MELBOURNE, Australia (AP) -- One of the things Sloane Stephens likes about winning at the Australian Open is that her tech-savvy grandparents can keep watching her from back home.
"My grandpa texted me,'' the 19-year-old Stephens said. "He said they stayed up again to watch me `on the machine' as my grandpa calls it.''
That's the computer.
Grandpa got to see Stephens advance Thursday to the third round, beating France's Kristina Mladenovic 6-4, 6-3. It's one of many reasons to be proud of her.
Stephens is the No. 3-ranked American woman and has climbed to a career high world ranking of No. 25. Her ascent has been quick after ending 2012 ranked 38th, which made her the youngest player inside the year-end top 50.
Last year, Stephens was one of the up-and-coming players to watch. She reached the third round at Wimbledon and the U.S. Open and the fourth round at the French Open. She has achieved her best result in Melbourne after exiting in the second round at last year's Australian Open.
For Stephens, Thursday's match was personal.
She has played the 19 -year-old Mladenovic on big stages before, namely the semifinals of the 2009 French Open juniors tournament, where she lost.
Asked if she remembered that match, Stephens replied: "How could I forget?''
"That match made my career. I was devastated,'' said Stephens, who is bubbly and charmingly confident. "I cried for like a month after that.
"But if we had never played before, it would have been super difficult to get out there and play now, so I think that kind of helped.''
By her accounting, Stephens "didn't play that great'' on Thursday. The 98th-ranked Mladenovic was hitting big serves and big forehands and Stephens had trouble finding her rhythm. She felt her mind wander but then she steered it back to the game.
When asked how she pulled herself out of tight spots, Stephens talked more about her mindset than her tennis.
"I think it's a mixture of things. Concentration, confidence, willing to run every ball down,'' she said. "Today I was determined to get the next ball back.''
Staying focused leads to other rewards, she smiled.
Like a pair of Jimmy Choos.
Before coming to Melbourne, Stephens had promised herself: "If I stay focused and concentrate, then I'll reward myself with Jimmy Choo shoes.''
How much will those shoes set her back?
"You don't want to know,'' she said with big eyes. "It's like five meals. And I eat a lot.''
Stephens' next opponent is Laura Robson, a British teenager she has known since she was 12.
The 53rd-ranked Robson upset No. 8 Petra Kvitova 2-6, 6-3, 11-9 in a 3-hour battle on center court that ended after midnight.
After the 18-year-old Robson politely thanked the crowd for staying to watch, she said she needed to check her phone.
"I think my mum is back home bombarding my phone with text messages,'' she said.
The Frenchman explained that he felt so tired during his match that he was desperately trying to keep points short.
"I wanted to finish with an ace, so I wouldn't have to play the point,'' he said.
Sometimes that worked. He served an impressive 29 aces.
Sometimes it didn't. Four of his double faults came in the last game as he served for the match. At one point, he stood on the service line laughing in disbelief.
Eventually, the 86th-ranked Monfils won the match to claim a spot in the third round, but it was painful.
"It's been a long time since I've felt that bad in a match,'' he said. "I didn't feel well. I struggled physically. I was extremely tired.''
It took five sets and lasted 3 hours, 38 minutes before he overcame a valiant effort by Yen-hsun Lu of Tawian 7-6 (5), 4-6, 0-6, 6-1, 8-6.
The scorching heat on Thursday didn't help Monfils - it reached 106 degrees. But he didn't blame the weather.
Monfils entered his first Grand Slam since last year's Australian Open, and he had entered it questioning if he was fit enough because of knee injuries. The Frenchman's ranking slumped from 13th in February 2012 to 99th in January while he battled injuries and other setbacks last year.
Three other Frenchman advanced Thursday without much difficulty. Monfils faces one of them in the third round: No. 14-seed Gilles Simon.
Also, No. 7 Jo-Wilfried Tsonga beat Japan's Go Soeda, 6-3, 7-6 (1), 6-3, and No. 9 Richard Gasquet defeated Alejandro Falla of Columbia 6-3, 6-2, 6-2.
On the hottest day of this year's Australian Open at 106 degrees, the distinction of the longest match goes to Duckworth of Australia and Slovenia's Blaz Kavcic. Both struggled with cramps during the 4-hour, 52-minute match before Kavcic won 3-6, 6-3, 6-4, 6-7 (3), 10-8.
"We both just were hanging on for dear life,'' said Duckworth, who won a wildcard entry to the main draw and is ranked 209th.
The 94th-ranked Kavcic needed on-court treatment from a trainer during the fourth set tiebreaker for what appeared to be a cramp in his left thigh. He tweeted after the match he had a "total physical collapse after the match.''
Duckworth saved five match points in the fifth set despite leg cramps that made his hamstring and quads "lock up.''
During changeovers, he downed energy drinks and had some cola for caffeine, he ate bananas for energy and tried eating salt to ease his cramps.
After the match, he got on a bike at the gym.
"Thought I'd smash out a 10k time trial,'' he joked. "No, just a light cool down.''