Two problems in the study of elastic filaments are considered.First, a reliable numerical algorithm is developed that candetermine the shape of a static elastic rod under a variety ofconditions. In this algorithm the governing equations are writtenentirely in terms of local coordinates and are discretized usingfinite differences. The algorithm has two significant advantages:firstly, it can be implemented for a wide variety of the boundaryconditions and, secondly, it enables the user to work with generalconstitutive relationships with only minor changes to thealgorithm. In the second problem a model is presented describingthe dynamics of an elastic tube conveying a fluid. First weanalyze instabilities that are present in a straight rod or tubeunder tension subject to increasing twist in the absence of afluid. As the twist is increased beyond a critical value, thefilament undergoes a twist-to-writhe bifurcation. A multiplescales expansion is used to derive nonlinear amplitude equationsto examine the dynamics of the elastic rod beyond the bifurcationthreshold. This problem is then reinvestigated for an elastic tubeconveying a fluid to study the effect of fluid flow on thetwist-to-writhe instability. A linear stability analysisdemonstrates that for an infinite rod the twist-to-writhethreshold is lowered by the presence of a fluid flow. Amplitudeequations are then derived from which the delay of bifurcation dueto finite tube length is determined. It is shown that the delayedbifurcation threshold depends delicately on the length of the tubeand that it can be either raised or lowered relative to thefluid-free case. The amplitude equations derived for the case of aconstant average fluid flux are compared to the case where theflux depends on the curvature. In this latter case it is shownthat inclusion of curvature results in small changes in some ofthe coefficients in the amplitude equations and has only a smalleffect on the post-bifurcation dynamics.

<p>The surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation. </p><p>In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport, as has been observed in several experimental studies on GUVs. In this study, shape changes are assumed to be instantaneous, while species transport, which is modeled by phase separation and domain coarsening, follows a natural time scale described by the Cahn--Hilliard dynamics.</p><p>The curvature energy of the vesicle membrane is defined by the classical Canham--Helfrich--Evans model. Dependence of flexural rigidity and spontaneous curvature on the lipid species is built into the energy functional. The chemical energy is characterized by a Cahn--Hilliard type density function that intrinsically captures the line energy of interfaces between two phases. Both curvature and chemical contributions to the vesicle energetics are consistently non-dimensionalized.</p><p>The coupled model is cast in a diffuse-interface form using the phase-field framework. The phase-field form of the governing equations describing shape equilibrium and species transport are both fourth-order and nonlinear. The system of equations is discretized using the finite element method with a uniform cubic-spline basis that satisfies global higher-order continuity. For shape equilibrium, geometric constraints of constant internal volume and constant surface area of the vesicle are imposed weakly using the penalty approach. A time-stepping scheme based on the unconditionally gradient-stable convexity-splitting technique is employed for explicit time integration of nonlocal integrals arising from the geometric constraints.</p><p>Numerical examples of axisymmetric stationary shapes of uniform vesicles are presented. Further, two- and three-dimensional numerical examples of domain formation and growth coupled to vesicle shape changes are discussed. Simulations qualitatively depicting curvature-dependent domain sorting and shape changes to minimize line tension are presented. The effect of capturing the difference in time scales is also brought out in a few numerical simulations that predict a starkly different pathway to equilibrium.</p> / Dissertation

Tobulėjant skaitiniams metodams ir kompiuterinei technikai atsivėrė galimybė naujų, sudėtingesnių mechaninių objektų modeliavimui. Turėdami naujus sudėtingesnių objektų modelius tyrėjai gali pritaikyti aprašytas ir sumodeliuotas šių objektų savybes su mikro struktūros ypatumais esamų ar busimų savybių nustatymui bei naujų medžiagų kūrimui. Tam intensyviai naudojami kaip eksperimentiniai taip ir skaitiniai metodai, kurių tobulinimui šiuo metu yra skiriamas labai didelis dėmesys. Skaitinis eksperimentas, kaip medžiagos tyrimo būdas pasitelkiamas dar ir todėl kad yra pigesnis ir leidžia interpretuoti jau žinomus eksperimentų rezultatus, o taip suteikia žinių naujiems tyrimams. Vienas iš metodų, kuris modeliuoja makroskopines medžiagų savybes remdamasis medžiagos mikro savybėmis yra diskrečiųjų elementų metodas (DEM). DEM metodas remiasi idėja, kad bet kokia fizikinė struktūra gali būti aprašyta kaip judančių dalelių sistema. Ši idėja pradėta taikyti ir vientisam deformuojamam kūnui aprašyti. Skirtingai nuo biriųjų medžiagų, vientiso kūno dalelės ir tarp jų egzistuojančios sąveikos yra kitokios prigimties, o jų modeliai yra fizikinės ir matematinės abstrakcijos rezultatas. Vientiso deformuojamo kūno modeliavimas diskrečiais elementais yra tik pradinėje stadijoje, o vientiso požiūrio į diskrečių elementų modelius dar nėra. Yra kelios hipotetinės versijos, grindžiamos skirtingais požiūriais. Taikant DEM kūnui, pirmas žingsnis būtu tampriųjų savybių modeliavimas. Tai yra... [toliau žr. visą tekstą] / Development of numerical methods and computation environments opened the possibility of new, more sophisticated mechanical objects modelling. In this context it is natural desire of the researchers to describe macroscopic mechanical characteristics of the materials by their microstructure, which can be adapted for simulation of the existing and future materials. For this purpose researchers are using intensively experimental and numerical methods for the development of which the highest priority is given. Numerical experiments are used because they are cheaper and allow the interpretation of already known results of experiments and provide information to new investigations. One of the methods used for modelling of macroscopic properties modelling is based on microscopic properties of material is discrete element method (DEM). The DEM traditionally was applied for the granular materials. The basic idea of DEM is that any physical structure could be described as a system of moving particles. This idea could be also applied to the description of solid deformable body. Particles forming solid body and existing interaction between them are of different nature than the granular materials because their models are often the result of physical and mathematical abstraction. The modelling of solid deformable body with the discrete elements is just at the initial stage and the unified approach to discrete elements models doesn’t exist. There are several versions of models, based... [to full text]

Development of numerical methods and computation environments opened the possibility of new, more sophisticated mechanical objects modelling. In this context it is natural desire of the researchers to describe macroscopic mechanical characteristics of the materials by their microstructure, which can be adapted for simulation of the existing and future materials. For this purpose researchers are using intensively experimental and numerical methods for the development of which the highest priority is given. Numerical experiments are used because they are cheaper and allow the interpretation of already known results of experiments and provide information to new investigations. One of the methods used for modelling of macroscopic properties modelling is based on microscopic properties of material is discrete element method (DEM). The DEM traditionally was applied for the granular materials. The basic idea of DEM is that any physical structure could be described as a system of moving particles. This idea could be also applied to the description of solid deformable body. Particles forming solid body and existing interaction between them are of different nature than the granular materials because their models are often the result of physical and mathematical abstraction. The modelling of solid deformable body with the discrete elements is just at the initial stage and the unified approach to discrete elements models doesn’t exist. There are several versions of models, based on... [to full text] / Tobulėjant skaitiniams metodams ir kompiuterinei technikai atsivėrė galimybė naujų, sudėtingesnių mechaninių objektų modeliavimui. Turėdami naujus sudėtingesnių objektų modelius tyrėjai gali pritaikyti aprašytas ir sumodeliuotas šių objektų savybes su mikro struktūros ypatumais esamų ar busimų savybių nustatymui bei naujų medžiagų kūrimui. Tam intensyviai naudojami kaip eksperimentiniai taip ir skaitiniai metodai, kurių tobulinimui šiuo metu yra skiriamas labai didelis dėmesys. Skaitinis eksperimentas, kaip medžiagos tyrimo būdas pasitelkiamas dar ir todėl kad yra pigesnis ir leidžia interpretuoti jau žinomus eksperimentų rezultatus, o taip suteikia žinių naujiems tyrimams. Vienas iš metodų, kuris modeliuoja makroskopines medžiagų savybes remdamasis medžiagos mikro savybėmis yra diskrečiųjų elementų metodas (DEM). DEM metodas remiasi idėja, kad bet kokia fizikinė struktūra gali būti aprašyta kaip judančių dalelių sistema. Ši idėja pradėta taikyti ir vientisam deformuojamam kūnui aprašyti. Skirtingai nuo biriųjų medžiagų, vientiso kūno dalelės ir tarp jų egzistuojančios sąveikos yra kitokios prigimties, o jų modeliai yra fizikinės ir matematinės abstrakcijos rezultatas. Vientiso deformuojamo kūno modeliavimas diskrečiais elementais yra tik pradinėje stadijoje, o vientiso požiūrio į diskrečių elementų modelius dar nėra. Yra kelios hipotetinės versijos, grindžiamos skirtingais požiūriais. Taikant DEM kūnui, pirmas žingsnis būtu tampriųjų savybių modeliavimas. Tai yra... [toliau žr. visą tekstą]

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The present study investigated the effect of dilute polymer solutions on the size, shape, and roughness of channels and holes, machined in metal and glass using a novel abrasive slurry-jet micro-machining (ASJM) apparatus. The apparatus consisted of a slurry pump and a pulsation damper connected to an open reservoir tank to generate a 140-micron turbulent jet containing 1 wt% 10-micron alumina particles. With the addition of 50 wppm of 8-M (million) molecular weight polyethylene oxide (PEO), the widths of the channels and diameters of holes machined in glass decreased by an average amount of 25%. These changes were accompanied by approximately a 20% decrease in depth and more V-shaped profiles compared with the U-shape of the reference channels and holes machined without additives. The present results demonstrate that a small amount of a high-molecular-weight polymer can significantly decrease the size of machined channels and holes for a given jet diameter.

The present study investigated the effect of dilute polymer solutions on the size, shape, and roughness of channels and holes, machined in metal and glass using a novel abrasive slurry-jet micro-machining (ASJM) apparatus. The apparatus consisted of a slurry pump and a pulsation damper connected to an open reservoir tank to generate a 140-micron turbulent jet containing 1 wt% 10-micron alumina particles. With the addition of 50 wppm of 8-M (million) molecular weight polyethylene oxide (PEO), the widths of the channels and diameters of holes machined in glass decreased by an average amount of 25%. These changes were accompanied by approximately a 20% decrease in depth and more V-shaped profiles compared with the U-shape of the reference channels and holes machined without additives. The present results demonstrate that a small amount of a high-molecular-weight polymer can significantly decrease the size of machined channels and holes for a given jet diameter.

Mielių (Saccharomyces cerevisiae) taikymas biologiniuose jutikliuose ar biokatalizėje ribojamas jų ląstelės sienelės struktūros, kuri apsunkina reikiamų medžiagų transportą. Todėl darbo tikslas – ištirti mielių ląstelių mechaninių savybių ir plazminės membranos bei sienelės pralaidumo pakitimus, veikiant mielių ląsteles cheminėmis medžiagomis bei mikro- ir nanosekundžių trukmės didelės galios impulsais naudojant atominių jėgų mikroskopą bei tetrafenilfosfonio katijonų elektrocheminę analizę. Nustatyta, kad ditiotreitolis (DTT) keisdamas mielių sienelių pralaidumą, pakeičia mielių ląstelių mechanines savybes. Esant didelėms deformacijoms mielių ląstelių tamprumo modulis (Young‘o) padidėjo nuo 1,00 ± 0,04 MPa nepaveiktoms iki 2,14 ± 0,1 MPa DTT paveiktoms mielėms. Tiriant impulsinio elektrinio lauko (IEL) poveikį mielių sienelės pralaidumui, impulso trukmių nuo mikrosekundžių iki nanosekundžių diapazone stebima tiesinė TPP+ absorbcijos greičio priklausomybė nuo impulso energijos. Nustatyta, kad veikiat mieles 60 ns trukmės impulsais ląstelių pralaidumas TPP+ molekulėms, nepažeidžiant mielų gyvybingumo, padidėjo iki 65 kartų lyginant su nepaveiktomis elektriniu lauku mielių ląstelėmis, t.y. 3,5 karto daugiau negu mieles paveikus 150 μs impulsais. Tyrimų rezultatai rodo, kad IEL galima didinti visos ląstelės biologinių jutiklių spartą ir atrankumą. / The application of yeast (Saccharomyces cerevisiae) in the biosensors or in the biocatalysis is limited due to the structure of their cell walls, which complicates the transport of necessary materials. The aim of this work was to investigate the mechanical properties of the yeast cells and the changes of permeability of cell plasma membrane and cell wall, after the impact of chemical compounds on the cell wall permeability and after their exposure of pulsed electric field (PEF) in the range from microsecond till nanosecond pulse duration. For analysis the atomic force microscopy and the electrochemical detection of tetraphenylphosphonium ions were used. Dithiothreitol (DTT) modifies the yeast cell wall permeability changing the mechanical properties of the cells and for high indentations Young modulus increasing from 1.00 ± 0.04 MPa for intact cells to 2.14 ± 0.1 MPa for DTT treated ones. The linear relation between TPP+ absorption rate and pulse energy was determined after investigations of PEF effect to the yeast cell permeability in the range of pulse duration from microseconds to nanoseconds. The obtained 65 time increase of yeast cell wall permeability to TPP+ molecules after the exposure of 60 ns PEF, which does not affect the cell viability, comparing with the intact yeast cells. Such permeability increment was 3.5 times higher in comparison to the yeast cells exposure to 150 µs duration PEF. The finding can be useful for the enhancement of selectivity and response of... [to full text]

The application of yeast (Saccharomyces cerevisiae) in the biosensors or in the biocatalysis is limited due to the structure of their cell walls, which complicates the transport of necessary materials. The aim of this work was to investigate the mechanical properties of the yeast cells and the changes of permeability of cell plasma membrane and cell wall, after the impact of chemical compounds on the cell wall permeability and after their exposure of pulsed electric field (PEF) in the range from microsecond till nanosecond pulse duration. For analysis the atomic force microscopy and the electrochemical detection of tetraphenylphosphonium ions were used. Dithiothreitol (DTT) modifies the yeast cell wall permeability changing the mechanical properties of the cells and for high indentations Young modulus increasing from 1.00 ± 0.04 MPa for intact cells to 2.14 ± 0.1 MPa for DTT treated ones. The linear relation between TPP+ absorption rate and pulse energy was determined after investigations of PEF effect to the yeast cell permeability in the range of pulse duration from microseconds to nanoseconds. The obtained 65 time increase of yeast cell wall permeability to TPP+ molecules after the exposure of 60 ns PEF, which does not affect the cell viability, comparing with the intact yeast cells. Such permeability increment was 3.5 times higher in comparison to the yeast cells exposure to 150 µs duration PEF. The finding can be useful for the enhancement of selectivity and response of... [to full text] / Mielių (Saccharomyces cerevisiae) taikymas biologiniuose jutikliuose ar biokatalizėje ribojamas jų ląstelės sienelės struktūros, kuri apsunkina reikiamų medžiagų transportą. Todėl darbo tikslas – ištirti mielių ląstelių mechaninių savybių ir plazminės membranos bei sienelės pralaidumo pakitimus, veikiant mielių ląsteles cheminėmis medžiagomis bei mikro- ir nanosekundžių trukmės didelės galios impulsais naudojant atominių jėgų mikroskopą bei tetrafenilfosfonio katijonų elektrocheminę analizę. Nustatyta, kad ditiotreitolis (DTT) keisdamas mielių sienelių pralaidumą, pakeičia mielių ląstelių mechanines savybes. Esant didelėms deformacijoms mielių ląstelių tamprumo modulis (Young‘o) padidėjo nuo 1,00 ± 0,04 MPa nepaveiktoms iki 2,14 ± 0,1 MPa DTT paveiktoms mielėms. Tiriant impulsinio elektrinio lauko (IEL) poveikį mielių sienelės pralaidumui, impulso trukmių nuo mikrosekundžių iki nanosekundžių diapazone stebima tiesinė TPP+ absorbcijos greičio priklausomybė nuo impulso energijos. Nustatyta, kad veikiat mieles 60 ns trukmės impulsais ląstelių pralaidumas TPP+ molekulėms, nepažeidžiant mielų gyvybingumo, padidėjo iki 65 kartų lyginant su nepaveiktomis elektriniu lauku mielių ląstelėmis, t.y. 3,5 karto daugiau negu mieles paveikus 150 μs impulsais. Tyrimų rezultatai rodo, kad IEL galima didinti visos ląstelės biologinių jutiklių spartą ir atrankumą.