Initial Volume Research Articles

Preoperative embolization of brain arteriovenous malformation and efficacy in intraoperative blood loss reduction: a quantitative study

BackgroundEmbolization of brain arteriovenous malformations (bAVMs) is often used as adjuvant therapy to microsurgical resection to reduce the high-risk features of bAVMs such as large size and high flow. However,...

Middle meningeal artery embolization associated with reduced chronic subdural hematoma volume and midline shift in the acute postoperative period

BackgroundMiddle meningeal artery (MMA) embolization for endovascular treatment of chronic subdural hematoma (cSDH) is growing in popularity. cSDH volume and midline shift were analyzed in the immediate postoperative window after...

Cyclic liquefaction in transitional and non-transitional tailings

Tailings have previously been identified as having the types of mixed mineralogies and gradings that can make them susceptible to having non-unique critical states and normally compressed states in laboratory element tests. This paper addresses how this mode of behaviour would affect their resistance to undrained cyclic loading, contrasting two triaxial studies, one on a tailings that has a conventional behaviour and one transitional. To demonstrate the influence of transitional behaviour it was necessary to create samples with as wide a range of initial specific volumes as possible, while trying keep the sample preparation methods the same for loose and dense samples. It was also necessary to examine the cyclic data in non-conventional ways, notably in the volumetric plane to highlight better the effects of initial sample specific volume. It is shown that, as previously determined for monotonic loading, the initial density has much less influence on the cyclic behaviour of a soil with transitional behaviour than it would for a conventional soil, and it is instead the stress history that is very much more important. Samples following their respective normal compression lines exhibit similar behaviour, but overconsolidation significantly enhances resistance and a sample that arrives at a given state by the undrained reduction of p′ due to cycling also has a much higher resistance.

Predictive Modeling of Fracture Behavior in Ti6Al4V Alloys Manufactured by SLM Process

This study focuses on ductile fracture behavior prediction for Ti6Al4V alloys fabricated via Selective Laser Melting (SLM). A modified Gurson-Tvergaard-Needleman (GTN) model characterizes void growth and shear mechanisms under uniaxial stress. The research explores the impact of Artificial Neural Network (ANN) architecture, specifically hidden layers and neurons, on predicting fracture parameters. Results reveal that increasing hidden layers substantially enhances accuracy, particularly for fracture displacement. Notably, predicting maximum force requires fewer layers than fracture displacement. Using selected layers and neurons, the system consistently achieved R2-values exceeding 0.99 for both maximum force and fracture displacement. The study identifies the initial void volume fraction (f0) parameter as having the most significant influence on both properties.

Programmable intratumoral drug delivery to breast cancer using wireless bioelectronic device with electrochemical actuation

ABSTRACT Objective Breast cancer is a global health concern that demands attention. In our contribution to addressing this disease, our study focuses on investigating a wireless micro-device for intratumoral drug delivery, utilizing electrochemical actuation. Microdevices have emerged as a promising approach in this field due to their ability to enable controlled injections in various applications. Methods Our study is conducted within a computational framework, employing models that simulate the behavior of the microdevice and drug discharge based on the principles of the ideal gas law. Furthermore, the distribution of the drug within the tissue is simulated, considering both diffusion and convection mechanisms. To predict the therapeutic response, a pharmacodynamic model is utilized, considering the chemotherapeutic effects and cell proliferation. Results The findings demonstrate that an effective current of 3 mA, along with an initial gas volume equal to the drug volume in the microdevice, optimizes drug delivery. Microdevices with multiple injection capabilities exhibit enhanced therapeutic efficacy, effectively suppressing cell proliferation. Additionally, tumors with lower microvascular density experience higher drug concentrations in the extracellular space, resulting in significant cell death in hypoxic regions. Conclusions Achieving an efficient therapeutic response involves considering both the characteristics of the tumor microenvironment and the frequency of injections within a specific time frame.

Optimization of the Conditions for the Growth and Ethanol Production of Strain Bacillus sp. EtOH

Numerous factors can influence the growth, reproduction, and metabolism of microbes, which influence the yield and production cost. Bacillus sp. EtOH is a bacterial strain with a high yield of ethanol. In this paper, medium of Bacillus sp. EtOH was optimized. Different carbon/nitrogen sources were investigated, and the best carbon source (sucrose) and nitrogen source (ammonium sulfate) were determined to improve ethanol production. In addition, the best initial pH, temperature, and inoculation volume were 7, 37 °C and 1%, respectively. This study will be conducive to the subsequent ethanol fermentation, and improve application level of Bacillus sp. EtOH.

Instabilities of a circular moderately dense particle cloud impacted by an incident shock

Shock-driven gas-particle flows exist in a wide variety of physical systems, covering the range from dilute to dense regime. There are a lot of fundamental questions remaining to be answered, like the evolutions of flow instability, two-phase interactions, and inter-particle collision effects. In this work, the Eulerian-Lagrangian approach with gas-particle four-way coupling is applied to model two-dimensional shock-driven gas-particle flow under the moderately dense regime. For the gas flow, the formation mechanism of primary and secondary vortexes is discussed. The primary vortex is caused by the roll-up of slip line, while the secondary vortexes are induced by the velocity and density difference between the penetrating flow of particle-laden zone and the outside mainstream. Parametric studies of different Mach numbers, particle diameters and initial volume fractions have been performed to investigate the effects on shock behaviours and slip line instabilities. For the particle phase, a high-volume-fraction compression region forms at the upstream cloud zone, which blocks the penetrating gas, and results in the formation of slip line. The cloud tail is mainly composed of the upstream edge particles. The inter-particle collisions have impact on the particle distributions, and greatly affect the slip line stability at the upstream cloud edge. This work provides valuable insights into the instability mechanism of compressible gas-solid flow and the particle dispersion behaviours. However, it is important to note that our analysis is based on a two-dimensional configuration. In a real three-dimensional context, the generation of vortices is likely to differ, and may affect the particle dynamics to a certain degree.

Volume contractible Antimony bromide electrode as negative electrode for long-lasting Li-ion batteries

Antimony is one of the promising anode materials for lithium-ion batteries due to its high volumetric and gravimetric capacity (theoretical specific capacity 660 mAh g-1) and stable voltage window (0.87-0.91V vs Li/Li+). However, a high-volume expansion ( ∼130%) of Sb on lithiation degrades the electrochemical performance and restricts its application. In this work, a novel strategy is explored to use antimony halide (SbBr3) instead of Sb as the starting anode material. In the first step, Li will react with SbBr3 to form LiBr and pure Sb, leading to a 78% contraction in volume, and then this pure Sb further lithiates to form Li3Sb expanding the volume (of the lithiated Sb by 130%). LiBr, which is a byproduct of the first reaction, dissolves into the solvent, leaving a porous Sb. In a nutshell, the two-step lithiation process results in a net volume-contacted porous antimony, ideal as an electrode to counter volumetric stress in subsequent charge-discharge cycles. The electrochemical performance of this electrode is much superior when compared with the pure antimony electrode, taking advantage of initial volume reduction and porous scaffold. It achieves a high specific discharge capacity of 345 mAh g-1 at a rate of 100mAg-1 even after the end of the 100th cycle and losing only 20% of its capacity. This shows that this volume contractible technique can be successfully employed for metals and metallic alloys having drastically higher Li-storing capacities than graphite.

Experimental study on the evolution process of hydrate deposition, blockage and decomposition in reducing pipeline

BackgroundIn the process of deep-water oil and gas extraction, due to the special structure of the reducing pipeline, the flow field of the pipeline changes here, making it easier for hydrates to form and accumulate at reduced-diameter zone and increasing the risk of pipeline blockage. MethodsAiming at the problem of hydrate deposition and blockage in reducing pipeline, an experimental study was carried out through the self-designed and reduced-diameter transparent flow loop to investigate the hydrate deposition and blockage and decomposition evolution of hydrate at reduced-diameter zone under different conditions of flow velocities and initial cyclopentane volume contents. Significant FindingsThe study found that the flow field formed at reduced-diameter zone was the main reason affecting the distribution of hydrate particles, and the flow velocity and the initial hydrate volume fraction were the main controlling factors affecting the blockage in reducing pipeline. The flow velocity of 1.6 m/s was determined as the safe boundary for cyclopentane hydrate in reducing pipeline. Based on the experimental results, the mechanism of cyclopentane hydrate deposition and blockage in reducing pipeline was revealed, and targeted prevention and control methods for hydrate blockage at reduced-diameter zone were proposed. It is of great significance to ensure the safe flow of hydrate in reducing pipeline.

Method of Selecting Surgical Treatment for Children with Congenital Deformity of the Spine and Thorax

Introduction. Spinal anomalies are considered to be the most severe pathology of the axial skeleton. Intrauterine formation of deformity with its subsequent progression during growth is the reason for the need for surgical intervention. The prevalence of patients with congenital scoliosis in the total structure of spinal deformities is up to 2%. In terms of the malignancy of the course of the disease, children with unsegmented rod and rib synostosis represent one of the most unfavorable groups of patients. Aim. To perform a comparative analysis of the results of surgical treatment of children with congenital scoliosis with unilateral lateral vertebral segmentation disorder and rib synostosis using different techniques. Methods. The work is a monocenter cohort study of “case-control” type (III level of evidence). The design of the work is a monocenter cohort retro and prospective study. The results of surgical treatment of patients between 2010 and 2020 were analyzed. The study included 45 patients aged 3 to 7 years with the diagnosis of congenital scoliosis with unilateral lateral segmentation disorder of vertebral bodies and rib synostosis. The patients were divided into 2 groups depending on the surgical treatment method applied. In the first group (n = 24), patients underwent thoracoplasty with implantation of an individual rib/rib/vertebral distractor; in the second group (n = 21), patients underwent spinal surgery in the scope of vertebrotomy at the apex of the curvature and correction of the deformity with a multifocal spinal system. The data of medical records, as well as MSCT, radiographs, and pulse oscillometry were included in the analysis of the results. Results. Me (median) of scoliosis before treatment in group 1 patients 58.5, IQR = 19.75; after treatment — Me = 40.0, IQR = 20.0. Me of kyphosis before surgery 22, IQR = 4.5; after surgery Me = 26.0, IQR = 4.0. In the second group, Me of scoliosis before treatment 58.0, IQR = 3.0; after treatment, Me = 20.0, IQR = 6.0. Me of kyphosis before surgery 22, IQR = 2.0; after surgery Me 28.0, IQR = 4.0. When comparing MSCT data, group 1 patients showed an increase in lung tissue volume by 21% of the initial lung volume, in group 2 the increase amounted to 27%. The analysis of external respiratory function indices demonstrates improvement of reactive component indices by 21.1%, frequency dependence of resistive component by 46.4%, resistive component by 50% in group 1 patients, in group 2 there is an improvement of reactive component indices by 21.1%, resistive component by 50.9% and frequency dependence of reactive component by 46.7%. Conclusion. Corrective intervention on the spine at an early age makes it possible to achieve effective correction of the deformity; similar changes are observed both in lung volume and functional state of the respiratory system due to the mediated correction of the thorax shape.

Non-navigated 2D intraoperative ultrasound: An unsophisticated surgical tool to achieve high standards of care in glioma surgery.

In an era characterized by rapid progression in neurosurgical technologies, traditional tools such as the non-navigated two-dimensional intraoperative ultrasound (nn-2D-IOUS) risk being overshadowed. Against this backdrop, this study endeavors to provide a comprehensive assessment of the clinical efficacy and surgical relevance of nn-2D-IOUS, specifically in the context of glioma resections. This retrospective study undertaken at a single center evaluated 99 consecutive, non-selected patients diagnosed with both high-grade and low-grade gliomas. The primary objective was to assess the proficiency of nn-2D-IOUS in generating satisfactory image quality, identifying residual tumor tissue, and its influence on the extent of resection. To validate these results, early postoperative MRI data served as the reference standard. The nn-2D-IOUS exhibited a high level of effectiveness, successfully generating good quality images in 79% of the patients evaluated. With a sensitivity rate of 68% and a perfect specificity of 100%, nn-2D-IOUS unequivocally demonstrated its utility in intraoperative residual tumor detection. Notably, when total tumor removal was the surgical objective, a resection exceeding 95% of the initial tumor volume was achieved in 86% of patients. Additionally, patients in whom residual tumor was not detected by nn-2D-IOUS, the mean volume of undetected tumor tissue was remarkably minimal, averaging at 0.29 cm3. Our study supports nn-2D-IOUS's invaluable role in glioma surgery. The results highlight the utility of traditional technologies for enhanced surgical outcomes, even when compared to advanced alternatives. This is particularly relevant for resource-constrained settings and emphasizes optimizing existing tools for efficient patient care. NCT05873946 - 24/05/2023 - Retrospectively registered.

Computer-Assisted Evaluation Confirms Spontaneous Healing of Donor Site One Year following Bone Block Harvesting from Mandibular Retromolar Region-A Cohort Study.

The study was conducted on patients who underwent an alveolar ridge augmentation using an intraoral retromolar bone graft. Three CBCT scans were performed-intraoperative, and at six months and one year after the surgical procedure. By using the Materialise Mimics Innovation Suite software 26.0 features segmentation by thresholding, Hounsfield unit averaging, and superimposition of the tomographies, we could precisely quantify the healing process utilizing spatial and characteristic measures. In all cases, the computer-aided quantification showed that six months following surgery, the donor site had recovered up to 64.5% ± 4.24 of its initial volume, and this recovery increased to 89.2% ± 2.6 after one year. Moreover, the Hounsfield unit averaging confirmed dynamic bone quality healing, starting at 690.3 ± 81 HU for the bone block, decreasing to 102 ± 27.8 HU at six months postoperatively, and improving to 453.9 ± 91.4 HU at the donor site after a year. This study demonstrates that there is no need for additional replanting at the donor site following retromolar bone block harvesting, whether autogenous or allograft, since spontaneous healing occurs 12 months following the surgery.

Extreme Flood Flow Routing for Panchet and Maithan Reservoirs of India Using Modified Puls Technique

An important aspect of economic considerations is the routing and safety of hydraulic storage facilities such as dams for extreme probable water flooding. The routing of dam reservoirs requires more attention for determining the magnitude of extreme probable flooding. Apparently, the type of structure, importance, and economic development of the surrounding area guide the routing criteria for choosing the extreme flood magnitude. The Maithan and Panchet Dams in India have faced several major floods with diversified magnitudes since 1978. The present study aims to estimate the storage and routing of extreme probable floodings for these two dams based on real-time flood data like inflow, outflow, and elevation for the extreme flood years of 1978, 2009, and 2014. Reservoir storages at different elevations are calculated from the initial storage volumes. For both reservoirs, discharge equations are derived and calculated at given elevations during extreme floods. The Modified Puls technique is used for routing extreme floods. At the end of each extreme flood in 1978, 2009, and 2014, the variation in outflow discharges at different elevations and flood hydrographs is predicted. Finally, estimated outflow discharges are compared with the actual outflow discharges for the given inflows during extreme floods. Using this approach, extreme floods that occurred in 1978 are predicted with less than 10% error. Outcomes from this study may help in the future planning and routing of flood-control detention facilities and in predicting the variation in outflow discharges at different elevations. Based on this work, alternative studies and regional drainage planning can also be carried out.

Natural History of Quantitative Fatty Infiltration and 3D Muscle Volume After Nonoperative Treatment of Symptomatic Rotator Cuff Tears: A Prospective MRI Study of 79 Patients.

The severity of fatty infiltration (FI) predicts the treatment outcome of rotator cuff tears. The purpose of this investigation was to quantitatively analyze supraspinatus (SSP) muscle FI and volume at the initial presentation and after a 3-month minimum of conservative management. We hypothesized that progression of FI could be predicted with initial tear size, FI, and muscle volume. Seventy-nine shoulders with rotator cuff tears were prospectively enrolled, and 2 magnetic resonance imaging (MRI) scans with 6-point Dixon sequences were acquired. The fat fraction within the SSP muscle was measured on 3 sagittal slices, and the arithmetic mean was calculated (FI SSP ). Advanced FI SSP was defined as ≥8%, pathological FI SSP was defined as ≥13.5%, and relevant progression was defined as a ≥4.5% increase in FI SSP . Furthermore, muscle volume, tear location, size, and Goutallier grade were evaluated. Fifty-seven shoulders (72.2%) had normal FI SSP , 13 (16.5%) had advanced FI SSP , and 9 (11.4%) had pathological FI SSP at the initial MRI scan. Eleven shoulders (13.9%) showed a ≥4.5% increase in FI SSP at 19.5 ± 14.7 months, and 17 shoulders (21.5%) showed a ≥5-mm 3 loss of volume at 17.8 ± 15.3 months. Five tears (7.1%) with initially normal or advanced FI SSP turned pathological. These tears, compared with tears that were not pathological, had significantly higher initial mediolateral tear size (24.8 compared with 14.3 mm; p = 0.05), less volume (23.5 compared with 34.2 mm 3 ; p = 0.024), more FI SSP (9.6% compared with 5.6%; p = 0.026), and increased progression of FI SSP (8.6% compared with 0.5%; p < 0.001). An initial mediolateral tear size of ≥20 mm yielded a relevant FI SSP progression rate of 81.8% (odds ratio [OR], 19.0; p < 0.001). Progression rates of 72.7% were found for both initial FI SSP of ≥9.9% (OR, 17.5; p < 0.001) and an initial anteroposterior tear size of ≥17 mm (OR, 8.0; p = 0.003). Combining these parameters in a logistic regression analysis led to an area under the receiver operating characteristic curve (AUC) of 0.913. The correlation between FI SSP progression and the time between MRI scans was weak positive (ρ = 0.31). Three risk factors for relevant FI progression, quantifiable on the initial MRI, were identified: ≥20-mm mediolateral tear size, ≥9.9% FI SSP , and ≥17-mm anteroposterior tear size. These thresholds were associated with a higher risk of tear progression: 19 times higher for ≥20-mm mediolateral tear size, 17.5 times higher for ≥9.9% FI SSP , and 8 times higher for ≥17-mm anteroposterior tear size. The presence of all 3 yielded a 91% chance of ≥4.5% progression of FI SSP within a mean of 19.5 months. Diagnostic Level II . See Instructions for Authors for a complete description of levels of evidence.

Towards the mechanical characterisation of unruptured intracranial aneurysms: Numerical modelling of interactions between a deformation device and the aneurysm wall

Intracranial aneurysm is a critical pathology related to the arterial wall deterioration. This work is an essential aspect of a large scale project aimed at providing clinicians with a non-invasive patient-specific decision support tool regarding the rupture risk assessment. A machine learning algorithm links the aneurysm shape observed and a database of UIA clinical images associated with in vivo wall mechanical properties and rupture characterisation. The database constitution is derived from a device prototype coupled with medical imaging. It provides the mechanical characterisation of the aneurysm from the wall deformation obtained by inverse analysis based on the variation of luminal volume. Before performing in vivo tests of the device on small animals, a numerical model was built to quantify the device’s impact on the aneurysm wall under natural blood flow conditions. As the clinician will never be able to precisely situate the device, several locations were considered. In preparation for the inverse analysis procedure, artery material laws of increasing complexity were studied (linear elastic, hyper elastic Fung-like).Considering all the device locations and material laws, the device induced relative displacements to the Systole peak (worst case scenario with the highest mechanical stimulus linked to the blood flow) ranging from 375 μm to 1.28 mm. The variation of luminal volume associated with the displacements was between 0.95 % and 4.3 % compared to the initial Systole volume of the aneurysm. Significant increase of the relative displacements and volume variations were found with the study of different cardiac cycle moments between the blood flow alone and the device application. For forthcoming animal model studies, Spectral Photon CT Counting, with a minimum spatial resolution of 250 μm, was selected as the clinical imaging technique. Based on this preliminary study, the displacements and associated volume variations (baseline for inverse analyse), should be observable and exploitable.

Innovative sodium acrylate wastewater resource recovery through electrodialysis with integrated bipolar membranes

With the process of industrialization, many production fields produce high-salt organic wastewater. In this work, we have employed an electrodialysis (ED)-resin-bipolar membrane electrodialysis (BMED) mixed process to address sodium acrylate wastewater, achieving resource recovery. The influences of the initial volume ratio and applied voltage were investigated. In the ED-resin, the separation of organic compounds and pigments such as sodium acrylate and phenol was realized. The desalting rate could reach 93.1%, the energy consumption is 0.6 kWh/kg C3H3O2Na, and the chroma removal rate can reach 99%. In the subsequent BMED phase, we attain notable acrylic acid and base concentrations, reaching levels of 1.59 mol/L and 3.12 mol/L, with a current efficiency of 58.14% and an energy consumption of 3.28 kWh/kg NaOH. In addition, economic and environmental evaluations verify the feasibility of this process, which is indicative of its prospect of industrial application.

Surface wear of attachments in patients during clear aligner therapy: a prospective clinical study

BackgroundThis prospective clinical study aimed to quantitatively evaluate the surface wear of attachments and investigate the associated risk factors. Additionally, the wear values and regions of three types of commonly used attachments were explored.MethodsParticipants were recruited from the population of patients who received clear aligner therapy from October to December 2022. Intraoral scanning was performed on eligible participants before treatment (T0), immediately after initial bonding of attachments (T1), and at 2 months (T2), 4 months (T3), 6 months (T4), and 8 months (T5) after starting treatment. The attachment volume, average depth and regions of attachment wear were measured using superimposed digitized models. The Kruskal–Wallis test was performed to compare data between multiple groups. Multiple linear regression analyses were performed to evaluate risk factors for the volume of attachment wear.ResultsA total of 47 patients with 617 attachments were included. As treatment time increased, the attachment volume decreased significantly (P = 0.003). The initial attachment volume was positively related to the volume of attachment wear (β = 0.527, P < 0.001). The volume of attachment wear was significantly greater in females than in males (β = 0.147, P = 0.020) and in optimized attachments than in conventional attachments (β = 0.308, P < 0.001). The wear of 3-mm rectangular attachments progressed from edges to buccal surfaces, with the deepest wear at corners of gingival edges; the wear of the optimized attachments was primarily located on surface ridges. The wear volume ratio of the optimized root control attachments was significantly greater than that of the 3-mm rectangular attachments at T3 (P = 0.011), T4 (P < 0.001), and T5 (P < 0.001).ConclusionsThe volume of attachment wear increased gradually with treatment time. Sex, attachment type, and initial attachment volume were risk factors for the volume of attachment wear. The deepest wear regions of 3-mm rectangular attachments were at the corners of gingival edges, while the deepest wear regions of optimized attachments were at surface ridges. Four months after treatment, optimized root control attachments showed more relative wear than 3-mm rectangular attachments.

Study of microstructure, magnetic and gas sensing properties of porous Ni0.4+xZn0.6-xCeyFe2-yO4 magnetic nanoparticles

The spinel ferrite systemsNi0.4+xZn0.6−xCeyFe2−yO4 (0≤x+y≤0.3) were synthesized by a modified glycol-thermal technique. X-ray diffractometer (XRD) confirmed formation of single phase cubic spinel structure with average crystallite sizes 8–21 nm. The crystallite sizes were found to be in agreement with the particle sizes obtained from the high resolution transmission electron microscopy (HRTEM) indicating formation of single domain nanoparticles. Scanning electron microscopy (SEM) showed a homogeneous spread of semi-spherical nanoparticles. Brunauer-Emmett-Teller (BET) revealed specific surface area ranging between 64 and 108 m2/g, while Barrett-Joyner-Halenda (BJH) showed the pore sizes varying between 48 and 126 nm. Cation distribution obtained from Rietveld refinement revealed all Ce3+ occupied B- sites whilst Ni2+, Zn2+, Fe3+ occupied both A and B sites. Magnetization measurements were performed using the vibration samples magnetometer (VSM). The saturation magnetization varied between 51 and 60 emu/g, while the coercivity dropped from 114 to 89Oe. The remnant magnetization varied between 3 and 12 emu/g. A correlation was observed between the saturation magnetization and the effective magnetic moments confirming cation distribution to be reliable. A strong correlation between initial susceptibility and unit cell volume was found. The crystallite sizes varied inversely with initial magnetic susceptibility. The magnetic characteristics of presented materials make them useful in high frequency device applications and has potential use as contrast agent in magnetic resonance imaging (MRI). 57Fe Mössbauer spectroscopy revealed the strengthening of ferromagnetic coupling. Gas sensing tests revealed a decrease in sensing response with the transition from paramagnetic state to ferromagnetic state. The Ni0.4Zn0.6Fe2O4 sample showed the best sensing response to SO2 at 100 °C compared to CO gas. However, at 150 °C the sample was more sensitive to CO gas than SO2 gas.

Polynomial Voting Rules

We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.

Granular-fluid avalanches: the role of vertical structure and velocity shear

Field observations of debris flows often show that a deep dry granular front is followed by a progressively thinner and increasingly watery tail. These features have been captured in recent laboratory flume experiments (Taylor-Noonan et al., J. Geophys. Res.: Earth Surf., vol. 127, 2022, e2022JF006622). In these experiments different initial release volumes were used to investigate the dynamics of an undersaturated monodisperse grain–water mixture as it flowed downslope onto a horizontal run-out pad. Corresponding dry granular flows, with the same particle release volumes, were also studied to show the effect of the interstitial fluid. The inclusion of water makes debris flows much more mobile than equivalent volumes of dry grains. In the wet flows, the formation of a dry front is crucially dependent on the heterogeneous vertical structure of the flow and the velocity shear. These effects are included in the depth-averaged theory of Meng et al. (J. Fluid Mech., vol. 943, 2022, A19), which is used in this paper to quantitatively simulate both the wet and dry experimental flows using a high-resolution shock-capturing scheme. The results show that velocity shear causes dry grains (located near the free surface) to migrate forwards to create a dry front. The front is more resistant to motion than the more watery material behind, which reduces the overall computed run-out distance compared with debris-flow models that assume plug flow and develop only small dry snouts. Velocity shear also implies that there is a net transport of water to the back of the flow. This creates a thin oversaturated tail that is unstable to roll waves in agreement with experimental observations.