International Journal of Non-Linear Mechanics, 2013
ABSTRACT The problem of hydrodynamic instability of a very thin UCM liquid film flowing down on t... more ABSTRACT The problem of hydrodynamic instability of a very thin UCM liquid film flowing down on the outer surface of an inclined plane is investigated. In order to improve the accuracy of numerical results, the viscoelastic parameters and van der Waals forces have been included into the governing equations. Also, the analytical solutions are obtained by utilizing the long-wave perturbation method. The influence of some physical parameters is discussed in both linear and non-linear steps of the problem. It has been revealed that the instability of the film flow is weakened when Reynolds number, viscoelastic property and attractive van der Waals force are reduced. Further, the thin film flow can be stabilized by short-range Born repulsion. The results show that both supercritical stability and subcritical instability may take place within the film flow system. Moreover, the presence of non-linear terms leads to an obvious difference in the behavior of some physical parameters.
The problem of nonlinear instability of interfacial waves between two immiscible conducting cylin... more The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.
To assess the efficacy and stability of simultaneous topography-guided photorefractive keratectom... more To assess the efficacy and stability of simultaneous topography-guided photorefractive keratectomy (PRK) and crosslinking (Athens protocol) followed by phakic intraocular lens (IOL) implantation for managing keratoconus. Ain-Shams University, Cairo, Egypt. Prospective non-randomized study. All patients underwent topography-guided PRK followed immediately by collagen crosslinking (Athens protocol), 2-4 months later, eyes were implanted with either an iris claw or an angle-supported phakic IOL. Statistical analysis was performed with SigmaPlot software version 11.0 (Systat Software, Inc.). This study evaluated 22 eyes of 14 patients. Follow-up interval was at least 6 months. A Veriflex phakic IOL was implanted in 14 eyes (63.6 %), and a Cachet phakic IOL was implanted in 8 eyes (36.4 %). The mean preoperative keratometric reading (45.57 ± 1.51 D) was significantly reduced at 3 months and at 6 months after treatment (43.82 ± 1.98 D, P < 0.001). The mean spherical equivalent was significantly reduced from -9.08 ± 2.5 to -0.69 ± 0.67 D, P = <0.001. The mean UCVA improved from 1.24 ± 0.49 to 0.37 ± 0.08 logMAR. The mean corrected distance visual acuity (CDVA; logMAR) improved from 0.69 ± 0.3 preoperatively to 0.35 ± 0.01 postoperatively (P = <0.001). At last follow-up, all eyes could achieve CDVA of 0.3 or better. The difference between pre- and postoperative endothelial cell counts was not statistically significant. Combining phakic IOLs and the Athens protocol improved and stabilized visual performance in patients with keratoconus. These results justify a future, large-scale study with a longer follow-up.
Fifty-two children with infantile esotropia had surgery for their esotropia between two and seven... more Fifty-two children with infantile esotropia had surgery for their esotropia between two and seven years of age. Another 49 had similar surgery before the age of two years. Of these 101 operated children, the esotropia in 70 patients was aligned to within 10 prism diopters. The patients with successful alignment were reviewed to study the effect of early versus late surgical intervention of their deviation, i.e. before and after two years of age. The motor and sensory states of the selected patients were analysed before and after surgical correction. The choice and number of surgical procedures employed are discussed. It appears that patients two years and older when strabismus was surgically corrected have a good chance of alignment, but less chance of attaining binocularity. In many cases there was a V-pat-tern esotropia, requiring surgery on the overacting inferior oblique muscles. In comparison, the younger group with earlier surgery appeared to show a better chance of attaining binocularity and fewer patients had significant V-pattern requiring surgery on the inferior oblique muscles.
We report an unusual case of self-mutilation by insertion of multiple foreign bodies in the orbit... more We report an unusual case of self-mutilation by insertion of multiple foreign bodies in the orbit. A 26-year-old female psychiatric patient with a severe emotionally unstable personality disorder was reviewed in the ophthalmology clinic. She had allegedly inserted a metal staple into her right eye 2 days previously and was complaining of pain around the right eye. Radiography showed multiple foreign bodies in the right orbit and one in the left orbit. Self-mutilation in psychiatric patients has been well documented. The management of nonorganic, nontoxic intraorbital foreign bodies is discussed. A low threshold for imaging in these cases is of vital importance.
Glucose-6-phosphate dehydrogenase (G-6-PD) deficiency plays an important biochemical role in the ... more Glucose-6-phosphate dehydrogenase (G-6-PD) deficiency plays an important biochemical role in the metabolism of the lens. Controversies exist in the literature on the possible association between G-6-PD deficiency and the development of cataracts. The authors present ten patients, aged between infancy and 40 years of age, who were admitted for bilateral congenital or presenile cataracts. These patients had no ocular or systemic disease which might have caused their cataract. The only systemic finding they had was G-6-PD deficiency. Two other patients among the families described suffered from bilateral congenital or presenile cataracts with no G-6-PD deficiency. This deficiency state does not appear to play a role in the production of their cataracts.
Journal of Pediatric Ophthalmology & Strabismus, 2010
The authors report a case of symptomatic antipodean strabismus caused by a combination of mechani... more The authors report a case of symptomatic antipodean strabismus caused by a combination of mechanical restriction of eye movement secondary to thyroid eye disease, longstanding intermittent divergence, and convergence weakness, which was alleviated by simultaneous resection of all four horizontal recti muscles.
To study spherical aberration, coma, and trefoil after implantation of a single-piece aspheric Te... more To study spherical aberration, coma, and trefoil after implantation of a single-piece aspheric Tecnis intraocular lens (IOL) in cataract patients and the influence on photopic and mesopic contrast sensitivity. Ophthalmology Department, Ain-Shams University Hospitals, Cairo, Egypt. In this randomized prospective contralateral comparative study, patients had bilateral senile cataract. Eyes with a pathological condition other than cataract that might influence postoperative visual function were excluded. The aspheric IOL was compared with the Sensar AR40e spherical IOL. The IOL selection was randomized. Study criteria included corrected distance visual acuity (CDVA), wavefront aberrometry, and contrast visual acuity. Fifty-six eyes of 28 patients were enrolled. All patients completed the 2-month postoperative visit. There was no significant difference between the IOLs in CDVA (P>.05). Ocular spherical aberration was significantly lower with aspheric IOLs than spherical IOLs (P<.001). Two months after surgery, eyes with the aspheric IOL had better photopic contrast sensitivity and better mesopic contrast sensitivity at all cycles per degree. There was no significant difference in 3rd-order aberrations (coma and trefoil) between IOLs. After cataract surgery, the single-piece aspheric IOL resulted in significantly lower ocular spherical aberration and significantly better mesopic contrast sensitivity. No significant difference in 3rd-order aberrations indicates that both IOLs had satisfactory centration in the capsular bag.
A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element sub... more A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element subsets, called blocks of a set V such that every 2-subset of V occurs in at most 1 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve the packing problem with K = 5, 1=8, 12, 16, and all positive integers o with the possible exceptions of (u, A)=
Let V be a finite set of order m × n, and assume that the points of V are arranged in an array of... more Let V be a finite set of order m × n, and assume that the points of V are arranged in an array of size m x n. A modified group divisible design is a group divisible design with the difference that each 2-subset {x, y} of V such that x and y are neither in the same row nor in the same column occurs A times. In this paper we apply modified group divisible designs to construct covering designs, packing designs, and group divisible designs with block size 5.
An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element s... more An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element subsets, called blocks, of a set V such that every 2-subsets of V occurs in at most 2 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we provide a powerful technique for constructing designs and solve the packing problem in the case tc = 5, 2 = 2, and v is even.
This article looks at (5, k) GDDs and (v, 5, k) pair packing and pair covering designs. For packi... more This article looks at (5, k) GDDs and (v, 5, k) pair packing and pair covering designs. For packing designs, we solve the (4t, 5, 3) class with two possible exceptions, solve 16 open cases with k odd, and improve the maximum number of blocks in some (v, 5, k) packings when v small (here, the Schönheim bound is not always attainable). When k = 1, we construct v = 432 and improve the spectrum for v ≡ 14, 18 (mod 20). We also extend one of Hanani's conditions under which the Schönheim bound cannot be achieved (this extension affects (20t+9, 5, 1), (20t+17, 5, 1) and (20t+13, 5, 3)) packings. For covering designs we find the covering numbers C(280, 5, 1), C(44, 5, 17) and C(44, 5, k) with k ≡ 13 (mod 20). We also know that the covering number, C(v, 5, 2), exceeds the Schönheim bound by 1 for v = 9, 13 and 15. For GDDs of type g n , we have one new design of type 30 9 when k = 1, and three new designs for k = 2, namely, types g 15 with g ∈{13, 17, 19}. If k is even and a (5, k) GDD of type g u is known, then we also have a directable (5, k) GDD of type g u . q NEW RESULTS ON GDDS, COVERING, PACKING AND DIRECTABLE DESIGNS 339 2. AUXILIARY DESIGNS Some of the terminology we will use is quite standard in design theory; see . For clarification of our notation (specifically how we indicate the standard parameters), we refer to pairwise balanced designs (PBDs), (including BIBDs), as (v, K , ) designs, where K is a list of block sizes that possibly occur. A group divisible design is referred to as a (K , ) GDD of group type g t 1 1 , . . . , g t n n if there are t i groups of size g i and transversal designs of order n as TD (k, n), dropping the subscript when = 1; note that a TD (k, n) is a (k, ) GDD of group type n k . The prefix "R" will denote a resolvable design.
A (v, K , A) covering design of order v, block size K , and index A is a collection of K-element ... more A (v, K , A) covering design of order v, block size K , and index A is a collection of K-element subsets, called blocks, of a set V such that every 2-subset of V occurs in at least A blocks. The covering problem is to determine the minimum number of blocks, a ( v , K , A), in a covering design. It is well known that cr (v, K , A) 2 r f [ 2 A] 1 = 4(v, K , A), where 1x1 is the smallest integer satisfying , y 5 [XI. It is shown here that a (v, 5, A) = 4 ( v , 5, A) + e where A= 0 (mod 4) and e= 1 if A (v-l)= 0 (mod 4) and Av (v-1)/4 = -1 (mod 5) and e= 0 otherwise with the possible exception of (v,A) = (28,4). 0 1993 John Wiley & Sons, Inc.
A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are ... more A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function
International Journal of Non-Linear Mechanics, 2013
ABSTRACT The problem of hydrodynamic instability of a very thin UCM liquid film flowing down on t... more ABSTRACT The problem of hydrodynamic instability of a very thin UCM liquid film flowing down on the outer surface of an inclined plane is investigated. In order to improve the accuracy of numerical results, the viscoelastic parameters and van der Waals forces have been included into the governing equations. Also, the analytical solutions are obtained by utilizing the long-wave perturbation method. The influence of some physical parameters is discussed in both linear and non-linear steps of the problem. It has been revealed that the instability of the film flow is weakened when Reynolds number, viscoelastic property and attractive van der Waals force are reduced. Further, the thin film flow can be stabilized by short-range Born repulsion. The results show that both supercritical stability and subcritical instability may take place within the film flow system. Moreover, the presence of non-linear terms leads to an obvious difference in the behavior of some physical parameters.
The problem of nonlinear instability of interfacial waves between two immiscible conducting cylin... more The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.
To assess the efficacy and stability of simultaneous topography-guided photorefractive keratectom... more To assess the efficacy and stability of simultaneous topography-guided photorefractive keratectomy (PRK) and crosslinking (Athens protocol) followed by phakic intraocular lens (IOL) implantation for managing keratoconus. Ain-Shams University, Cairo, Egypt. Prospective non-randomized study. All patients underwent topography-guided PRK followed immediately by collagen crosslinking (Athens protocol), 2-4 months later, eyes were implanted with either an iris claw or an angle-supported phakic IOL. Statistical analysis was performed with SigmaPlot software version 11.0 (Systat Software, Inc.). This study evaluated 22 eyes of 14 patients. Follow-up interval was at least 6 months. A Veriflex phakic IOL was implanted in 14 eyes (63.6 %), and a Cachet phakic IOL was implanted in 8 eyes (36.4 %). The mean preoperative keratometric reading (45.57 ± 1.51 D) was significantly reduced at 3 months and at 6 months after treatment (43.82 ± 1.98 D, P < 0.001). The mean spherical equivalent was significantly reduced from -9.08 ± 2.5 to -0.69 ± 0.67 D, P = <0.001. The mean UCVA improved from 1.24 ± 0.49 to 0.37 ± 0.08 logMAR. The mean corrected distance visual acuity (CDVA; logMAR) improved from 0.69 ± 0.3 preoperatively to 0.35 ± 0.01 postoperatively (P = <0.001). At last follow-up, all eyes could achieve CDVA of 0.3 or better. The difference between pre- and postoperative endothelial cell counts was not statistically significant. Combining phakic IOLs and the Athens protocol improved and stabilized visual performance in patients with keratoconus. These results justify a future, large-scale study with a longer follow-up.
Fifty-two children with infantile esotropia had surgery for their esotropia between two and seven... more Fifty-two children with infantile esotropia had surgery for their esotropia between two and seven years of age. Another 49 had similar surgery before the age of two years. Of these 101 operated children, the esotropia in 70 patients was aligned to within 10 prism diopters. The patients with successful alignment were reviewed to study the effect of early versus late surgical intervention of their deviation, i.e. before and after two years of age. The motor and sensory states of the selected patients were analysed before and after surgical correction. The choice and number of surgical procedures employed are discussed. It appears that patients two years and older when strabismus was surgically corrected have a good chance of alignment, but less chance of attaining binocularity. In many cases there was a V-pat-tern esotropia, requiring surgery on the overacting inferior oblique muscles. In comparison, the younger group with earlier surgery appeared to show a better chance of attaining binocularity and fewer patients had significant V-pattern requiring surgery on the inferior oblique muscles.
We report an unusual case of self-mutilation by insertion of multiple foreign bodies in the orbit... more We report an unusual case of self-mutilation by insertion of multiple foreign bodies in the orbit. A 26-year-old female psychiatric patient with a severe emotionally unstable personality disorder was reviewed in the ophthalmology clinic. She had allegedly inserted a metal staple into her right eye 2 days previously and was complaining of pain around the right eye. Radiography showed multiple foreign bodies in the right orbit and one in the left orbit. Self-mutilation in psychiatric patients has been well documented. The management of nonorganic, nontoxic intraorbital foreign bodies is discussed. A low threshold for imaging in these cases is of vital importance.
Glucose-6-phosphate dehydrogenase (G-6-PD) deficiency plays an important biochemical role in the ... more Glucose-6-phosphate dehydrogenase (G-6-PD) deficiency plays an important biochemical role in the metabolism of the lens. Controversies exist in the literature on the possible association between G-6-PD deficiency and the development of cataracts. The authors present ten patients, aged between infancy and 40 years of age, who were admitted for bilateral congenital or presenile cataracts. These patients had no ocular or systemic disease which might have caused their cataract. The only systemic finding they had was G-6-PD deficiency. Two other patients among the families described suffered from bilateral congenital or presenile cataracts with no G-6-PD deficiency. This deficiency state does not appear to play a role in the production of their cataracts.
Journal of Pediatric Ophthalmology & Strabismus, 2010
The authors report a case of symptomatic antipodean strabismus caused by a combination of mechani... more The authors report a case of symptomatic antipodean strabismus caused by a combination of mechanical restriction of eye movement secondary to thyroid eye disease, longstanding intermittent divergence, and convergence weakness, which was alleviated by simultaneous resection of all four horizontal recti muscles.
To study spherical aberration, coma, and trefoil after implantation of a single-piece aspheric Te... more To study spherical aberration, coma, and trefoil after implantation of a single-piece aspheric Tecnis intraocular lens (IOL) in cataract patients and the influence on photopic and mesopic contrast sensitivity. Ophthalmology Department, Ain-Shams University Hospitals, Cairo, Egypt. In this randomized prospective contralateral comparative study, patients had bilateral senile cataract. Eyes with a pathological condition other than cataract that might influence postoperative visual function were excluded. The aspheric IOL was compared with the Sensar AR40e spherical IOL. The IOL selection was randomized. Study criteria included corrected distance visual acuity (CDVA), wavefront aberrometry, and contrast visual acuity. Fifty-six eyes of 28 patients were enrolled. All patients completed the 2-month postoperative visit. There was no significant difference between the IOLs in CDVA (P>.05). Ocular spherical aberration was significantly lower with aspheric IOLs than spherical IOLs (P<.001). Two months after surgery, eyes with the aspheric IOL had better photopic contrast sensitivity and better mesopic contrast sensitivity at all cycles per degree. There was no significant difference in 3rd-order aberrations (coma and trefoil) between IOLs. After cataract surgery, the single-piece aspheric IOL resulted in significantly lower ocular spherical aberration and significantly better mesopic contrast sensitivity. No significant difference in 3rd-order aberrations indicates that both IOLs had satisfactory centration in the capsular bag.
A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element sub... more A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element subsets, called blocks of a set V such that every 2-subset of V occurs in at most 1 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve the packing problem with K = 5, 1=8, 12, 16, and all positive integers o with the possible exceptions of (u, A)=
Let V be a finite set of order m × n, and assume that the points of V are arranged in an array of... more Let V be a finite set of order m × n, and assume that the points of V are arranged in an array of size m x n. A modified group divisible design is a group divisible design with the difference that each 2-subset {x, y} of V such that x and y are neither in the same row nor in the same column occurs A times. In this paper we apply modified group divisible designs to construct covering designs, packing designs, and group divisible designs with block size 5.
An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element s... more An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element subsets, called blocks, of a set V such that every 2-subsets of V occurs in at most 2 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we provide a powerful technique for constructing designs and solve the packing problem in the case tc = 5, 2 = 2, and v is even.
This article looks at (5, k) GDDs and (v, 5, k) pair packing and pair covering designs. For packi... more This article looks at (5, k) GDDs and (v, 5, k) pair packing and pair covering designs. For packing designs, we solve the (4t, 5, 3) class with two possible exceptions, solve 16 open cases with k odd, and improve the maximum number of blocks in some (v, 5, k) packings when v small (here, the Schönheim bound is not always attainable). When k = 1, we construct v = 432 and improve the spectrum for v ≡ 14, 18 (mod 20). We also extend one of Hanani's conditions under which the Schönheim bound cannot be achieved (this extension affects (20t+9, 5, 1), (20t+17, 5, 1) and (20t+13, 5, 3)) packings. For covering designs we find the covering numbers C(280, 5, 1), C(44, 5, 17) and C(44, 5, k) with k ≡ 13 (mod 20). We also know that the covering number, C(v, 5, 2), exceeds the Schönheim bound by 1 for v = 9, 13 and 15. For GDDs of type g n , we have one new design of type 30 9 when k = 1, and three new designs for k = 2, namely, types g 15 with g ∈{13, 17, 19}. If k is even and a (5, k) GDD of type g u is known, then we also have a directable (5, k) GDD of type g u . q NEW RESULTS ON GDDS, COVERING, PACKING AND DIRECTABLE DESIGNS 339 2. AUXILIARY DESIGNS Some of the terminology we will use is quite standard in design theory; see . For clarification of our notation (specifically how we indicate the standard parameters), we refer to pairwise balanced designs (PBDs), (including BIBDs), as (v, K , ) designs, where K is a list of block sizes that possibly occur. A group divisible design is referred to as a (K , ) GDD of group type g t 1 1 , . . . , g t n n if there are t i groups of size g i and transversal designs of order n as TD (k, n), dropping the subscript when = 1; note that a TD (k, n) is a (k, ) GDD of group type n k . The prefix "R" will denote a resolvable design.
A (v, K , A) covering design of order v, block size K , and index A is a collection of K-element ... more A (v, K , A) covering design of order v, block size K , and index A is a collection of K-element subsets, called blocks, of a set V such that every 2-subset of V occurs in at least A blocks. The covering problem is to determine the minimum number of blocks, a ( v , K , A), in a covering design. It is well known that cr (v, K , A) 2 r f [ 2 A] 1 = 4(v, K , A), where 1x1 is the smallest integer satisfying , y 5 [XI. It is shown here that a (v, 5, A) = 4 ( v , 5, A) + e where A= 0 (mod 4) and e= 1 if A (v-l)= 0 (mod 4) and Av (v-1)/4 = -1 (mod 5) and e= 0 otherwise with the possible exception of (v,A) = (28,4). 0 1993 John Wiley & Sons, Inc.
A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are ... more A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function
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Papers by Ahmed Assaf