Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method

This paper presents the numerical simulations of two Richtmyer-Meshkov （RM） instability experiments using the conservative front-tracking method developed in （Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550-1588 （2007））. The numerical results are compared with those obtained in （Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51-64 （1995））. The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.

DEALING WITH MOVINGS AND COLLISIONS OF ARBITRARY MANY DISCONTINUITIES IN CONSERVATIVE FRONT-TRACKING METHOD

An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an ＂all-purposed and robust＂ front-tracking algorithm. The algorithm with this approach may have some inconsistency and thus will have 0（1） magnitude errors in some grid cells at sometimes. Nevertheless, these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation. Numerical examples are presented to illustrate the efficiency of the approach.

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

Characteristic analysis of 5D symmetric Hamiltonian conservative hyperchaotic system with hidden multiple stability

Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.

Bilateral Congenital Upper Eyelid Eversion (Ectropion): A Rare Presentation Responded Well to Conservative Treatment at Temeke Regional Referral Hospital-Tanzania

Congenital eversion of the upper eyelids is a rare condition, the exact cause of which remains unknown. It is more frequently associated with Down’s syndrome and black babies. If diagnosed early and treated properly, the condition can be managed without surgery. We report a case of non syndromic congenital bilateral severe upper eyelid eversion in otherwise normal 3 days old neonate of African descent (Tanzanian), born by vaginal delivery. The case was conservatively managed by lubricants, antibiotics and eyelid patching. We report this case because from the best of our knowledge it has never been documented here at our hospital and Tanzania before.

Secondary Hyperparathyroidism in Dialysis Patients: Short- and Long-Term Outcomes of Conservative Parathyroidectomy

Secondary hyperparathyroidism (HPT) is frequent in dialysis patients. Parathyroidectomy (PTX) is indicated for patients who failed medical therapy. We reviewed the data from 184 dialysis patients who underwent PTX between January 2015 and January 2023. We aimed to evaluate the short and long term outcomes of PTX in dialysis patients, comparing the conservative 3/4 versus 7/8 techniques in this population.166 dialysis patients with secondary HPT were included. A conservative subtotal PTX (sPTX) 7/8 was performed in 72% of patients and sPTX 3/4 in 28% of them. Severe postoperative hypocalcaemiaocurred in 45 patients (27%). Hypocalcaemia was significantly more frequent in the sPTX 7/8 group (p = 0.012). One case of persistent HPT (0.6%) and 20 cases of recurrence (12%) were diagnosed. Recurrence was more frequent in the sPTX 3/4 group (15%). No deaths were reported during the perioperative period.

Indication of conservative treatment by antibiotics for uncomplicated and complicated acute appendicitis

BACKGROUND Acute appendicitis is one of the most common emergency abdominal disease,and recent studies have evaluated conservative treatment using antibiotics for uncomplicated appendicitis.Although the efficacy of conservative treatment for uncomplicated appendicitis is known,its efficacy for complicated appendicitis remains unknown,so are risk factors for the conservative treatment of appendi-citis.In our institution,conservative treatment has long been the first choice for most appendicitis cases,except for perforation.Therefore,this novel study inves-tigated the outcomes of conservative treatment for uncomplicated and compli-cated acute appendicitis and the risk factors associated with conservative treat-ment.treatment.The significant and independent predictors of resistance to conservative treatment were body temperature≥37.3℃,appendicolith and Douglas sinus fluid visible on computed tomography(CT).The rate of resistance to conservative treatment was 66.7%(6/9)for patients with the above three factors,22.9%(8/35)for patients with two factors(appendicolith and body temperature≥37.3℃),16.7%(2/12)for patients with two factors(Douglas sinus fluid and appendicolith)and 11.1%(1/9)for patients with two factors(Douglas sinus fluid and body temperature≥37.3℃).CONCLUSION A temperature≥37.3℃,appendicolith and Douglas sinus fluid on CT might be clinical risk factors of resistance to conservative treatment for acute appendicitis.

Entropy‑Conservative Discontinuous Galerkin Methods for the Shallow Water Equations with Uncertainty

In this paper,we develop an entropy-conservative discontinuous Galerkin(DG)method for the shallow water(SW)equation with random inputs.One of the most popular methods for uncertainty quantifcation is the generalized Polynomial Chaos(gPC)approach which we consider in the following manuscript.We apply the stochastic Galerkin(SG)method to the stochastic SW equations.Using the SG approach in the stochastic hyperbolic SW system yields a purely deterministic system that is not necessarily hyperbolic anymore.The lack of the hyperbolicity leads to ill-posedness and stability issues in numerical simulations.By transforming the system using Roe variables,the hyperbolicity can be ensured and an entropy-entropy fux pair is known from a recent investigation by Gerster and Herty(Commun.Comput.Phys.27(3):639–671,2020).We use this pair and determine a corresponding entropy fux potential.Then,we construct entropy conservative numerical twopoint fuxes for this augmented system.By applying these new numerical fuxes in a nodal DG spectral element method(DGSEM)with fux diferencing ansatz,we obtain a provable entropy conservative(dissipative)scheme.In numerical experiments,we validate our theoretical fndings.

Research Progress on Conservative Treatment of Lumbar Disc Herniation

Lumbar disc herniation(LDH)is a common orthopedic disease in clinical practice,with main symptoms of varying degrees of pain and functional impairment,seriously affecting the quality of work and life of patients,and also causing a certain degree of economic burden to the patient's family and society.At present,there are various conservative treatment methods for LDH in clinical practice.Conservative treatment has the characteristics of small trauma and high safety,which can achieve symptom relief and cure for most patients in clinical practice.This article aims to provide a scientific reference for the selection of treatment plans for LDH patients by reviewing relevant literature on conservative treatment of LDH that has been publicly reported both domestically and internationally in recent years.

CONSERVATIVE DIFFERENCE SCHEME BASED ON NUMERICAL ANALYSIS FOR NONLINEAR SCHRDINGER EQUATION WITH WAVE OPERATOR

A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

Successful conservative management with methotrexate and mifepristone of cervical pregnancy

This study investigated possible effective treatments for cervical pregnancy, a rare form of ectopic pregnancy. The clinical records of 11 cases of ectopic pregnancy admitted to the Third Affiliated Hospital of Sun Yat-sen University from 1998 to 2010 were analyzed. All patients were treated with intermuscular injection of methotrexate （MTX, 50 mg）, and oral mifepristone （25 mg, bid）. All cases were successfully cured by conservative treatments using methotrexate plus mifepristone. Cervical pregnancy is a contributive factor to mutiple abortions and curettages. Methotrexate plus mifepristone, curettage through hysteroscopy and intracervical obturation with gauze are effective treatments of cervical pregnancy without the need for surgical intervention.

Invasive versus conservative strategy in consecutive patients aged 80 years or older with non-ST-segment elevation myocardial infarction: a retrospective study in China

Objective To investigate whether the very elderly patients with non-ST-segment elevation myocardial infarction (NSTEMI) will benefit from an invasive strategy versus a conservative strategy. Methods 190 consecutive patients aged 80 years or older with NSTEMI were included in the retrospective study from September 2014 to August 2017, of which 69 patients received conservative strategy and 121 patients received invasive strategy. The primary outcome was death. Multivariate Cox regression models were used to assess the statistical association between strategies and mortality. The survival probability was further analyzed. Results The primary outcome occurred in 17.4% patients in the invasive group and in 42.0% patients in the conservative group (P = 0.0002). The readmission rate in the invasive group (14.9%) was higher than that in the conservative group (7.2%). Creatinine level (OR = 1.01, 95% CI: 0.10–1.03, P = 0.05) and use of diuretic (OR = 3.65, 95% CI: 1.56–8.53, P = 0.003) were independent influential factors for invasive strategy. HRs for multivariate Cox regression models were 3.45 (95% CI: 1.77–6.75, P = 0.0003), 3.02 (95% CI: 1.52–6.01, P = 0.0017), 2.93 (95% CI: 1. 46–5.86, P = 0.0024) and 2.47 (95% CI: 1.20–5.07, P = 0.0137). Compared with the patients received invasive strategy, the conservative group had remarkably reduced survival probability with time since treatment (P < 0.001). Conclusions An invasive strategy is superior to a conservative strategy in reducing mortality of patients aged 80 years or older with NSTEMI. Our results suggest that an invasive strategy is more suitable for the very elderly patients with NSTEMI in China.

A CONSERVATIVE DIFFERENCE SCHEME FOR CONSERVATIVE DIFFERENTIAL EQUATION WITH PERIODIC BOUNDARY

The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.

Conservative pulp treatment for Oehlers type Ⅲ dens invaginatus: A case report

BACKGROUND Diverse presentations of dens invaginatus (DI) and root canal treatment with an immature open apex often pose challenges to dentists. Adequate treatment planning for DI is the main reason for successful approach, i.e., we should consider the shape and depth of the concave folding, the condition of the original pulp, and the growth stage of the root formation. CASE SUMMARY A 9-year-old girl complained of severe pain of the right maxillary incisor (tooth 12) when chewing for two weeks. Following clinical and radiographic examinations, Oehlers type III DI of tooth 12, with an immature open apical foramen and a symptomatic periapical pathosis, was diagnosed. Cone-beam computed tomography verified the specific spatial and stereoscopic data regarding the communication between the main root canal and pseudo root canal of the involved tooth. After removing the source of infection, a mineral trioxide aggregate was selected to fill and seal the pseudo root canal;additionally, pulp capping of the main canal was performed through the interconnections between the root canals in the middle segment to preserve pulp vitality and enable continual root formation and eventual root apex closure. CONCLUSION We propose to conduct main root canal pulp capping for DI with communication between the main and pseudo root canals.

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrdinger system

We derive a new method for a coupled nonlinear Schr/Sdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.

Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

A CLASS OF EXPLICIT FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE SCHEMES

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

Postpartum pubic symphysis diastasis-conservative and surgical treatment methods, incidence of complications: Two case reports and a review of the literature

BACKGROUND Widening of the pubic joint of more than 10 mm is diagnostic and defined as pubic symphysis diastasis and is considered a complication of vaginal childbirth or pregnancy.As it is a rare pathology(ranging from 1 in 300 to 1 in 30000 pregnancies),no gold standard treatment has been defined.CASE SUMMARY This study examines two cases,a 27-year-old woman(gravida 1,para 1)and a 32-year-old woman(gravida 2,para 2),who presented to the clinic after uneventful vaginal deliveries.A normal pregnancy with no complications was observed in both patients.Severe pain in the pubic region occurred after labour and was accompanied by complicated locomotion.Pubic symphysis diastasis was confirmed radiologically and bed rest with lateral decubitus positioning was recommended.Oral non-steroidal antiinflammatory drugs were administered to relieve pain exacerbations.The symptoms decreased after treatment.Posttreatment magnetic resonance imaging(MRI)in the first case showed a reduction in symphyseal separation with no signs of osteitis.Three years later the symptoms recurred;MRI examination showed no further symphyseal widening or signs of osteitis.A relapse of symphyseal separation was diagnosed and conservative treatment was re-administered resulting in successful recovery.In the second case,pain recurred when the patient conceived for the second time.This time no benefit following conservative treatment was observed.Persistent pain and complicated locomotion led to scoliotic deformation of the lumbar part of the spine and leg length discrepancy,thus surgical treatment was chosen and internal pubic synthesis was performed.CONCLUSION Overall,surgical treatment resulting from insufficient conservative treatment showed a high risk of postoperative complications following the treatment of postpartum pubic symphysis diastasis.