorrelation function exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.

Viscoelastic response of Yukawa liquids

The viscoelastic properties of strongly coupled Yukawa liquids are characterized by computing the complex shear viscosity η(ω) . This is done using three methods of molecular-dynamics simulation: equilibrium, nonequilibrium, and Langevin dynamics, all with a mutually repulsive Yukawa interparticle potential. A change from viscous to elastic response is observed with increasing frequency, as well as a decrease of the magnitude of the viscosity with increasing frequency. The Langevin simulation reveals that the dependence of the complex viscosity on the friction has a different character for hot and cool liquids. At ω=0 , we find that as friction increases, the viscosity diminishes at high temperature but increases at low temperature. In addition to finding its frequency dependence, we also derive the wave-number (length-scale) dependence of the shear viscosity.

Evolution of shear-induced melting in a dusty plasma

The spatiotemporal development of melting is studied experimentally in a 2D dusty plasma suspension. Starting with an ordered lattice, and then suddenly applying localized shear, a pair of counterpropagating flow regions develop. A transition between two melting stages is observed before a steady state is reached. Melting spreads with a front that propagates at the transverse sound speed. Unexpectedly, coherent longitudinal waves are excited in the flow region.

Gas flow driven by thermal creep in dusty plasma

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.

Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.