Polymer stress growth in viscoelastic fluids in oscillating extensional flows with applications to micro-organism locomotion

Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) case, and similar stress behavior is observed. The flow around tips of a time-reversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories, and the stress response exhibits similar transitions. However in the high amplitude, high De regime the stress feedback on the flow leads to non time-reversible particle trajectories that experience asymmetric stretching and compression, and the stress grows more significantly in this regime. These results help explain past observations of large stress concentration for large amplitude swimmers and non-monotonic dependence on De of swimming speeds

Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids

Elastic stress concentration at tips of long slender objects moving in viscoelastic fluids has been observed in numerical simulations, but despite the prevalence of flagellated motion in complex fluids in many biological functions, the physics of stress accumulation near tips has not been analyzed. Here we theoretically investigate elastic stress development at tips of slender objects by computing the leading order viscoelastic correction to the equilibrium viscous flow around long cylinders, using the weak-coupling limit. In this limit nonlinearities in the fluid are retained allowing us to study the biologically relevant parameter regime of high Weissenberg number. We calculate a stretch rate from the viscous flow around cylinders to predict when large elastic stress develops at tips, find thresholds for large stress development depending on orientation, and calculate greater stress accumulation near tips of cylinders oriented parallel to motion over perpendicular.Comment: Supplementary information include

Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems

South American Coccinellidae (Coleoptera) : part 15, systematic revision of Dilatitibialis Duverger (Coccidulinae; Hyperaspidini)

Dilatitibialis Duverger (61 species) (Coleoptera: Coccinelidae: Coccidulinae; Hyperaspidini) is discussed, species described, illustrations provided, and a key to all recognized taxa included. Cleothera cognata Mulsant, Cleothera cruciferae Mulsant, Cleothera fuscomaculata Mulsant, Cleothera gaynoni Mulsant, Cleothera glyphica Mulsant, Cleothera jucunda Mulsant, Cleothera luteola Mulsant, Cleothera mulsanti Kirsch, Cleothera oseryi Mulsant, Cleothera poortmanni Mulsant, Cleothera scenica Mulsant, Cleothera semicincta Weise, Cleothera tropicalis Mulsant, Hinda guttipennis Weise, Hyperaspis carolinae Crotch, Hyperaspis ceciliae Crotch, Hyperaspis dilatata Crotch, Hyperaspis florifera Vogel, Hyperaspis gravabilis Brèthes, Hyperaspis hybridula Crotch, Hyperaspis laterinotata Brèthes, Hyperaspis silvani Crotch, and Hyperaspis suzannae Crotch are transferred to Dilatitibialis, becoming new combinations. Lectotypes are designated for D. boliviana, D. cognata, D. florifera, D. fuscomaculata, D. gaynoni, D. glyphica, D. gravabilis, D. guttipennis, D. luteola, D. jucunda, D. mulsanti. D. poortmanni, D. retigera, D. scenica, D. semicincta, and D. staudingeri. A total of 38 new species of Dilatitibialis are described: Dilatitibialis annie, D. carmen, D. cindy, D. connie, D. crystal, D. dawn, D. diana, D. edith, D. edna, D. elaine, D. ellen, D. emily, D. ethel, D. fallax, D. florence, D. gladys, D. grace, D. josephine, D. kim, D. lillian, D. lois, D. marjorie, D. norma, D. paula, D. peggy, D. phyllis, D. rita, D. robin, D. rosa, D. shannon, D. sheila, D. sherry, D. sylvia, D. thelma, D. tiffany, D. tina, D. tracy, and D. wendy. Corrections are made to titles of previous Parts of this series, as follows: South American Coccinellidae, Part XII (Gordon 2007) is changed to Part XIII; South American Coccinellidae, Part XII (Gordon et al. 2013) is changed to Part XIV

South American Coccinellidae (Coleoptera) : part 7, new name for Cyra Mulsant, review of Brachiacanthini genera, and systematic revision of Cleothera Mulsant, Hinda Mulsant and Serratitibia Gordon and Canepari, new genus

Genera of Brachiacanthini (Coleoptera: Coccinellidae: Hyperaspidinae) are discussed and a key to all recognized genera provided. Cyrea, new genus, is proposed, and Serratitibia, new genus, is erected and revised, Cleothera Mulsant and Hinda Mulsant are recognized as valid genera and revised. Helesius caseyi Sicard is transferred to Hinda and recognized as a synonym of Hinda designata Mulsant, new synonymy. Brachiacantha brethesi (Korschefsky), Cleothera abendrothi Kirsch, Cleothera ambigua Mulsant, Cleothera bisquatuorpustulata Mulsant, Cleothera decemsignata Mulsant, Cleothera gaillardi Mulsant, Cleothera humerata Mulsant, Cleothera tortuosa Mulsant, Cleothera traili Brèthes, Cleothera uncinata Mulsant, Hinda joeli Almeida and Milléo, Hinda modesta Weise, Hinda regularis Kirsch, Hyperaspis aliciae Crotch, and Hyperaspis fraudulenta Kirsch are transferred to Serratitibia, becoming new combinations. One new species of Hinda, H. ecuadorica, is described. A total of 73 new species of Serratitibia are described: Serratitibia amanda, S. andrea, S. angela, S. anna, S. ashley, S. barbara, S. barclayi, S. betty, S. beverly, S. bonnie, S. brenda, S. cheryl, S. christine, S. cynthia, S. debra, S. denise, S. donna, S. doris, S. elizabeth, S. evelyn, S. frances, S. gloria, S. heather, S. helen, S. irene, S. jacqueline, S. janet, S. janice, S. jean, S. jennifer, S. joan, S. joyce, S. judith, S. judy, S. julie, S. karen, S. katherine, S. kathleen, S. kathy, S. kelly, S. kimberly, S. laura, S. linda, S. lisa, S. loreto, S. lori, S. louise, S. margaret, S. marilyn, S. mary, S. martha, S. melissa, S. michelle, S. mildred, S. nancy, S. nicole, S. pamela, S. paprzycki, S. patricia, S. quincemil, S. rachel, S. rebecca, S. rose, S. ruby, S. ruth, S. sarah, S. satipoensis, S. shirley, S. stephanie, S. susan, S. tammy, S. teresa, and S. virginia. Lectotypes are here designated for Serratitibia lividipes, S. gaillardi, S. decemsignata, S. abendrothi, and S. ambigua

Immersed Boundary Double Layer Method

The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB framework yields a robust numerical scheme that can efficiently handle immersed deformable structures. Additionally, the IB method has been adapted to problems with prescribed motion and other PDEs with given boundary data. IB methods for these problems traditionally involve penalty forces which only approximately satisfy boundary conditions, or they are formulated as constraint problems. In the latter approach, one must find the unknown forces by solving an equation that corresponds to a poorly conditioned first-kind integral equation. This operation can require a large number of iterations of a Krylov method, and since a time-dependent problem requires this solve at each time step, this method can be prohibitively inefficient without preconditioning. In this work, we introduce a new, well-conditioned IB formulation for boundary value problems, which we call the Immersed Boundary Double Layer (IBDL) method. We present the method as it applies to Poisson and Helmholtz problems to demonstrate its efficiency over the original constraint method. In this double layer formulation, the equation for the unknown boundary distribution corresponds to a well-conditioned second-kind integral equation that can be solved efficiently with a small number of iterations of a Krylov method. Furthermore, the iteration count is independent of both the mesh size and immersed boundary point spacing. The method converges away from the boundary, and when combined with a local interpolation, it converges in the entire PDE domain. Additionally, while the original constraint method applies only to Dirichlet problems, the IBDL formulation can also be used for Neumann conditions

South American Coccinellidae (Coleoptera), Part XVII: systematic revision of Western Hemisphere Cephaloscymnini (Coccinellinae) with description of a cryptic new genus and species of Coccidulini (Coccinellinae)

Genera of Cephaloscymnini (Coleoptera: Coccinellidae: Coccidulinae) are discussed and a key to all recognized genera and species is provided. Succinctonotum, new genus, is proposed. Scymnus laboulbenii Mulsant and Prodilis maculata Weise are transferred to Neaporia as new combinations. Prodiloides bipunctata Weise, and Neaporia compta are transferred to Prodilis as new combinations. Neaporia cuprea Gorham is considered a junior synonym of Neaporia viridiscens Gorham and Cephaloscymnus bruchi Weise a junior synonym of Prodilis volgus Mulsant. New species described in Cephaloscymnus are C. beulah, C. candice, C. juanita. New species described in Neaporia are N. becky, N. bobbie, N. brandy, N. carole, N. cassandra, N. christy, N. daisy, N. deanna, N. dianne, N. felicia, N. gwendolyn, N. hilda, N. irma, N. jennie, N. jenny, N. kay, N. kayla, N. kristine, N. leah, N. lena, N. leona, N. longifrons, N. mabel, N. mae, N. margie, N. marsha, N. miriam, N. misty, N. myrtle, N. naomi, N. nina, N. nora, N. olga, N. opal, N. patsy, N. penny, N. priscilla, N. shelley, N. sonia, N. tracey, and N. violet. New species described in Succinctonotum is S. frosti. New species described in Prodilis are P. ada, P. alberta, P. alison, P. amelia, P. angie, P. araguaensis, P. bartletti, P. belinda, P. blanche, P. brandi, P. cecilia, P. claire, P. cora, P. dubitalis, P. erika, P. eunice, P. fannie, P. faye, P. flora, P. geneva, P. guadalupe, P. harriet, P. hattie, P. inez, P. iris, P. isabel, P. jan, P. janie, P. joanna, P. jodi, P. katrina, P. kristi, P. kristy, P. lindsey, P. lola, P. lula, P. lynda, P. madeline, P. maggie, P. mamie, P. margarita, P. maryann, P. melody, P. molly, P. monique, P. natasha, P. olivia, P. pecki, P. ramona, P. rosie, P. sabrina, P. sandy, P. shelley, P. sherri, P. sheryl, P. sonya, P. susie, and P. yvette. Ponaria, new genus of Coccidulini is proposed. Neaporia caerulea Gorham is transferred to Ponaria as a new combination. New species described in Ponaria are P. daviesi, P. hurtadoi, and P. paprzyckii. Lectotypes are here designated for Neaporia arrowi, N. coelestis, N. metallica, N. guatemalana, N. indagator, and Prodilis pallidifrons

South American Coccinellidae (Coleoptera), Part XVII: systematic revision of Western Hemisphere Cephaloscymnini (Coccinellinae) with description of a cryptic new genus and species of Coccidulini (Coccinellinae)

Genera of Cephaloscymnini (Coleoptera: Coccinellidae: Coccidulinae) are discussed and a key to all recognized genera and species is provided. Succinctonotum, new genus, is proposed. Scymnus laboulbenii Mulsant and Prodilis maculata Weise are transferred to Neaporia as new combinations. Prodiloides bipunctata Weise, and Neaporia compta are transferred to Prodilis as new combinations. Neaporia cuprea Gorham is considered a junior synonym of Neaporia viridiscens Gorham and Cephaloscymnus bruchi Weise a junior synonym of Prodilis volgus Mulsant. New species described in Cephaloscymnus are C. beulah, C. candice, C. juanita. New species described in Neaporia are N. becky, N. bobbie, N. brandy, N. carole, N. cassandra, N. christy, N. daisy, N. deanna, N. dianne, N. felicia, N. gwendolyn, N. hilda, N. irma, N. jennie, N. jenny, N. kay, N. kayla, N. kristine, N. leah, N. lena, N. leona, N. longifrons, N. mabel, N. mae, N. margie, N. marsha, N. miriam, N. misty, N. myrtle, N. naomi, N. nina, N. nora, N. olga, N. opal, N. patsy, N. penny, N. priscilla, N. shelley, N. sonia, N. tracey, and N. violet. New species described in Succinctonotum is S. frosti. New species described in Prodilis are P. ada, P. alberta, P. alison, P. amelia, P. angie, P. araguaensis, P. bartletti, P. belinda, P. blanche, P. brandi, P. cecilia, P. claire, P. cora, P. dubitalis, P. erika, P. eunice, P. fannie, P. faye, P. flora, P. geneva, P. guadalupe, P. harriet, P. hattie, P. inez, P. iris, P. isabel, P. jan, P. janie, P. joanna, P. jodi, P. katrina, P. kristi, P. kristy, P. lindsey, P. lola, P. lula, P. lynda, P. madeline, P. maggie, P. mamie, P. margarita, P. maryann, P. melody, P. molly, P. monique, P. natasha, P. olivia, P. pecki, P. ramona, P. rosie, P. sabrina, P. sandy, P. shelley, P. sherri, P. sheryl, P. sonya, P. susie, and P. yvette. Ponaria, new genus of Coccidulini is proposed. Neaporia caerulea Gorham is transferred to Ponaria as a new combination. New species described in Ponaria are P. daviesi, P. hurtadoi, and P. paprzyckii. Lectotypes are here designated for Neaporia arrowi, N. coelestis, N. metallica, N. guatemalana, N. indagator, and Prodilis pallidifrons