Quantization of the Kinetic Energy of Deterministic Chaos

In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Stochastic Chaos of Exponential Oscillons and Pulsons

An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the Helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagonal, and external group oscillons, a random energy pulson, random internal, diagonal, and external energy oscillons, and a random cumulative energy pulson.

Modeling the Impact of Testing Mode on the Viscoelastic Behavior of Asphalt Concrete

The variations in the viscoelastic characteristics of asphalt concrete due to testing mode are assessed and modeled in the present investigation.Asphalt concrete mixture was prepared at its optimum asphalt binder requirement and compacted in slab mold with the aid of roller compaction.Beam specimens of 6.2 cm width,5.6 cm depth,and 40 cm length,were obtained from the slab samples with the aid of a diamond saw,and tested using controlled stress and strain techniques under dynamic flexural stresses.The viscoelastic properties such as the phase angle,cumulative dissipated energy,permanent deformation,flexural stiffness,and micro strain were monitored and modeled among the two testing techniques.It was noticed that higher micro strain and permanent deformation are detected when testing the asphalt concrete specimens under constant strain mode.However,higher phase angle,flexural stiffness,and energy dissipation could be observed under the constant stress mode of the test.

Effect of IOP based infusion system with and without balanced phaco tip on cumulative dissipated energy and estimated fluid usage in comparison to gravity fed infusion in torsional phacoemulsification

Background:To evaluate the effect of three different combinations of tip designs and infusion systems in torsional phacoemulsification(INFINITI and CENTURION)in patients with cataract.According to the manufacturer,two unique improvements in the Centurion are:active fluid dynamic management system and use of an intrepid balanced tip.The study specifically aimed to evaluate the beneficial effects,if any,of change in tip design and infusion system individually and in combination on both per-operative parameters as well as endothelial health over 6 months.Methods:One hundred and twenty six consenting patients of grade 4.0-6.9 senile cataract were randomized into three groups for phacoemulsification:Group A(n=42):Gravity fed infusion system and 45° Kelman miniflared ABS phaco tip;Group B(n=42):intraocular pressure(IOP)based infusion system and 45° Kelman miniflared ABS phaco tip;Group C(n=42):IOP based infusion system and 45° Intrepid balanced phaco tip.The cumulative dissipated energy(CDE),estimated fluid usage(EFU)and total aspiration time(TAT)were compared peroperatively.The endothelial parameters were followed up postoperatively for six months.Results:The three arms were matched for age(p=0.525),gender(p=0.96)and grade of cataract(p=0.177).Group C was associated with significant reductions in CDE(p=0.001),EFU(p<0.0005)as well as TAT(p=0.001)in comparison to the other groups.All three groups had comparable baseline endothelial cell density(p=0.876)and central corneal thickness(p=0.561).On post-operative evaluation,although all groups were comparable till 3 months,by 6 months,the percentage losses in endothelial cell density were significantly lower in group C as compared to the other groups.Conclusions:Use of an IOP based phacoemulsification system in association with use of the Intrepid balanced tip reduces the CDE,EFU and TAT in comparison to a gravity fed system with a mini flared tip or IOP based system with a mini flared tip while also providing better endothelial preservation thus favouring the use of an IOP fed system with a balanced tip.

Comparing surgical efficiencies between phacoemulsification systems: a single surgeon retrospective study of 2000 eyes

AIM: To compare under similar conditions intraoperative surgical efficiencies metrics between an active fluidics and a gravity based phacoemulsification systems.METHODS: Adult patients who were diagnosed with a cataract that compromised visual acuity inferior to 20/40 were included in the study. Patients were excluded from the study if they had a history of severe retinal disorders, clinically significant corneal endothelial dystrophy or history of corneal disease. All phacoemulsification surgeries were performed by a single surgeon. Both phacoemulsification systems used the 0.9 mm 45-degree aspiration bypass system Intrepid Balanced tip and the 0.9 mm Intrepid Ultra infusion sleeve. All cataracts were classified using the Lens Opacities Classification System III, cumulative dissipated energy(CDE) and aspiration fluids were measured in each surgery.RESULTS: Totally 2000 eyes were included in the study. Phacoemulsification was performed in 1000(50%) eyes with an active fluid dynamics system and in 1000(50%) eyes with a gravity-based fluidic system. Mean CDE until fracture of the lens was 1.1 and 1.9 percent-seconds and total mean CDE used was 5.6 and 7.2 percent-seconds using an active fluidics dynamics system and gravity-based fluidic system, respectively(P<0.001). Mean aspiration fluids used were 70 m L using an active fluidics dynamics system and 85 m L using a gravity-based fluidic system(P<0.001).CONCLUSION: This study evidences that surgeries performed under similar conditions(same surgeon, phaco tip and sleeve) with the active fluidics dynamics system required significantly lower CDE and aspiration fluids.

Prospective study of Centurion~？ versus Infiniti~？ phacoemulsification systems： surgical and visual outcomes

AIM： To evaluate surgical outcomes（SOs） and visual outcomes（VOs） in cataract surgery comparing the Centurion？ phacoemulsification system（CPS） with the Infiniti？ phacoemulsification system（IPS）.METHODS： Prospective, consecutive study in a singlesite private practice. Totally 412 patients undergoing cataract surgery with either the CPS using the 30-degree balanced？ tip（n=207） or the IPS using the 30-degree Kelman？ tip（n=205）. Intraoperative and postoperative outcomes were documented prospectively up to one month follow-up. Nuclear sclerosis（NS） grade, cumulated dissipated energy（CDE）, preoperative corrected distance visual acuity（CDVA）, and CDVA at one month were recorded. RESULTS： CDE was 13.50% less in the whole CPS compared with the whole IPS subcohort. In eyes with NS grade III or greater, CDE was 28.87% less with CPS（n=70） compared with IPS（n=44）（P=0.010）. Surgical complications were not statistically different between the two subcohorts（P=0.083）, but in the one case of vitreous loss using the CPS, CDVA of 6/4 was achieved at one month. The mean CDVAs（VOs） at one month for NS grade III and above cataracts were-0.17 log MAR（6/4.5） in the CPS and-0.15 log MAR（6/4.5） in the IPS subcohort respectively（P=0.033）.CONCLUSION： CDE is 28.87% less, and VOs are significantly improved, in denser cataracts in the CPS compared with the IPS. The authors recommend the CPS for cases with denser nuclei.

Comparison of clinical outcomes between femtosecond laser-assisted versus conventional phacoemulsification

Background:To compare femtosecond laser-assisted versus conventional phacoemulsification in terms of visual and refractive outcomes,cumulative dissipated energy,anterior chamber inflammation and endothelial cell loss.Methods:In this retrospective cohort study,records of eyes that underwent femtosecond laser-assisted cataract surgery(FLACS)or conventional phacoemulsification(CP)were reviewed.The Victus femtosecond laser(Bausch and Lomb,Germany)was used to carry out corneal incisions,anterior capsulotomy,and lens fragmentation in FLACS procedures.Manifest refraction spherical equivalence(MRSE),uncorrected distance visual acuity(UDVA),corrected distance visual acuity(CDVA),cumulative dissipated energy(CDE),postoperative cells and flare and endothelial cell count data were collected.Subgroup analysis of the visual acuity tests was performed based on the type of intraocular lens implanted(monofocal,monofocal toric,multifocal,multifocal toric,accommodating).Results:A total of 735 eyes were included in the study(296 eyes for the FLACS group and 439 eyes for the CP group).At one year follow-up,120 eyes comprised the FLACS group and 265 eyes for the CP group.MRSE in the FLACS group was−0.16±0.58 D and−0.20±0.52 D in the CP group(P=0.50).UDVA in the FLACS group was 20/25(mean logMAR 0.12±0.13)and 20/25(mean logMAR 0.11±0.13)in the CP group(P=0.48).CDVA was 20/20(mean logMAR 0.03±0.07)in the FLACS group and 20/20(mean logMAR 0.02±0.06)in the CP group(P=0.15).No statistically significant trend was seen for FLACS versus CP by intraocular type for visual acuity.CDE for the different cataract grades ranged from 6.97±5.74 to 29.02±16.07 in the FLACS group and 7.59±6.42 to 35.69±18.30 in the CP group.The FLACS group was significantly lower for post-operative central corneal edema(P=0.05),cells and flare(P=0.01),and endothelial cell loss(P=0.04).Conclusions:Femtosecond laser-assisted cataract surgery and conventional phacoemulsification had similar refractive and visual outcomes.Phacoemulsification energy,anterior chamber inflammation and corneal endothelial cell loss were less in the femtosecond laser group.